Class of distorted Landau levels and Hall phases in a two-dimensional electron gas subject to an inhomogeneous magnetic field

An analytic closed form solution is derived for the bound states of a two-dimensional electron gas subject to a static, inhomogeneous (1/r in plane decaying) magnetic field, including the Zeeman interaction. The solution provides access to many-body properties of a two-dimensional, noninteracting, electron gas in the thermodynamic limit. Radially distorted Landau levels can be identified as well as magnetic field induced density and current oscillations close to the magnetic impurity. These radially localized oscillations depend strongly on the coupling of the spin to the magnetic field, which gives rise to nontrivial spin currents. Moreover, the Zeeman interaction introduces a unique flat band, i.e., infinitely degenerate energy level in the ground state, assuming a spin gs-factor of two. Surprisingly, the charge and current densities can be computed analytically for this fully filled flat band in the thermodynamic limit. Numerical calculations show that the total magnetic response of the electron gas remains diamagnetic (similar to Landau levels) independent of the Fermi energy. However, the contribution of certain, infinitely degenerate energy levels may become paramagnetic. Furthermore, numerical computations of the Hall conductivity reveal asymptotic properties of the electron gas, which are driven by the anisotropy of the vector potential instead of the magnetic field, i.e., become independent of spin. Eventually, the distorted Landau levels give rise to negative and positive Hall conductivity phases, with sharp transitions at specific Fermi energies. Overall, our work merges "impurity" with Landau-level physics, which provides novel physical insights, not only locally, but also in the asymptotic limit. This paves the way for a large number of future theoretical as well as experimental investigations, e.g., to include electronic correlations and to investigate two-dimensional systems such as graphene or transition metal dichalcogenides under the influence of inhomogeneous magnetic fields.We thank Simone Latini for inspiring discussions. This work was made possible through the support of the RouTe Project (13N14839) , financed by the Federal Ministry of Education and Research (Bundesministerium fur Bildung und Forschung (BMBF) ) and supported by the European Research Council (ERC-2015-AdG694097) , the Cluster of Excellence "CUI: Advanced Imaging of Matter" of the Deutsche Forschungsgemeinschaft (DFG) , EXC 2056, project ID 390715994 and the Grupos Consolidados (IT1249-19) . V.R. acknowledges support from the NSF through a grant for ITAMP at Harvard University. The Flatiron Institute is a division of the Simons Foundation. D.S. initiated the project, discovered the simple closed form solution and performed corresponding analytic as well as numerical calculations. M.R. contributed to the mathematical accuracy and rigorosity. V.R. added expertise and calculations to connect with the homogeneous Landau setting. All authors developed the physical interpretation and wrote the manuscript. Numerical data available upon request

Electronic non-adiabatic dynamics in enhanced ionization of isotopologues of hydrogen molecular ions from the exact factorization perspective

It was recently shown that the exact potential driving the electron's dynamics in enhanced ionization of H-2(+) can have large contributions arising from dynamic electron-nuclear correlation, going beyond what any Coulombic-based model can provide. This potential is defined via the exact factorization of the molecular wavefunction that allows the construction of a Schro "dinger equation for the electronic system, in which the potential contains exactly the effect of coupling to the nuclear system and any external fields. Here we study enhanced ionization in isotopologues of H-2(+) in order to investigate the nuclear-mass-dependence of these terms for this process. We decompose the exact potential into components that naturally arise from the conditional wavefunction, and also into components arising from the marginal electronic wavefunction, and compare the performance of propagation on these different components as well as approximate potentials based on the quasi-static or Hartree approximation with the exact propagation. A quasiclassical analysis is presented to help analyse the structure of different non-Coulombic components of the potential driving the ionizing electron.We acknowledge support from the European Research Council (ERC-2015-AdG-694097), Grupos Consolidados (IT578-13), and the European Union's Horizon 2020 Research and Innovation programme under grant agreement no. 676580. A. K. and A. A. acknowledge funding from the European Union's Horizon 2020 research and innovation programme under the Marie SklodowskaCurie grant agreement no. 704218 and 702406, respectively. N. T. M. thanks the National Science Foundation, grant CHE1566197, for support. Open Access funding provided by the Max Planck Society

Nematicity Arising from a Chiral Superconducting Ground State in Magic-Angle Twisted Bilayer Graphene under In-Plane Magnetic Fields

Recent measurements of the resistivity in magic-angle twisted bilayer graphene near the superconducting transition temperature show twofold anisotropy, or nematicity, when changing the direction of an in-plane magnetic field [Cao et al., Science 372, 264 (2021)]. This was interpreted as strong evidence for exotic nematic superconductivity instead of the widely proposed chiral superconductivity. Counter-intuitively, we demonstrate that in two-dimensional chiral superconductors the in-plane magnetic field can hybridize the two chiral superconducting order parameters to induce a phase that shows nematicity in the transport response. Its paraconductivity is modulated as cos(2 theta(B)), with theta(B) being the direction of the in-plane magnetic field, consistent with experiment in twisted bilayer graphene. We therefore suggest that the nematic response reported by Cao et al. does not rule out a chiral superconducting ground state.We thank Rafael Fernandes and Liang Fu for useful discussions. T. Y. and M. A. S. acknowledge financial support by Deutsche Forschungsgemeinschaft through the Emmy Noether program (SE 2558/2). D. M. K. acknowledges support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via RTG 1995, within the Priority Program SPP 2244 "2DMP" and Germany's Excellence StrategyCluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1-390534769. A. R. acknowledges support from the European Research Council (ERC-2015-AdG-694097), UPV/EHU Grupos Consolidados (IT1249-19) and the Cluster of Excellence "CUI: Advanced Imaging of Matter" of the Deutsche Forschungsgemeinschaft (DFG)-EXC 2056-project ID 390715994. The Flatiron Institute is a division of the Simons Foundation. We acknowledge support from the Max Planck-New York City Center for Non-Equilibrium Quantum Phenomena

Simulating Vibronic Spectra without Born-Oppenheimer Surfaces

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 H2 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 systemsThis work was supported by the European Research Council (ERC-2015-AdG694097), the Cluster of Excellence Advanced Imaging of Matter (AIM), JSPS KAKENHI Grant Number 20K14382, Grupos Consolidados (IT1249-19), and SFB925. The Flatiron Institute is a division of the Simons Foundatio

Light-Driven Extremely Nonlinear Bulk Photogalvanic Currents

We predict the generation of bulk photocurrents in materials driven by bichromatic fields that arc 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 (similar to 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 effectsWe thank Dr. Shunsuke A. Sato for helpful discussions. We acknowledge financial support from the European Research Council (ERC-2015-AdG-694097), by the Cluster of Excellence "Advanced Imaging of Matter" (AIM), Grupos Consolidados (IT1249-19) and SFB925 "Light induced dynamics and control of correlated quantum systems." The Flatiron Institute is a division of the Simons Foundation. O. N. gratefully acknowledges the support of the Humboldt Foundatio

Engineering Three-Dimensional Moire Flat Bands

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 moire 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 moire interference patterns are spatially shifted from one twisted layer to the next. We exemplify the general concept by considering graphitic systems, boron nitride, and WSe2, 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.This work is supported by the European Research Council (ERC-2015-AdG-694097), Grupos Consolidados (IT124919), and SFB925. A.R. is supported by the Flatiron Institute, a division of the Simons Foundation. We acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under RTG 1995 within the Priority Program SPP 2244 2DMP under Germany's Excellence Strategy -Cluster of Excellence and Advanced Imaging of Matter (AIM) EXC 2056-390715994 and RTG 2247. L.X. acknowledges the support from Distinguished Junior Fellowship program by the South Bay Interdisciplinary Science Center in the Songshan Lake Materials Laboratory. J.Z. acknowledges funding received from the European Union Horizon 2020 research and innovation program under Marie Sklodowska-Curie Grant Agreement 886291 (PeSD-NeSL)

The ferroelectric photo ground state of SrTiO3: Cavity materials engineering

Optical cavities confine light on a small region in space, which can result in a strong coupling of light with materials inside the cavity. This gives rise to new states where quantum fluctuations of light and matter can alter the properties of the material altogether. Here we demonstrate, based on first-principles calculations, that such light-matter coupling induces a change of the collective phase from quantum paraelectric to ferroelectric in the SrTiO3 ground state, which has thus far only been achieved in outof-equilibrium strongly excited conditions [X. Li et al., Science 364, 1079-1082 (2019) and T. F. Nova, A. S. Disa, M. Fechner, A. Cavalleri, Science 364, 1075-1079 (2019)]. This is a light-matter hybrid ground state which can only exist because of the coupling to the vacuum fluctuations of light, a photo ground state. The phase transition is accompanied by changes in the crystal structure, showing that fundamental ground state properties of materials can be controlled via strong light-matter coupling. Such a control of quantum states enables the tailoring of materials properties or even the design of novel materials purely by exposing them to confined light.We are grateful for the illuminating discussions with Dmitri Basov, Atac Imamoglu, Jerome Faist, Jean-Marc Triscone, Peter Littlewood, Andrew Millis, Michael Ruggenthaler, Michael A. Sentef, and Eugene Demler. We acknowledge financial support from the European Research Council (Grant ERC2015AdG694097) , Grupos Consolidados (Grant IT124919) , the Japan Society for the Promotion of Science KAKENHI program (Grant JP20K14382) , and the Cluster of Excellence "CUI: Advanced Imag-ing of Matter" of the Deutsche Forschungsgemeinschaft (Grant EXC 2056 Project 390715994) . The Flatiron Institute is a division of the Simons Foundation. S.L. and D.S. acknowledge support from the Alexander von Humboldt Foundation

Excited-state band structure mapping

[EN] Angle-resolved photoelectron spectroscopy is an extremely powerful probe of materials to access the occupied electronic structure with energy and momentum resolution. However, it remains blind to those dynamic states above the Fermi level that determine technologically relevant transport properties. In this work we extend band structure mapping into the unoccupied states and across the entire Brillouin zone by using a state-of-the-art high repetition rate, extreme ultraviolet femtosecond light source to probe optically excited samples. The wideranging applicability and power of this approach are demonstrated by measurements on the two-dimensional semiconductor WSe2, where the energy-momentum dispersion of valence and conduction bands are observed in a single experiment. This provides a direct momentum-resolved view, not only on the complete out-of-equilibrium band gap but also on its renormalization induced by electronic screening. Our work establishes a benchmark for measuring the band structure of materials, with direct access to the energy-momentum dispersion of the excited-state spectral function.A This work was funded by the Max-Planck-Gesellschaft, by the German Research Foundation (DFG) , within the Emmy Noether Program (Grant No. RE 3977/1) , and Grants No. FOR1700 (Project E5) , No. SPP2244 (Project No. 443366970) , and from the European Research Council, Grant ERC-2015-CoG-682843. M.P. acknowledges financial support from the Swiss National Science Foundation (SNSF) through Grant No. CRSK-2_196756. C.W.N. and C.M. ac-knowledge financial support by Swiss National Science Foundation (SNSF) Grant No. P00P2_170597. A.R. and H.H. acknowledge financial support from the European Research Council (Grant No. ERC-2015-AdG-694097) and the Cluster of Excellence "CUI: Advanced Imaging of Matter" of the Deutsche Forschungsgemeinschaft (Grant EXC 2056, Project No. 390715994)

Nanometer-Scale Lateral p–n Junctions in Graphene/α-RuCl3 Heterostructures

[EN] The ability to create nanometer-scale lateral p-n junctions is essential for the next generation of two-dimensional (2D) devices. Using the charge-transfer heterostructure graphene/alpha-RuCl3, we realize nanoscale lateral p-n junctions in the vicinity of graphene nanobubbles. Our multipronged experimental approach incorporates scanning tunneling microscopy (STM) and spectroscopy (STS) and scattering-type scanning near-field optical microscopy (s-SNOM) to simultaneously probe the electronic and optical responses of nanobubble p-n junctions. Our STM/STS results reveal that p-n junctions with a band offset of 0.6 eV can be achieved with widths of 3 nm, giving rise to electric fields of order 108 V/m. Concurrent s-SNOM measurements validate a point-scatterer formalism for modeling the interaction of surface plasmon polaritons (SPPs) with nanobubbles. Ab initio density functional theory (DFT) calculations corroborate our experimental data and reveal the dependence of charge transfer on layer separation. Our study provides experimental and conceptual foundations for generating p-n nanojunctions in 2D materials.Research at Columbia University was supported as part of the Energy Frontier Research Center on Programmable Quantum Materials funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No DE-SC0019443. Plasmonic nano-imaging at Columbia University was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No DE-SC0018426. J.Z. and A.R. were supported by the European Research Council (ERC-2015-AdG694097), the Cluster of Excellence “Advanced Imaging of Matter” (AIM) EXC 2056-390715994, funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under RTG 2247, Grupos Consolidados (IT1249-19), and SFB925 “Light induced dynamics and control of correlated quantum systems”. J.Z. and A.R. would like to acknowledge Nicolas Tancogne-Dejean and Lede Xian for fruitful discussions and also acknowledge support by the Max Planck Institute-New York City Center for Non-Equilibrium Quantum Phenomena. The Flatiron Institute is a division of the Simons Foundation. J.Z. acknowledges funding received from the European Union Horizon 2020 research and innovation programme under Marie Skłodowska-Curie Grant Agreement 886291 (PeSD-NeSL). STM support was provided by the National Science Foundation via Grant DMR-2004691. C.R.-V. acknowledges funding from the European Union Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement 844271. D.G.M. acknowledges support from the Gordon and Betty Moore Foundation’s EPiQS Initiative, Grant GBMF9069. J.Q.Y. was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. S.E.N. acknowledges support from the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Division of Scientific User Facilities. Work at University of Tennessee was supported by NSF Grant 180896

One-dimensional flat bands in twisted bilayer germanium selenide

Experimental advances in the fabrication and characterization of few-layer materials stacked at a relative twist of small angle have recently shown the emergence of flat energy bands. As a consequence electron interactions become relevant, providing inroads into the physics of strongly correlated two-dimensional systems. Here, we demonstrate by combining large scale ab initio simulations with numerically exact strong correlation approaches that an effective one-dimensional system emerges upon stacking two twisted sheets of GeSe, in marked contrast to all moire systems studied so far. This not only allows to study the necessarily collective nature of excitations in one dimension, but can also serve as a promising platform to scrutinize the crossover from two to one dimension in a controlled setup by varying the twist angle, which provides an intriguing benchmark with respect to theory. We thus establish twisted bilayer GeSe as an intriguing inroad into the strongly correlated physics of lowdimensional systems. Twisting the relative orientation of the sheets in few-layer van der Waals materials can cause drastic changes in the electronic bandstructure. Here, the authors predict that twisted bilayer GeSe realises an effective one-dimensional flat-band electronic system with exotic, strongly correlated behaviour.This work was supported by the European Research Council (ERC-2015-AdG694097) and Grupos Consolidados (IT578-13). The Flatiron Institute is a division of the Simons Foundation. L.X. acknowledges the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 709382 (MODHET). M.C. is supported by the Flatiron Institute, a division of the Simons Foundation. D.M.K. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy-Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1-390534769. Gefordert durch die Deutsche Forschungsgemeinschaft(DFG) im Rahmen der Exzellenzstrategie des Bundes und der Lander-Exzellenzcluster Materie und Licht fur Quanteninformation (ML4Q) EXC 2004/1-390534769. D.M.K. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under RTG 1995. We acknowledge support by the Max Planck Institute-New York City Center for Non-Equilibrium Quantum Phenomena. D.M.R.G. calculations were performed with computing resources granted by RWTH Aachen University under projects prep0010. We acknowledge computing resources from Columbia University's Shared Research Computing Facility project, which is supported by NIH Research Facility Improvement Grant 1G20RR030893-01, and associated funds from the New York State Empire State Development, Division of Science Technology and Innovation (NYSTAR) Contract C090171, both awarded April 15, 2010