Session M59: First Principles Modeling of Excited-State Phenomena in Materials: Excitons and BSE

Non-linear Optics and Exciton Condensation in Low-dimensional Materials

Strong Coulomb interactions in low-dimensional materials result in the formation of bound and resonant electron-hole pairs, or excitons, which can dramatically change the optical response in these materials. In this talk, I will largely focus on the effect of excitons on the non-linear optical response. We develop and implement an approach to compute the non-linear optical response within the framework of the GW-Bethe Salpeter equation. Examples of different non-linear phenomena will be given, including second harmonic generation, spontaneous parametric down-conversion [1], and shift currents. I will describe how excitons and the coupling between excitons changes the origins of these non-linear phenomena, in comparison with the independent particle picture. On a separate note, I will also discuss our predictions of high temperature exciton condensation in heterostructures of organic phthalocyanine molecules on two-dimensional materials [2].

[1] F. Xuan, M. Lai, Y. Wu, S.Y. Quek, arXiv:2305.08345

[2] K. Ulman, S.Y. Quek, Nano Letters, 21, 8888 (2021)   

Excitonic effects in nonlinear optical responses: Diagrammatic approach, exciton-state formalism and first-principles calculations

Nonlinear optical (NLO) responses have garnered tremendous interest for decades due to their fundamental and technological interests. The theory and calculations of NLO responses including electron-hole interactions, which is especially crucial for reduced-dimensional materials, however, remain underdeveloped. Here, we develop an ab initio approach to calculate second-order and third-order nonlinear responses with excitonic effects in an exciton-state basis, going beyond the independent-particle approximation. We compute second harmonic generation (SHG) and third harmonic generation (THG) in monolayer h-BN and MoS₂ employing exciton states from GW-Bethe-Salpeter equation (GW-BSE) calculations and show both materials exhibit huge excitonic enhancement. The physical origin of the enhancement is directly understood through the coupling amplitudes among exciton states, assisted with diagrammatic representations. Our method provides an accurate and ab initio description of NLO responses, capturing self-energy and electron-hole interaction effects.   

Ab initio optical absorption spectra for excitonic insulators

Excitonic insulators are a strongly correlated phase of matter whose electronic ground state is a condensate of electron-hole pairs, which may be viewed as a BCS-like state in a certain limit. In this talk, we present an ab initio framework for determining the optical absorption spectrum for this phase. Here we start with the electronic band structure of the normal phase within the GW approximation, and then utilize an ab initio electron-hole interaction kernel for an iterative computation of the BCS gap function. Within this framework, the interaction kernel matrix elements are the same ones used to compute excitonic effects on the optical absorption of the normal phase in standard GW plus Bethe Salpeter Equation (GW-BSE) calculations. Finally, the excitonic insulator optical response is evaluated from the resultant excitonic insulator band structure.

As a first study, this method is applied to a Kagome lattice 4-triangulene covalent organic framework, which was recently conjectured to be an excitonic insulator candidate, using the BerkeleyGW code for normal phase and interaction kernel calculations.   

Strongly localized exciton states in layered BiI3: From bulk to monolayer

In this work, we carry out a detailed theoretical study of the electronic and optical properties of bulk and monolayer bismuth triiodide BiI₃, a layered metal halide, using the ab initio GW+BSE scheme with a full spinorial formulation. We discuss the dimensionality effects in detail along with the role of spin-orbit coupling. Moreover, we compute the exciton dispersion by solving the BSE at finite momentum, also analysing transverse (TE) and longitudinal (LE) excitons, and the longitudinal-transverse splitting at q->0. In bulk, we find a peculiar direction-dependent hybridization of exciton with different character mediated by the long-range Coulomb interaction. Our work provides theoretical support to existing experiment, demonstrate that BiI₃ is an important testbed for the theoretical study of fundamental exciton physics (such as phonon-mediated exciton interaction and localization) and finally confirms that this system is a promising material for the experimental investigation of exciton dynamics (such as tr-ARPES measurements).   

Inverse Design of Tetracene Polymorphs with Enhanced Singlet Fission Performance by Property-Based Genetic Algorithm Optimization

The efficiency of solar cells may be improved by using singlet fission (SF), in which one singlet exciton splits into two triplet excitons. SF occurs in molecular crystals. A molecule may crystallize in more than one form, a phenomenon known as polymorphism. Crystal structure may affect SF performance. In the common form of tetracene, SF is experimentally known to be slightly endoergic. A second, metastable polymorph of tetracene has been found to exhibit better SF performance. Here, we conduct inverse design of the crystal packing of tetracene using a genetic algorithm (GA) with a fitness function tailored to simultaneously optimize the SF rate and the lattice energy. The property-based GA successfully generates more structures predicted to have higher SF rates and provides insight into packing motifs associated with improved SF performance. For the structures within the polymorph energy range, we use many-body perturbation theory within the GW approximaiton and the Bethe-Salpeter equaiton (GW+BSE) to evaluate the singlet and triplet exciton energies and the degree of charge transfer character of the singlet exciton wave-funciton. We find a putative polymorph predicted to have superior SF performance to the two forms of tetracene, whose structures have been determined experimentally. The putative structure has a lattice energy within 1.5 kJ/mol of the most stable common form of tetracene.   

Excitonic band topology in two-dimensional topological materials

In recent years, the interplay of topological and excitonic effects in low-dimensional materials has been under significant investigation, especially in relation to a topological excitonic condensate (TEC) state. However, it is still not clear how the single excitonic band topology is affected by the underlying conduction and valence band topology which ultimately leads to the TEC state. In this work, we study this interplay of excitonic and topological effects using the ab initio GW plus Bethe-Salpeter equation approach. We calculate excitonic band structure, excitonic Berry curvature, and phase symmetry of the lowest excitonic band of candidate TEC materials, including monolayer 1T’ MoS₂ monolayer, and bilayer InAs/GaSb. Our work provides interesting avenues to study topological excitonic effects in semiconductors/semi-metals and explains the possible origin of the TEC state in two-dimensional topological materials.   

Ab initio GW-Bethe-Salpeter Equation Approach using Optimally Tuned Range-Separated Hybrid Functionals and Non-Uniform Reciprocal Space Sampling

One of the gold standard methods for predictive calculation of optical properties of solids is the ab initio GW-Bethe Salpeter equation (GW-BSE) approach. Two challenges in predicting excited state properties within the GW-BSE framework are the input Kohn-Sham eigensystem (or “starting point”)  and the reciprocal space sampling of the exciton wavefunction. Recently, the Wannier-localized optimally tuned screened range separated hybrid (WOT-SRSH) functional [1] has been shown to be an excellent starting point eigensystem for “single shot” ab initio G0W0 and G0W0-BSE calculations [2,3]. Moreover, when solving the BSE, it is now possible via Wannier interpolation to finely sample the exciton wavefunction in nonuniform regions of reciprocal space [4] even when using hybrid functionals as a starting point, avoiding the need for an extremely dense uniform grid. Here, we present absorption spectra and excited state properties, including exciton binding energies, for prototypical semiconductors and halide perovskites computed using the GW-BSE framework with a WOT-SRSH starting point, solving the BSE with a dense nonuniform reciprocal space sampling. We discuss the convergence of our results relative to prior calculations and compare with experiments.

[1] D. Wing, et al., PNAS 118, (2021).

[2] G. Ohad, S. E. Gant, et al., arXiv:2309.02117 (2023).

[3] S. E. Gant, et al., Phys. Rev. Materials 6, 053802 (2022).

[4] A. Alvertis, A. Champagne, et al., Submitted (2023).   

Moiré effect on the higher-energy excitonic states in WSe2/WS2 superlattice

Moiré superlattices in two-dimensional van der Waals heterostructures have recently emerged as a platform for tailoring electronic and optical properties at the nanoscale. Recent studies have shown that exciton states in moiré superlattice have highly exotic electron-hole correlation, including unusual charge distribution and distinctive momentum space selection rule. While most moiré exciton studies to date have focused on the lowest energy excitations, our study here extends the exploration to the higher energy excited-state excitons. We present a first-principles study on the electronic and optical properties of these higher energy excitons in WS₂/WSe₂ moiré heterostructure utilizing the GW plus Bethe-Salpeter equation (GW-BSE) calculation combined with the recently developed pristine unit-cell matrix projection (PUMP) method. We study the interplay between the moiré potential and the fine structure of the higher energy exciton wavefunctions, mostly focusing on the 2s exciton within the WSe₂ layer, and how such interplay changes the exciton binding energies and manifest new optical features in the absorption spectra.   

Effect of scattering and recombination on photocurrent in non-centrosymmetric systems from ab-initio density matrix dynamics

Uniform illumination of crystals lacking a center of symmetry generates a direct photocurrent. The phenomenon, also referred to as photogalvanic effect, has been intensively investigated both experimentally and theoretically since its discovery in the late 1960s. The interest remains now due to its important impact on bulk photovoltaic applications and nonlinear optics. Although various prior theoretical approaches have made significant progress on its physical understanding, they have been largely limited to model Hamiltonians or perturbative methods with relaxation time approximation. An ab-initio predictive tool including various kinetic processes simultaneously remains to be developed. In this talk, we show, by building on our recent development of a general-purpose ab-initio real-time density-matrix dynamics approach that includes various quantum scattering channels [1] and takes into account the effect of recombinations, the further development of the method for computing transient and steady-state photocurrents. We analyze the nature of the photocurrent under linear and circularly polarized light, and investigate the photocurrent dependence on electron-phonon, electron-electron, electron-impurity scatterings as well as electron-hole recombination, as a function of temperature and doping density in noncentro-symmetric semiconductors and semimetals. Our work can provide the useful physical insights into the dominant mechanism and guide experiments for optimal photocurrents in applications.

[1]  J. Xu, A. Habib, R. Sundararaman, and Y. Ping, Ab initio ultrafast spin dynamics in solids, Phys. Rev. B 104, 184418 (2021).   

Exciton-enhanced electrooptic effect in GaN: a time-dependent GW study

 The Franz-Keldysh effect refers to the change in the optical absorption with an electric field applied to a semiconductor. However, previous interpretations of this phenomenon often overlook the significant role played by excitonic effects (electron-hole interactions), especially near the absorption spectrum edge. Therefore, an accurate incorporation of electron-hole interactions (excitonic effects) is essential for a comprehensive understanding of the Franz-Keldysh phenomenon. In this work, based on an ab initio time-dependent adiabatic GW approach, we investigate the modifications in the optical absorption induced by a DC electric field in gallium nitride (GaN), which is a wide bandgap semiconductor with numerous practical applications, particularly in power devices. Our findings show that the prominent variations at the spectral edge of the optical absorption of GaN are dominated by excitonic effects, which cannot be captured by the independent-particle interpretation of the Franz-Keldysh effect. Additionally, we study second harmonic generation in the system and discuss potential applications.   

Many-Body Enhancement of High-harmonic Generation in monolayer MoS2

Many-body effects play an important role in enhancing and modifying optical absorption and other excited-state properties of solids in the perturbative regime, but their role in high harmonic generation (HHG) and other nonlinear response beyond the perturbative regime is not well-understood.

We present here an ab initio many-body method based on the real-time propagation of the non-equilibrium Green’s function with the GW self energy to the study of nonperturbative HHG. We calculate the HHG of monolayer MoS2 and obtain excellent agreement with experiment, including the reproduction of patterns of monotonic and nonmonotonic harmonic yield in the parallel and perpendicular responses, respectively. We find that many-body effects are essential to reproducing these spectral features, which represent the complex interplay of electron-hole interactions (or exciton effects) in tandem with the many-body renormalization of the independent quasiparticle bandstructure.   

Light-induced shift current vortex crystals in moiré heterobilayers

Transition metal dichalcogenide (TMD) moiré superlattices provide an emerging platform to explore various light-induced phenomena. Recently, the discoveries of novel moiré excitons have attracted great interest. The nonlinear optical responses of these systems are however still underexplored. Here, we report investigation of light-induced shift currents in the WSe₂/WS₂ moiré superlattice. We discover a striking phenomenon of the formation of shift current vortex crystals -- i.e., two-dimensional periodic arrays of moiré-scale current vortices and associated magnetic fields with remarkable intensity under laboratory laser setup. Furthermore, we demonstrate high optical tunability of these current vortices – their location, shape, chirality and magnitude can be tuned by the frequency, polarization and intensity of the incident light. Our findings provide a promising all-optical control route to manipulate nanoscale shift current density distributions and magnetic field patterns, as well as shed light on nonlinear optical responses in moiré quantum matter and their possible applications.