# Project A7

## 2022

### Shining light on the microscopic resonant mechanism responsible for cavity-mediated chemical reactivity

*Schäfer, C., Flick, J., Ronca, E. et al.*

Strong light–matter interaction in cavity environments is emerging as a promising approach to control chemical reactions in a non-intrusive and efficient manner. The underlying mechanism that distinguishes between steering, accelerating, or decelerating a chemical reaction has, however, remained unclear, hampering progress in this frontier area of research. We leverage quantum-electrodynamical density-functional theory to unveil the microscopic mechanism behind the experimentally observed reduced reaction rate under cavity induced resonant vibrational strong light-matter coupling. We observe multiple resonances and obtain the thus far theoretically elusive but experimentally critical resonant feature for a single strongly coupled molecule undergoing the reaction. While we describe only a single mode and do not explicitly account for collective coupling or intermolecular interactions, the qualitative agreement with experimental measurements suggests that our conclusions can be largely abstracted towards the experimental realization. Specifically, we find that the cavity mode acts as mediator between different vibrational modes. In effect, vibrational energy localized in single bonds that are critical for the reaction is redistributed differently which ultimately inhibits the reaction.

### Effect of spin-orbit coupling on the high harmonics from the topological Dirac semimetal Na3Bi

*Tancogne-Dejean, N., Eich, F.G. & Rubio, A.*

In this work, we performed extensive first-principles simulations of high-harmonic generation in the topological Diract semimetal Na3Bi using a first-principles time-dependent density functional theory framework, focusing on the effect of spin-orbit coupling (SOC) on the harmonic response. We also derived an analytical model describing the microscopic mechanism of strong-field dynamics in presence of spin-orbit coupling, starting from a locally *U*(1) × *SU*(2) gauge-invariant Hamiltonian. Our results reveal that SOC: (i) affects the strong-field excitation of carriers to the conduction bands by modifying the bandstructure of Na3Bi, (ii) makes each spin channel reacts differently to the driven laser by modifying the electron velocity (iii) changes the emission timing of the emitted harmonics. Moreover, we show that the SOC affects the harmonic emission by directly coupling the charge current to the spin currents, paving the way to the high-harmonic spectroscopy of spin currents in solids.

### Unconventional excitonic states with phonon sidebands in layered silicon diphosphide

*Zhou, L., Huang, J., Windgaetter, L. et al.*

Complex correlated states emerging from many-body interactions between quasiparticles (electrons, excitons and phonons) are at the core of condensed matter physics and material science. In low-dimensional materials, quantum confinement affects the electronic, and subsequently, optical properties for these correlated states. Here, by combining photoluminescence, optical reflection measurements and ab initio theoretical calculations, we demonstrate an unconventional excitonic state and its bound phonon sideband in layered silicon diphosphide (SiP_{2}), where the bound electron–hole pair is composed of electrons confined within one-dimensional phosphorus–phosphorus chains and holes extended in two-dimensional SiP_{2} layers. The excitonic state and emergent phonon sideband show linear dichroism and large energy redshifts with increasing temperature. Our ab initio many-body calculations confirm that the observed phonon sideband results from the correlated interaction between excitons and optical phonons. With these results, we propose layered SiP_{2} as a platform for the study of excitonic physics and many-particle effects.

### Probing phonon dynamics with multidimensional high harmonic carrier-envelope-phase spectroscopy

*Ofer Neufeld, Jin Zhang, Umberto De Giovannini, and Angel Rubio*

High harmonic generation (HHG) has recently been established as a powerful method for probing ultrafast electron dynamics in solids. However, it remains unknown if HHG can be similarly applied for probing lattice distortions such as phonons. Specifically, it is unclear if the extreme nonlinearity of HHG can contribute to enhanced temporal resolution or sensitivity for probing lattice dynamics (compared to other, perturbative, methods). Here, we theoretically explore HHG in solids with active phonons. We present a pump-probe and multidimensional spectroscopy approach that relies on carrier-envelope-phase-sensitivity, in which HHG is highly sensitive for phonon dynamics. Strikingly, the predicted temporal resolution is ∼1 femtosecond, much below the probe pulse duration, owing to the subcycle nature of the approach.

### Ultrafast dynamics of adenine following XUV ionization

*Erik P Månsson, Simone Latini, Fabio Covito, Vincent Wanie, Mara Galli, Enrico Perfetto, Gianluca Stefanucci, Umberto De Giovannini, Mattea C Castrovilli, Andrea Trabattoni, Fabio Frassetto, Luca Poletto, Jason B Greenwood, François Légaré, Mauro Nisoli, Angel Rubio, Francesca Calegari*

The dynamics of biologically relevant molecules exposed to ionizing radiation contains many facets and spans several orders of magnitude in time and energy. In the extreme ultraviolet (XUV) spectral range, multi-electronic phenomena and bands of correlated states with inner-valence holes must be accounted for in addition to a plethora of vibrational modes and available dissociation channels. The ability to track changes in charge density and bond length during ultrafast reactions is an important endeavor toward more general abilities to simulate and control photochemical processes, possibly inspired by those that have evolved biologically. By using attosecond XUV pulses extending up to 35 eV and few-femtosecond near-infrared pulses, we have previously time-resolved correlated electronic dynamics and charge migration occurring in the biologically relevant molecule adenine after XUV-induced sudden ionization. Here, using additional experimental data, we comprehensively report on both electronic and vibrational dynamics of this nucleobase in an energy range little explored to date with high temporal resolution. The time-dependent yields of parent and fragment ions in the mass spectra are analyzed to extract exponential time constants and oscillation periods. Together with time-dependent density functional theory and ab-initio Green’s function methods, we identify different vibrational and electronic processes. Beyond providing further insights into the XUV-induced dynamics of an important nucleobase, our work demonstrates that yields of specific dissociation outcomes can be influenced by sufficiently well-timed ultrashort pulses, therefore providing a new route for the control of the multi-electronic and dissociative dynamics of a DNA building block.

## 2021

### Making ab initio QED functional(s): Nonperturbative and photon-free effective frameworks for strong light–matter coupling

*Schäfer, C., Buchholz, F., Penz, M., Ruggenthaler, M., & Rubio, A.*

Strong light–matter coupling provides a promising path for the control of quantum matter where the latter is routinely described from first principles. However, combining the quantized nature of light with this ab initio tool set is challenging and merely developing as the coupled light–matter Hilbert space is conceptually different and computational cost quickly becomes overwhelming. In this work, we provide a nonperturbative photon-free formulation of quantum electrodynamics (QED) in the long-wavelength limit, which is formulated solely on the matter Hilbert space and can serve as an accurate starting point for such ab initio methods. The present formulation is an extension of quantum mechanics that recovers the exact results of QED for the zero- and infinite-coupling limit and the infinite-frequency as well as the homogeneous limit, and we can constructively increase its accuracy. We show how this formulation can be used to devise approximations for quantum-electrodynamical density-functional theory (QEDFT), which in turn also allows us to extend the ansatz to the full minimal-coupling problem and to nonadiabatic situations. Finally, we provide a simple local density–type functional that takes the strong coupling to the transverse photon degrees of freedom into account and includes the correct frequency and polarization dependence. This QEDFT functional accounts for the quantized nature of light while remaining computationally simple enough to allow its application to a large range of systems. All approximations allow the seamless application to periodic systems.

### Engineering Three-Dimensional Moiré Flat Bands

*Xian, L. D., Fischer, A., Claassen, M., Zhang, J., Rubio, A., & Kennes, D. M.*

Twisting two adjacent layers of van der Waals materials with respect to each other can lead to flat two-dimensional electronic bands which enables a wealth of physical phenomena. Here, we generalize this concept of so-called moiré flat bands to engineer flat bands in all three spatial dimensions controlled by the twist angle. The basic concept is to stack the material such that the large spatial moiré interference patterns are spatially shifted from one twisted layer to the next. We exemplify the general concept by considering graphitic systems, boron nitride, and WSe_{2}, but the approach is applicable to any two-dimensional van der Waals material. For hexagonal boron nitride, we develop an *ab initio* fitted tight binding model that captures the corresponding three-dimensional low-energy electronic structure. We outline that interesting three-dimensional correlated phases of matter can be induced and controlled following this route, including quantum magnets and unconventional superconducting states.

### Realization of nearly dispersionless bands with strong orbital anisotropy from destructive interference in twisted bilayer MoS2

*Xian, L. D., Claassen, M., Kiese, D., Scherer, M. M., Trebst, S., Kennes, D. M., & Rubio, A.*

Recently, the twist angle between adjacent sheets of stacked van der Waals materials emerged as a new knob to engineer correlated states of matter in two-dimensional heterostructures in a controlled manner, giving rise to emergent phenomena such as superconductivity or correlated insulating states. Here, we use an ab initio based approach to characterize the electronic properties of twisted bilayer MoS_{2}. We report that, in marked contrast to twisted bilayer graphene, slightly hole-doped MoS_{2} realizes a strongly asymmetric p_{x}-p_{y} Hubbard model on the honeycomb lattice, with two almost entirely dispersionless bands emerging due to destructive interference. The origin of these dispersionless bands, is similar to that of the flat bands in the prototypical Lieb or Kagome lattices and co-exists with the general band flattening at small twist angle due to the moiré interference. We study the collective behavior of twisted bilayer MoS_{2} in the presence of interactions, and characterize an array of different magnetic and orbitally-ordered correlated phases, which may be susceptible to quantum fluctuations giving rise to exotic, purely quantum, states of matter.

### Approximations based on density-matrix embedding theory for density-functional theories

*Theophilou, I., Reinhard, T., Rubio, A., & Ruggenthaler, M. *

Recently a novel approach to find approximate exchange–correlation functionals in density-functional theory was presented (Mordovina et al 2019 J. Chem. Theory Comput. 15 5209), which relies on approximations to the interacting wave function using density-matrix embedding theory (DMET). This approximate interacting wave function is constructed by using a projection determined by an iterative procedure that makes parts of the reduced density matrix of an auxiliary system the same as the approximate interacting density matrix. If only the diagonal of both systems are connected this leads to an approximation of the interacting-to-non-interacting mapping of the Kohn–Sham approach to density-functional theory. Yet other choices are possible and allow to connect DMET with other density-functional theories such as kinetic-energy density functional theory or reduced density-matrix functional theory. In this work we give a detailed review of the basics of the DMET procedure from a density-functional perspective and show how both approaches can be used to supplement each other. We do not present a specific realization of combining density-functional methods with DMET but rather provide common grounds to facilitate future developments that encompass both approaches. We do so explicitly for the case of a one-dimensional lattice system, as this is the simplest setting where we can apply DMET and the one that was originally presented. Among others we highlight how the mappings of density-functional theories can be used to identify uniquely defined auxiliary systems and projections in DMET and how to construct approximations for different density-functional theories using DMET inspired projections. Such alternative approximation strategies become especially important for density-functional theories that are based on non-linearly coupled observables such as kinetic-energy density-functional theory, where the Kohn–Sham fields are no longer obtainable by functional differentiation of an energy expression, or for reduced density-matrix functional theories, where a straightforward Kohn–Sham construction is not feasible.

### Light-Driven Extremely Nonlinear Bulk Photogalvanic Currents

*Neufeld, O., Tancogne-Dejean, N., de Giovannini, U., Hübener, H., & Rubio, A.*

We predict the generation of bulk photocurrents in materials driven by bichromatic fields that are circularly polarized and corotating. The nonlinear photocurrents have a fully controllable directionality and amplitude without requiring carrier-envelope-phase stabilization or few-cycle pulses, and can be generated with photon energies much smaller than the band gap (reducing heating in the photoconversion process). We demonstrate with *ab initio* calculations that the photocurrent generation mechanism is universal and arises in gaped materials (Si, diamond, MgO, hBN), in semimetals (graphene), and in two- and three-dimensional systems. Photocurrents are shown to rely on sub-laser-cycle asymmetries in the nonlinear response that build-up coherently from cycle to cycle as the conduction band is populated. Importantly, the photocurrents are always transverse to the major axis of the co-circular lasers regardless of the material’s structure and orientation (analogously to a Hall current), which we find originates from a generalized time-reversal symmetry in the driven system. At high laser powers (∼10^{13} W/cm^{2}) this symmetry can be spontaneously broken by vast electronic excitations, which is accompanied by an onset of carrier-envelope-phase sensitivity and ultrafast many-body effects. Our results are directly applicable for efficient light-driven control of electronics, and for enhancing sub-band-gap bulk photogalvanic effects.

### All-optical generation of antiferromagnetic magnon currents via the magnon circular photogalvanic effect

*Viñas Boström, E., Parvini, T. S., McIver, J. W., Rubio, A., Kusminskiy, S. V., & Sentef, M. A.*

We introduce the magnon circular photogalvanic effect enabled by two-magnon Raman scattering. This provides an all-optical pathway to the generation of directed magnon currents with circularly polarized light in honeycomb antiferromagnetic insulators. The effect is the leading order contribution to magnon photocurrent generation via optical fields. Control of the magnon current by the polarization and angle of incidence of the laser is demonstrated. Experimental detection by sizable inverse spin Hall voltages in platinum contacts is proposed.

### The 2021 ultrafast spectroscopic probes of condensed matter roadmap

*Lloyd-Hughes, J., Oppeneer, P. M., Pereira dos Santos, T., Schleife, A., Meng, S., Sentef, M. A., Ruggenthaler, M., Rubio, A., Radu, I., Murnane, M., Shi, X., Kapteyn, H., Stadtmüller, B., Dani, K. M., da Jornada, F. H., Prinz, E., Aeschlimann, M., Milot, R. L., Burdanova, M., Boland, J., Cocker, T., & Hegmann, F.*

In the 60 years since the invention of the laser, the scientific community has developed numerous fields of research based on these bright, coherent light sources, including the areas of imaging, spectroscopy, materials processing and communications. Ultrafast spectroscopy and imaging techniques are at the forefront of research into the light–matter interaction at the shortest times accessible to experiments, ranging from a few attoseconds to nanoseconds. Light pulses provide a crucial probe of the dynamical motion of charges, spins, and atoms on picosecond, femtosecond, and down to attosecond timescales, none of which are accessible even with the fastest electronic devices. Furthermore, strong light pulses can drive materials into unusual phases, with exotic properties. In this roadmap we describe the current state-of-the-art in experimental and theoretical studies of condensed matter using ultrafast probes. In each contribution, the authors also use their extensive knowledge to highlight challenges and predict future trends.

### Light-Induced Charge Transfer from Transition-Metal-Doped Aluminum Clusters to Carbon Dioxide

*Göbel, A., Rubio, A., & Lischner, J.*

Charge transfer between molecules and catalysts plays a critical role in determining the efficiency and yield of photochemical catalytic processes. In this paper, we study light-induced electron transfer between transition-metal-doped aluminum clusters and CO_{2} molecules using first-principles time-dependent density-functional theory. Specifically, we carry out calculations for a range of dopants (Zr, Mn, Fe, Ru, Co, Ni, and Cu) and find that the resulting systems fall into two categories: Cu- and Fe-doped clusters exhibit no ground-state charge transfer, weak CO_{2} adsorption, and light-induced electron transfer into the CO_{2}. In all other systems, we observe ground-state electron transfer into the CO_{2} resulting in strong adsorption and predominantly light-induced electron back-transfer from the CO_{2} into the cluster. These findings pave the way toward a rational design of atomically precise aluminum photocatalysts.

### Down-conversion processes in ab initio nonrelativistic quantum electrodynamics

*Welakuh, D., Ruggenthaler, M., Tchenkoue Djouom, M.-L., Appel, H., & Rubio, A.*

The availability of efficient photon sources with specific properties is important for quantum-technological applications. However, the realization of such photon sources is often challenging and hence alternative perspectives that suggest different means to enhance desired properties while suppressing detrimental processes are valuable. In this work we highlight that *ab initio* simulations of coupled light-matter systems can provide such alternative avenues. We show for a simple model of a quantum ring that by treating light and matter on equal footing, we can create and enhance pathways for down-conversion processes. By changing the matter subsystem as well as the photonic environment in experimentally feasible ways, we can engineer hybrid light-matter states that enhance at the same time the efficiency of the down-conversion process and the nonclassicality of the created photons. Furthermore, we show that this also leads to a faster down-conversion, potentially avoiding detrimental decoherence effects.

### Nonlinear electric conductivity and THz-induced charge transport in graphene

*Sato, S., & Rubio, A.*

Based on the quantum master equation approach, the nonlinear electric conductivity of graphene is investigated under static electric fields for various chemical potential shifts. The simulation results show that, as the field strength increases, the effective conductivity is firstly suppressed, reflecting the depletion of effective carriers due to the large displacement in the Brillouin zone caused by the strong field. Then, as the field strength exceeds 1 MV m^{−1}, the effective conductivity increases, overcoming the carrier depletion via the Landau–Zener tunneling process. Based on the nonlinear behavior of the conductivity, the charge transport induced by few-cycle THz pulses is studied to elucidate the ultrafast control of electric current in matter.

### Strong chiral dichroism and enantiopurification in above-threshold ionization with locally chiral light

*Neufeld, O., Hübener, H., Rubio, A., & de Giovannini, U.*

We derive here a highly selective photoelectron-based chirality-sensing technique that utilizes “locally chiral” laser pulses. We show that this approach results in strong chiral discrimination, where the standard forwards/backwards asymmetry of photoelectron circular dichroism (PECD) is lifted. The resulting dichroism is larger and more robust than conventional PECD (especially in the high-energy part of the spectrum), is found in all hemispheres, and is not symmetric or antisymmetric with respect to any symmetry operator. Remarkably, chiral dichroism of up to 10% survives in the angularly integrated above-threshold ionization (ATI) spectra, and chiral dichroism of up to 5% survives in the total ionization rates. We demonstrate these results through *ab initio* calculations in the chiral molecules bromochlorofluoromethane, limonene, fenchone, and camphor. We also explore the parameter space of the locally chiral field and show that the observed dichroism is strongly correlated to the degree of chirality of the light, validating it as a measure for chiral-interaction strengths. Our results pave the way for highly selective probing of ultrafast chirality in ATI and motivate the use of locally chiral light for enhancing ultrafast spectroscopies. Most importantly, the technique can be implemented to achieve all-optical enantiopurification of chiral samples.

### Ultrafast dynamical Lifshitz transition

*Beaulieu, S., Dong, S., Tancogne-Dejean, N., Dendzik, M., Pincelli, T., Maklar, J., Xian, R. P., Sentef, M. A., Wolf, M., Rubio, A., Rettig, L., & Ernstorfer, R.*

Fermi surface is at the heart of our understanding of metals and strongly correlated many-body systems. An abrupt change in the Fermi surface topology, also called Lifshitz transition, can lead to the emergence of fascinating phenomena like colossal magnetoresistance and superconductivity. While Lifshitz transitions have been demonstrated for a broad range of materials by equilibrium tuning of macroscopic parameters such as strain, doping, pressure, and temperature, a nonequilibrium dynamical route toward ultrafast modification of the Fermi surface topology has not been experimentally demonstrated. Combining time-resolved multidimensional photoemission spectroscopy with state-of-the-art TDDFT+*U* simulations, we introduce a scheme for driving an ultrafast Lifshitz transition in the correlated type-II Weyl semimetal T_{d}-MoTe_{2}. We demonstrate that this nonequilibrium topological electronic transition finds its microscopic origin in the dynamical modification of the effective electronic correlations. These results shed light on a previously unexplored ultrafast scheme for controlling the Fermi surface topology in correlated quantum materials.

### Identification of the Mott Insulating Charge Density Wave State in 1T−TaS2

*Shin, D., Tancogne-Dejean, N., Zhang, J., Okyay, M. S., Rubio, A., & Park, N.*

We investigate the low-temperature charge density wave (CDW) state of bulk TaS_{2} with a fully self-consistent density-functional theory with the Hubbard *U* potential, over which the controversy has remained unresolved regarding the out-of-plane metallic band. By examining the innate structure of the Hubbard *U* potential, we reveal that the conventional use of atomic-orbital basis could seriously misevaluate the electron correlation in the CDW state. By adopting a generalized basis, covering the whole David star, we successfully reproduce the Mott insulating nature with the layer-by-layer antiferromagnetic order. Similar consideration should be applied for description of the electron correlation in molecular solid.

### Single and double charge transfer in the Ne2+ + He collision within time-dependent density-functional theory

*Yu, W., Gao, C.-Z., Sato, S., Castro, A., Rubio, A., & Wei, B.*

We calculate the charge-transfer cross sections for the Ne^{2+}+He collision. To this end, we employ Ehrenfest molecular dynamics with time-dependent density-functional theory. The active electrons of the projectile are handled by applying an initial velocity to the Kohn-Sham orbitals via a Galilean boost. The dynamical calculations are performed in an inverse collision framework—the reference frame considers Ne^{2+} to be initially at rest, which ensures numerically converged final-time scattering states. The charge-transfer probabilities are extracted by extending the particle number projection technique to be able to handle the degenerate Ne^{2+} ion. Compared with experimental data available at 10–3000 keV, a fairly good agreement is found for the calculated single- and double-charge transfer cross sections, superior to other theoretical calculations for this Ne^{2+}+He collision. A time-resolved analysis of the charge-transfer probabilities finds that ionization to the continuum also takes place after the charge transfer has occurred. To account for it, the final scattering states should be followed for a long time, approximately 350 fs, until they stabilize.

### Simulating Vibronic Spectra without Born–Oppenheimer Surfaces

*Lively, K., Albareda Piquer, G., Sato, S., Kelly, A., & Rubio, A.*

We show how linear vibronic spectra in molecular systems can be simulated efficiently using first-principles approaches without relying on the explicit use of multiple Born–Oppenheimer potential energy surfaces. We demonstrate and analyze the performance of mean-field and beyond-mean-field dynamics techniques for the H_{2} molecule in one dimension, in the later case capturing the vibronic structure quite accurately, including quantum Franck–Condon effects. In a practical application of this methodology we simulate the absorption spectrum of benzene in full dimensionality using time-dependent density functional theory at the multitrajectory Ehrenfest level, finding good qualitative agreement with experiment and significant spectral reweighting compared to commonly used single-trajectory Ehrenfest dynamics. These results form the foundation for nonlinear spectral calculations and show promise for future application in capturing phenomena associated with vibronic coupling in more complex molecular and potentially condensed phase systems.

### Higher-Order Band Topology in Twisted Moiré Superlattice.

*Liu, B., Xian, L. D., Mu, H., Zhao, G., Liu, Z., Rubio, A., & Wang, Z.*

The two-dimensional (2D) twisted bilayer materials with van der Waals coupling have ignited great research interests, paving a new way to explore the emergent quantum phenomena by twist degree of freedom. Generally, with the decreasing of twist angle, the enhanced interlayer coupling will gradually flatten the low-energy bands and isolate them by two high-energy gaps at zero and full filling, respectively. Although the correlation and topological physics in the low-energy flat bands have been intensively studied, little information is available for these two emerging gaps. In this Letter, we predict a 2D second-order topological insulator (SOTI) for twisted bilayer graphene and twisted bilayer boron nitride in both zero and full filling gaps. Employing a tight-binding Hamiltonian based on first-principles calculations, three unique fingerprints of 2D SOTI are identified, that is, nonzero bulk topological index, gapped topological edge state, and in-gap topological corner state. Most remarkably, the 2D SOTI exists in a wide range of commensurate twist angles, which is robust to microscopic structure disorder and twist center, greatly facilitating the possible experimental measurement. Our results not only extend the higher-order band topology to massless and massive twisted moiré superlattice, but also demonstrate the importance of high-energy bands for fully understanding the nontrivial electronics.

### Hydrated Alkali Atoms on Copper(111): A Density Functional Theory Study

*Pérez Paz, A., & Rubio, A.*

We present a systematic computational study of submonolayer coverage of alkali atoms (Na, K, Cs) on Cu(111) surface hydrated from 1 to 6 water molecules. Our calculations show that water molecules preferentially bind to the adsorbed alkali ion and that a gradual detachment of the alkali from the Cu(111) surface is found as the hydration increases. This decoupling of the alkali from the Cu(111) surface results in a linear decrease of the charge transfer to the substrate. The orientation of the water dipoles pointing toward the surface leads to a gradual increase of the work function of the substrate as the number of coordinated water molecules increases from 1 to 4. Beyond 5 coordinated water molecules, the alkali adatom becomes saturated, and water adsorption sets in on the Cu(111) surface with the expected decrease in the work function of the system, as measured in two-photon photoemission spectroscopy (2PPE) experiments. From the detailed analysis of the orientation of the water electric dipoles, we were able to understand the experimentally observed initial increase of work function upon hydration and its subsequent decrease after saturation of alkali sites with water molecules. From the calculated energetics, we gauge the relative strengths of the alkali–Cu(111), alkali–water, and water–Cu(111) interactions as we move across the alkaline group. We found an excellent linear correlation between experimental water desorption temperatures and our computed water–alkali binding energies on Cu(111).

### Real-time observation of a correlation-driven sub 3 fs charge migration in ionised adenine

*Erik P. Månsson, Simone Latini, Fabio Covito, Vincent Wanie, Mara Galli, Enrico Perfetto, Gianluca Stefanucci, Hannes Hübener, Umberto De Giovannini, Mattea C. Castrovilli, Andrea Trabattoni, Fabio Frassetto, Luca Poletto, Jason B. Greenwood, François Légaré, Mauro Nisoli, Angel Rubio & Francesca Calegari*

Sudden ionisation of a relatively large molecule can initiate a correlation-driven process dubbed charge migration, where the electron density distribution is expected to rapidly move along the molecular backbone. Capturing this few-femtosecond or attosecond charge redistribution would represent the real-time observation of electron correlation in a molecule with the enticing prospect of following the energy flow from a single excited electron to the other coupled electrons in the system. Here, we report a time-resolved study of the correlation-driven charge migration process occurring in the nucleic-acid base adenine after ionisation with a 15–35 eV attosecond pulse. We find that the production of intact doubly charged adenine – via a shortly-delayed laser-induced second ionisation event – represents the signature of a charge inflation mechanism resulting from many-body excitation. This conclusion is supported by first-principles time-dependent simulations. These findings may contribute to the control of molecular reactivity at the electronic, few-femtosecond time scale.

### Moiréless correlations in ABCA graphene

*Kerelsky, A., Rubio-Verdú, C., Xian, L. D., Kennes, D. M., Halbertal, D., Finney, N., Song, L., Turkel, S., Wang, L., Watanabe, K., Taniguchi, T., Hone, J., Dean, C., Basov, D., Rubio, A., & Pasupathy, A. N.*

Atomically thin van der Waals materials stacked with an interlayer twist have proven to be an excellent platform toward achieving gate-tunable correlated phenomena linked to the formation of flat electronic bands. In this work we demonstrate the formation of emergent correlated phases in multilayer rhombohedral graphene––a simple material that also exhibits a flat electronic band edge but without the need of having a moiré superlattice induced by twisted van der Waals layers. We show that two layers of bilayer graphene that are twisted by an arbitrary tiny angle host large (micrometer-scale) regions of uniform rhombohedral four-layer (ABCA) graphene that can be independently studied. Scanning tunneling spectroscopy reveals that ABCA graphene hosts an unprecedentedly sharp van Hove singularity of 3–5-meV half-width. We demonstrate that when this van Hove singularity straddles the Fermi level, a correlated many-body gap emerges with peak-to-peak value of 9.5 meV at charge neutrality. Mean-field theoretical calculations for model with short-ranged interactions indicate that two primary candidates for the appearance of this broken symmetry state are a charge-transfer excitonic insulator and a ferrimagnet. Finally, we show that ABCA graphene hosts surface topological helical edge states at natural interfaces with ABAB graphene which can be turned on and off with gate voltage, implying that small-angle twisted double-bilayer graphene is an ideal programmable topological quantum material.

### Vibrational coherent control of localized d–d electronic excitation

*Alexandre Marciniak, Stefano Marcantoni, Francesca Giusti, Filippo Glerean, Giorgia Sparapassi, Tobia Nova, Andrea Cartella, Simone Latini, Francesco Valiera, Angel Rubio, Jeroen van den Brink, Fabio Benatti & Daniele Fausti*

Addressing the role of quantum coherence in the interplay between the different matter constituents (electrons, phonons and spin) is a critical step towards understanding transition metal oxides and designing complex materials with new functionalities. Here we use coherent vibrational control of on-site *d*–*d* electronic transitions in a model edge-sharing insulating transition metal oxide (CuGeO_{3}) to single out the effects of vibrational coherence in electron–phonon coupling. By comparing time-domain experiments based on high- and low-photon-energy ultrashort laser excitation pulses with a fully quantum description of phonon-assisted absorption, we could distinguish the processes associated with incoherent thermal lattice fluctuations from those driven by the coherent motion of the atoms. In particular, while thermal fluctuations of the phonon bath uniformly increase the electronic absorption, the resonant excitation of phonon modes also results in light-induced transparency that is coherently controlled by the vibrational motion.

### Moiré metrology of energy landscapes in van der Waals heterostructures

*Dorri Halbertal, Nathan R. Finney, Sai S. Sunku, Alexander Kerelsky, Carmen Rubio-Verdú, Sara Shabani, Lede Xian, Stephen Carr, Shaowen Chen, Charles Zhang, Lei Wang, Derick Gonzalez-Acevedo, Alexander S. McLeod, Daniel Rhodes, Kenji Watanabe, Takashi Taniguchi, Efthimios Kaxiras, Cory R. Dean, James C. Hone, Abhay N. Pasupathy, Dante M. Kennes, Angel Rubio & D. N. Basov*

The emerging field of twistronics, which harnesses the twist angle between two-dimensional materials, represents a promising route for the design of quantum materials, as the twist-angle-induced superlattices offer means to control topology and strong correlations. At the small twist limit, and particularly under strain, as atomic relaxation prevails, the emergent moiré superlattice encodes elusive insights into the local interlayer interaction. Here we introduce moiré metrology as a combined experiment-theory framework to probe the stacking energy landscape of bilayer structures at the 0.1 meV/atom scale, outperforming the gold-standard of quantum chemistry. Through studying the shapes of moiré domains with numerous nano-imaging techniques, and correlating with multi-scale modelling, we assess and refine first-principle models for the interlayer interaction. We document the prowess of moiré metrology for three representative twisted systems: bilayer graphene, double bilayer graphene and H-stacked MoSe_{2}/WSe_{2}. Moiré metrology establishes sought after experimental benchmarks for interlayer interaction, thus enabling accurate modelling of twisted multilayers.

### High-order harmonic generation in graphene: nonlinear coupling of intra and interband transitions

*Shunsuke A. Sato, Hideki Hirori, Yasuyuki Sanari, Yoshihiko Kanemitsu, Angel Rubio*

We investigate high-order harmonic generation (HHG) in graphene with a quantum master equation approach. The simulations reproduce the observed enhancement in HHG in graphene under elliptically polarized light [N. Yoshikawa et al, Science 356, 736 (2017)]. On the basis of a microscopic decomposition of the emitted high-order harmonics, we find that the enhancement in HHG originates from an intricate nonlinear coupling between the intraband and interband transitions that are respectively induced by perpendicular electric field components of the elliptically polarized light. Furthermore, we reveal that contributions from different excitation channels destructively interfere with each other. This finding suggests a path to potentially enhance the HHG by blocking a part of the channels and canceling the destructive interference through band-gap or chemical potential manipulation.

## 2020

### Entangled photon assisted multidimensional nonlinear optics of exciton–polaritons

*Debnath, A., & Rubio, A. *

We present a theoretical formulation of the frequency domain multidimensional pump-probe analog spectroscopy, which utilizes the spectral–temporal entanglement features of the biphoton sources. It has been shown, via a compact multi-time, convolutional Green’s function expression and the accompanying numerical simulations, that utilizing the correlation properties of non-classical sources offers a viable scheme for the exploration of dissipative kinetics of the cavity confined quantum aggregates. The cooperative and competitive modifications brought in by the photonic cavity mode and the auxiliary vibrational modes into the scattering and dephasing properties of the exciton–polaritons have been explored via their signatures in the multidimensional correlation maps. The study offers a new parameter window for the investigation of the dynamical polariton characteristics and warrants the usage of multi-mode entanglement properties of the external photonic sources in future studies.Journal of Applied Physics 128, 113102 (2020)

### High-harmonic generation from spin-polarised defects in solids

*Mrudul, M. S., Tancogne-Dejean, N., Rubio, A., & Dixit, G.*

The generation of high-order harmonics in gases enabled to probe the attosecond electron dynamics in atoms and molecules with unprecedented resolution. Extending these techniques to solids, which were originally developed for atomic and molecular gases, requires a fundamental understanding of the physics that has been partially addressed theoretically. Here, we employ time-dependent density-functional theory to investigate how the electron dynamics resulting in high-harmonic emission in monolayer hexagonal boron nitride is affected by the presence of vacancies. We show how these realistic spin-polarised defects modify the harmonic emission and demonstrate that important differences exist between harmonics from a pristine solid and a defected solid. In particular, we found that the different spin channels are affected differently by the presence of the spin-polarised point defect. Moreover, the localisation of the wavefunction, the geometry of the defect, and the electron–electron interaction are all crucial ingredients to describe high-harmonic generation in defected solids.

### Electron–phonon-driven three-dimensional metallicity in an insulating cuprate

*Baldini, E., Sentef, M. A., Acharya, S., Brumme, T., Sheveleva, E., Lyzwa, F., et al.*

The role of the crystal lattice for the electronic properties of cuprates and other high-temperature superconductors remains controversial despite decades of theoretical and experimental efforts. While the paradigm of strong electronic correlations suggests a purely electronic mechanism behind the insulator-to-metal transition, recently the mutual enhancement of the electron–electron and the electron–phonon interaction and its relevance to the formation of the ordered phases have also been emphasized. Here, we combine polarization-resolved ultrafast optical spectroscopy and state-of-the-art dynamical mean-field theory to show the importance of the crystal lattice in the breakdown of the correlated insulating state in an archetypal undoped cuprate. We identify signatures of electron–phonon coupling to specific fully symmetric optical modes during the buildup of a three-dimensional (3D) metallic state that follows charge photodoping. Calculations for coherently displaced crystal structures along the relevant phonon coordinates indicate that the insulating state is remarkably unstable toward metallization despite the seemingly large charge-transfer energy scale. This hitherto unobserved insulator-to-metal transition mediated by fully symmetric lattice modes can find extensive application in a plethora of correlated solids.

### Correlated electronic phases in twisted bilayer transition metal dichalcogenides

*Wang, L., Shih, E.-M., Ghiotto, A., Xian, L. D., Rhodes, D. A., Tan, C., Claassen, M., Kennes, D. M., Bai, Y., Kim, B., Watanabe, K., Taniguchi, T., Zhu, X., Hone, J., Rubio, A., Pasupathy, A., & Dean, C. R.*

In narrow electron bands in which the Coulomb interaction energy becomes comparable to the bandwidth, interactions can drive new quantum phases. Such flat bands in twisted graphene-based systems result in correlated insulator, superconducting and topological states. Here we report evidence of low-energy flat bands in twisted bilayer WSe2, with signatures of collective phases observed over twist angles that range from 4 to 5.1°. At half-band filling, a correlated insulator appeared that is tunable with both twist angle and displacement field. At a 5.1° twist, zero-resistance pockets were observed on doping away from half filling at temperatures below 3 K, which indicates a possible transition to a superconducting state. The observation of tunable collective phases in a simple band, which hosts only two holes per unit cell at full filling, establishes twisted bilayer transition metal dichalcogenides as an ideal platform to study correlated physics in two dimensions on a triangular lattice.

### Light–Matter Hybrid-Orbital-Based First-Principles Methods: The Influence of Polariton Statistics

* Florian Buchholz, Iris Theophilou, Klaas J. H. Giesbertz, Michael Ruggenthaler, and Angel Rubio*

A detailed understanding of strong matter–photon interactions requires first-principle methods that can solve the fundamental Pauli–Fierz Hamiltonian of nonrelativistic quantum electrodynamics efficiently. A possible way to extend well-established electronic-structure methods to this situation is to embed the Pauli–Fierz Hamiltonian in a higher-dimensional light–matter hybrid auxiliary configuration space. In this work we show the importance of the resulting hybrid Fermi–Bose statistics of the polaritons, which are the new fundamental particles of the “photon-dressed” Pauli–Fierz Hamiltonian for systems in cavities. We show that violations of these statistics can lead to unphysical results. We present an efficient way to ensure the correct statistics by enforcing representability conditions on the dressed one-body reduced density matrix. We further present a general prescription how to extend a given first-principles approach to polaritons and as an example introduce polaritonic Hartree–Fock theory. While being a single-reference method in polariton space, polaritonic Hartree–Fock is a multireference method in the electronic space, i.e., it describes electronic correlations. We also discuss possible applications to polaritonic QEDFT. We apply this theory to a lattice model and find that, the more delocalized the bound-state wave function of the particles is, the stronger it reacts to photons. The main reason is that within a small energy range, many states with different electronic configurations are available as opposed to a strongly bound (and hence energetically separated) ground-state wave function. This indicates that under certain conditions coupling to the quantum vacuum of a cavity can indeed modify ground state properties.

### Coupled Cluster Theory for Molecular Polaritons: Changing Ground and Excited States

*Tor S. Haugland, Enrico Ronca, Eirik F. Kjønstad, Angel Rubio, and Henrik Koch*

We present an ab* initio* correlated approach to study molecules that interact strongly with quantum fields in an optical cavity. Quantum electrodynamics coupled cluster theory provides a nonperturbative description of cavity-induced effects in ground and excited states. Using this theory, we show how quantum fields can be used to manipulate charge transfer and photochemical properties of molecules. We propose a strategy to lift electronic degeneracies and induce modifications in the ground-state potential energy surface close to a conical intersection.

### Floquet dynamics in light-driven solid

*M. Nuske, L. Broers, B. Schulte, G. Jotzu, S. A. Sato, A. Cavalleri, A. Rubio, J. W. McIver, L. Mathey*

We demonstrate how the properties of light-induced electronic Floquet states in solids impact natural physical observables, such as transport properties, by capturing the environmental influence on the electrons. We include the environment as dissipative processes, such as inter-band decay and dephasing, often ignored in Floquet predictions. These dissipative processes determine the Floquet band occupations of the emergent steady state, by balancing out the optical driving force. In order to benchmark and illustrate our framework for Floquet physics in a realistic solid, we consider the light-induced Hall conductivity in graphene recently reported by J.~W.~McIver, et al., Nature Physics (2020). We show that the Hall conductivity is estimated by the Berry flux of the occupied states of the light-induced Floquet bands, in addition to the kinetic contribution given by the average band velocity. Hence, Floquet theory provides an interpretation of this Hall conductivity as a geometric-dissipative effect. We demonstrate this mechanism within a master equation formalism, and obtain good quantitative agreement with the experimentally measured Hall conductivity, underscoring the validity of this approach which establishes a broadly applicable framework for the understanding of ultrafast non-equilibrium dynamics in solids.

### Role of intraband dynamics in the generation of circularly polarized high harmonics from solids

*N. Klemke, O. D. Mücke, A. Rubio, F. X. Kärtner, and N. Tancogne-Dejean*

Recent studies have demonstrated that the polarization states of high harmonics from solids can differ from those of the driving pulses. To gain insights on the microscopic origin of this behavior, we perform one-particle intraband-only calculations and reproduce some of the most striking observations. For instance, our calculations yield circularly polarized harmonics from elliptically polarized pulses that sensitively depend on the driving conditions. Furthermore, we perform experiments on ZnS and find characteristics partly similar to those reported from silicon. Comparison to our intraband-only calculations shows reasonable qualitative agreement for a below-band-gap harmonic. We show that intraband dynamics predict depolarization effects that gain significance with higher field strengths and we observe such effects in the experimental data. For harmonics above the band gap, interband dynamics become important and the high-harmonic response to elliptical excitation looks systematically different. Our work proposes a method to distinguish between different high-harmonic generation mechanisms and it could pave the way to compact solid-state high-harmonic sources with controllable polarization states.

### Room Temperature Terahertz Electroabsorption Modulation by Excitons in Monolayer Transition Metal Dichalcogenides

*Shi, J., Baldini, E., Latini, S., Sato, S., Zhang, Y., Pein, B. C., Shen, P.-C., Kong, J., Rubio, A., Gedik, N., & Nelson, K. A.*

The interaction between off-resonant laser pulses and excitons in monolayer transition metal dichalcogenides is attracting increasing interest as a route for the valley-selective coherent control of the exciton properties. Here, we extend the classification of the known off-resonant phenomena by unveiling the impact of a strong THz field on the excitonic resonances of monolayer MoS_{2.} We observe that the THz pump pulse causes a selective modification of the coherence lifetime of the excitons, while keeping their oscillator strength and peak energy unchanged. We rationalize these results theoretically by invoking a hitherto unobserved manifestation of the Franz–Keldysh effect on an exciton resonance. As the modulation depth of the optical absorption reaches values as large as 0.05 dB/nm at room temperature, our findings open the way to the use of semiconducting transition metal dichalcogenides as compact and efficient platforms for high-speed electroabsorption devices.

### Light-Induced Renormalization of the Dirac Quasiparticles in the Nodal-Line Semimetal ZrSiSe

*G. Gatti, A. Crepaldi, M. Puppin, N. Tancogne-Dejean, L. Xian, U. De Giovannini, S. Roth, S. Polishchuk, Ph. Bugnon, A. Magrez, H. Berger, F. Frassetto, L. Poletto, L. Moreschini, S. Moser, A. Bostwick, Eli Rotenberg, A. Rubio, M. Chergui, and M. Grioni*

In nodal-line semimetals, linearly dispersing states form Dirac loops in the reciprocal space with a high degree of electron-hole symmetry and a reduced density of states near the Fermi level. The result is reduced electronic screening and enhanced correlations between Dirac quasiparticles. Here we investigate the electronic structure of ZrSiSe, by combining time- and angle-resolved photoelectron spectroscopy with ab initio density functional theory (DFT) complemented by an extended Hubbard model (DFT+*U*+*V*) and by time-dependent DFT+*U*+*V*. We show that electronic correlations are reduced on an ultrashort timescale by optical excitation of high-energy electrons-hole pairs, which transiently screen the Coulomb interaction. Our findings demonstrate an all-optical method for engineering the band structure of a quantum material.

### Virial Relations for Electrons Coupled to Quantum Field Modes

*Theophilou, I., Penz, M., Ruggenthaler, M., & Rubio, A.*

In this work, we present a set of virial relations for many electron systems coupled to both classical and quantum fields, described by the Pauli–Fierz Hamiltonian in dipole approximation and using length gauge. Currently, there is growing interest in solutions of this Hamiltonian because of its relevance for describing molecular systems strongly coupled to photonic modes in cavities and in the possible modification of chemical properties of such systems compared to the ones in free space. The relevance of such virial relations is demonstrated by showing a connection to mass renormalization and by providing an exact way to obtain total energies from potentials in the framework of quantum electrodynamical density functional theory.

### Effect of many modes on self-polarization and photochemical suppression in cavities

*Hoffmann, N., Lacombe, L., Rubio, A., & Maitra, N. T.*

The standard description of cavity-modified molecular reactions typically involves a single (resonant) mode, while in reality, the quantum cavity supports a range of photon modes. Here, we demonstrate that as more photon modes are accounted for, physicochemical phenomena can dramatically change, as illustrated by the cavity-induced suppression of the important and ubiquitous process of proton-coupled electron-transfer. Using a multi-trajectory Ehrenfest treatment for the photon-modes, we find that self-polarization effects become essential, and we introduce the concept of self-polarization-modified Born–Oppenheimer surfaces as a new construct to analyze dynamics. As the number of cavity photon modes increases, the increasing deviation of these surfaces from the cavity-free Born–Oppenheimer surfaces, together with the interplay between photon emission and absorption inside the widening bands of these surfaces, leads to enhanced suppression. The present findings are general and will have implications for the description and control of cavity-driven physical processes of molecules, nanostructures, and solids embedded in cavities.

### Parameter-free hybridlike functional based on an extended Hubbard model: DFT+U+V

*Tancogne-Dejean, N., & Rubio, A.*

In this paper, we propose an energy functional at the level of DFT+*U*+*V* that allows us to compute self-consistently the values of the onsite interaction, Hubbard *U* and Hund *J*, as well as the intersite interaction *V*. This functional extends the previously proposed ACBN0 functional [L. A. Agapito et al., Phys. Rev. X 5, 011006 (2015)] including both onsite and intersite interactions. We show that this ab initio self-consistent functional yields improved electronic properties for a wide range of materials, ranging from *sp* materials to strongly correlated materials. This functional can also be seen as an alternative general and systematic way to construct parameter-free hybrid functionals, based on the extended Hubbard model and a selected set of Coulomb integrals, and might be used to develop novel approximations. By extending the DFT+*U* method to materials where strong local and nonlocal interactions are relevant, this work opens the door to the *ab initio* study the electronic, ionic, and optical properties of a larger class of strongly correlated materials in and out of equilibrium.

### Dynamical amplification of electric polarization through nonlinear phononics in 2D SnTe

*Shin, D., Sato, S., Hübener, H., de Giovannini, U., Park, N., & Rubio, A.*

Ultrafast optical control of ferroelectricity using intense terahertz fields has attracted significant interest. Here we show that the nonlinear interactions between two optical phonons in SnTe, a two-dimensional in-plane ferroelectric material, enables a dynamical amplification of the electric polarization within subpicoseconds time domain. Our first-principles time-dependent simulations show that the infrared-active out-of-plane phonon mode, pumped to nonlinear regimes, spontaneously generates in-plane motions, leading to rectified oscillations in the in-plane electric polarization. We suggest that this dynamical control of ferroelectric material, by nonlinear phonon excitation, can be utilized to achieve ultrafast control of the photovoltaic or other nonlinear optical responses.

### Ultrafast Real-Time Dynamics of CO Oxidation over an Oxide Photocatalyst

*Wagstaffe, M., Wenthaus, L., Dominguez-Castro, A., Chung, S., Lana Semione, G. D., Palutke, S., Mercurio, G., Dziarzhytski, S., Redlin, H., Klemke, N., Yang, Y., Frauenheim, T., Dominguez, A., Kärtner, F., Rubio, A., Wurth, W., Stierle, A., & Noei, H.*

Femtosecond X-ray laser pulses synchronized with an optical laser were employed to investigate the reaction dynamics of the photooxidation of CO on the anatase TiO_{2}(101) surface in real time. Our time-resolved soft X-ray photoemission spectroscopy results provide evidence of ultrafast timescales and, coupled with theoretical calculations, clarify the mechanism of oxygen activation that is crucial to unraveling the underlying processes for a range of photocatalytic reactions relevant to air purification and self-cleaning surfaces. The reaction takes place between 1.2 and 2.8 (±0.2) ps after irradiation with an ultrashort laser pulse leading to the formation of CO_{2}, prior to which no intermediate species were observed on a picosecond time scale. Our theoretical calculations predict that the presence of intragap unoccupied O_{2} levels leads to the formation of a charge-transfer complex. This allows the reaction to be initiated following laser illumination at a photon energy of 1.6 eV (770 nm), taking place via a proposed mechanism involving the direct transfer of electrons from TiO_{2} to physisorbed O_{2}.

### Charge-Transfer Plasmon Polaritons at Graphene/α-RuCl3 Interfaces

* Daniel J. Rizzo, Bjarke S. Jessen, Zhiyuan Sun, Francesco L. Ruta, Jin Zhang, Jia-Qiang Yan, Lede Xian, Alexander S. McLeod, Michael E. Berkowitz, Kenji Watanabe, Takashi Taniguchi, Stephen E. Nagler, David G. Mandrus, Angel Rubio, Michael M. Fogler, Andrew J. Millis, James C. Hone, Cory R. Dean, and D. N. Basov*

Nanoscale charge control is a key enabling technology in plasmonics, electronic band structure engineering, and the topology of two-dimensional materials. By exploiting the large electron affinity of α-RuCl_{3}, we are able to visualize and quantify massive charge transfer at graphene/α-RuCl_{3} interfaces through generation of charge-transfer plasmon polaritons (CPPs). We performed nanoimaging experiments on graphene/α-RuCl_{3} at both ambient and cryogenic temperatures and discovered robust plasmonic features in otherwise ungated and undoped structures. The CPP wavelength evaluated through several distinct imaging modalities offers a high-fidelity measure of the Fermi energy of the graphene layer: *E*_{F} = 0.6 eV (*n* = 2.7 × 10^{13} cm^{–2}). Our first-principles calculations link the plasmonic response to the work function difference between graphene and α-RuCl_{3} giving rise to CPPs. Our results provide a novel general strategy for generating nanometer-scale plasmonic interfaces without resorting to external contacts or chemical doping.

### Photoelectron spectroscopy of large water clusters ionized by an XUV comb

*Andrea Trabattoni, Lorenzo Colaizzi, Loren Ban, Vincent Wanie, Krishna Saraswathula, Erik P Månsson, Philipp Rupp, Qingcao Liu, Lennart Seiffert, Elisabeth A Herzig, Andrea Cartella, Bruce L Yoder, François Légaré, Matthias F Kling, Thomas Fennel, Ruth Signorell and Francesca Calegari*

Detailed knowledge about photo-induced electron dynamics in water is key to the understanding of several biological and chemical mechanisms, in particular for those resulting from ionizing radiation. Here we report a method to obtain photoelectron spectra from neutral water clusters following ionization by an extreme-ultraviolet (XUV) attosecond pulse train, representing a first step towards a time-resolved analysis. Typically, a large background signal in the experiment arises from water monomers and carrier gas used in the cluster source. We report a protocol to quantify this background in order to eliminate it from the experimental spectra. We disentangle the accumulated XUV photoionization signal into contributions from the background species and the photoelectron spectra from the clusters. This proof-of-principle study demonstrates feasibility of background free photoelectron spectra of neutral water clusters ionized by XUV combs and paves the way for the detailed time-resolved analysis of the underlying dynamics.

### Relevance of the quadratic diamagnetic and self-polarization terms in cavity quantum electrodynamics

*Christian Schäfer, Michael Ruggenthaler, Vasil Rokaj, Angel Rubio*

Experiments at the interface of quantum optics and chemistry have revealed that strong coupling between light and matter can substantially modify the chemical and physical properties of molecules and solids. While the theoretical description of such situations is usually based on nonrelativistic quantum electrodynamics, which contains quadratic light–matter coupling terms, it is commonplace to disregard these terms and restrict the treatment to purely bilinear couplings. In this work, we clarify the physical origin and the substantial impact of the most common quadratic terms, the diamagnetic and self-polarization terms, and highlight why neglecting them can lead to rather unphysical results. Specifically, we demonstrate their relevance by showing that neglecting these terms leads to the loss of gauge invariance, basis set dependence, disintegration (loss of bound states) of any system in the basis set limit, unphysical radiation of the ground state, and an artificial dependence on the static dipole. Besides providing important guidance for modeling of strongly coupled light–matter systems, the presented results also indicate conditions under which those effects might become accessible.

### Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems

* Nicolas Tancogne-Dejean, Micael J. T. Oliveira, Xavier Andrade, Heiko Appel, Carlos H. Borca, Guillaume Le Breton, Florian Buchholz, Alberto Castro, Stefano Corni, Alfredo A. Correa, Umberto De Giovannini, Alain Delgado, Florian G. Eich, Johannes Flick, Gabriel Gil, Adrián Gomez, Nicole Helbig, Hannes Hübener, René Jestädt, Joaquim Jornet-Somoza, Ask H. Larsen, Irina V. Lebedeva, Martin Lüders, Miguel A. L. Marques, Sebastian T. Ohlmann, Silvio Pipolo, Markus Rampp, Carlo A. Rozzi, David A. Strubbe, Shunsuke A. Sato, Christian Schäfer, Iris Theophilou, Alicia Welden, and Angel Rubio*

Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind, i.e., to provide a unique framework that allows us to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory. This article aims to present the new features that have been implemented over the last few years, including technical developments related to performance and massive parallelism. We also describe the major theoretical developments to address ultrafast light-driven processes, such as the new theoretical framework of quantum electrodynamics density-functional formalism for the description of novel light–matter hybrid states. Those advances, and others being released soon as part of the Octopus package, will allow the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in molecules and materials, and new emergent states of matter (quantum electrodynamical-materials).

### Light-matter interactions within the Ehrenfest–Maxwell–Pauli–Kohn–Sham framework: fundamentals, implementation, and nano-optical applications

*René Jestädt, Michael Ruggenthaler, Micael J. T. Oliveira, Angel Rubio &Heiko Appel*

In recent years significant experimental advances in nano-scale fabrication techniques and in available light sources have opened the possibility to study a vast set of novel light-matter interaction scenarios, including strong coupling cases. In many situations nowadays, classical electromagnetic modeling is insufficient as quantum effects, both in matter and light, start to play an important role. Instead, a fully self-consistent and microscopic coupling of light and matter becomes necessary. We provide here a critical review of current approaches for electromagnetic modeling, highlighting their limitations. We show how to overcome these limitations by introducing the theoretical foundations and the implementation details of a density-functional approach for coupled photons, electrons, and effective nuclei in non-relativistic quantum electrodynamics. Starting point of the formalism is a generalization of the Pauli–Fierz field theory for which we establish a one-to-one correspondence between external fields and internal variables. Based on this correspondence, we introduce a Kohn-Sham construction which provides a computationally feasible approach for ab-initio light-matter interactions. In the mean-field limit, the formalism reduces to coupled Ehrenfest–Maxwell–Pauli–Kohn–Sham equations. We present an implementation of the approach in the real-space real-time code Octopus using the Riemann–Silberstein formulation of classical electrodynamics to rewrite Maxwell's equations in Schrödinger form. This allows us to use existing very efficient time-evolution algorithms developed for quantum-mechanical systems also for Maxwell's equations. We show how to couple the time-evolution of the electromagnetic fields self-consistently with the quantum time-evolution of the electrons and nuclei. This approach is ideally suited for applications in nano-optics, nano-plasmonics, (photo) electrocatalysis, light-matter coupling in 2D materials, cases where laser pulses carry orbital angular momentum, or light-tailored chemical reactions in optical cavities just to name but a few.

### Nature of Symmetry Breaking at the Excitonic Insulator Transition: Ta2NiSe5

*Giacomo Mazza, Malte Rösner, Lukas Windgätter, Simone Latini, Hannes Hübener, Andrew J. Millis, Angel Rubio, and Antoine Georges*

**Ta _{2}NiSe_{5}** is one of the most promising materials for hosting an excitonic insulator ground state. While a number of experimental observations have been interpreted in this way, the precise nature of the symmetry breaking occurring in

**Ta**, the electronic order parameter, and a realistic microscopic description of the transition mechanism are, however, missing. By a symmetry analysis based on first-principles calculations, we uncover the discrete lattice symmetries which are broken at the transition. We identify a purely electronic order parameter of excitonic nature that breaks these discrete crystal symmetries and contributes to the experimentally observed lattice distortion from an orthorombic to a monoclinic phase. Our results provide a theoretical framework to understand and analyze the excitonic transition in

_{2}NiSe_{5}**Ta**and settle the fundamental questions about symmetry breaking governing the spontaneous formation of excitonic insulating phases in solid-state materials.

_{2}NiSe_{5}## 2019

### Force balance approach for advanced approximations in density functional theories

*Tchenkoue Djouom, M.-L., Penz, M., Theophilou, I., Ruggenthaler, M., & Rubio, A.*

We propose a systematic and constructive way to determine the exchange-correlation potentials of density-functional theories including vector potentials. The approach does not rely on energy or action functionals. Instead, it is based on equations of motion of current quantities (force balance equations) and is feasible both in the ground-state and the time-dependent settings. This avoids, besides differentiability and causality issues, the optimized-effective-potential procedure of orbital-dependent functionals. We provide straightforward exchange-type approximations for different density functional theories that for a homogeneous system and no external vector potential reduce to the exchange-only local-density and Slater X*α* approximations.

### Microscopic theory for the light-induced anomalous Hall effect in graphene

*S. A. Sato, J. W. McIver, M. Nuske, P. Tang, G. Jotzu, B. Schulte, H. Hübener, U. De Giovannini, L. Mathey, M. A. Sentef, A. Cavalleri, and A. Rubio*

We employ a quantum Liouville equation with relaxation to model the recently observed anomalous Hall effect in graphene irradiated by an ultrafast pulse of circularly polarized light. In the weak-field regime, we demonstrate that the Hall effect originates from an asymmetric population of photocarriers in the Dirac bands. By contrast, in the strong-field regime, the system is driven into a nonequilibrium steady state that is well described by topologically nontrivial Floquet-Bloch bands. Here, the anomalous Hall current originates from the combination of a population imbalance in these dressed bands together with a smaller anomalous velocity contribution arising from their Berry curvature. This robust and general finding enables the simulation of electrical transport from light-induced Floquet-Bloch bands in an experimentally relevant parameter regime and creates a pathway to designing ultrafast quantum devices with Floquet-engineered transport properties.

### Light–Matter Response in Nonrelativistic Quantum Electrodynamics

*Johannes Flick, Davis M. Welakuh, Michael Ruggenthaler, Heiko Appel, and Angel Rubio*

We derive the full linear-response theory for nonrelativistic quantum electrodynamics in the long wavelength limit and provide a practical framework to solve the resulting equations by using quantum-electrodynamical density-functional theory. We highlight how the coupling between quantized light and matter changes the usual response functions and introduces cross-correlated light-matter response functions. These cross-correlation responses lead to measurable changes in Maxwell’s equations due to the quantum-matter-mediated photon–photon interactions. Key features of treating the combined matter-photon response are that natural lifetimes of excitations become directly accessible from first-principles, changes in the electronic structure due to strong light-matter coupling are treated fully nonperturbatively, and self-consistent solutions of the back-reaction of matter onto the photon vacuum and vice versa are accounted for. By introducing a straightforward extension of the random-phase approximation for the coupled matter-photon problem, we calculate the ab initio spectra for a real molecular system that is coupled to the quantized electromagnetic field. Our approach can be solved numerically very efficiently. The presented framework leads to a shift in paradigm by highlighting how electronically excited states arise as a modification of the photon field and that experimentally observed effects are always due to a complex interplay between light and matter. At the same time the findings provide a route to analyze as well as propose experiments at the interface between quantum chemistry, nanoplasmonics and quantum optics.