Session F39: First-principles modeling of excited-state phenomena in materials IV: GW+BSE for Low-Dimensional Materials and Interfaces

Nonlinear optics from first-principles real-time approaches

In the past decades, many-body approaches based on the GW approximation and the Bethe-Salpeter equation have become state-of-the-art for calculating optical absorption in solids and nanostructures. In this talk, I’ll first present a real-time approach derived from the non-equilibrium Green’s function, that allows extending the GW+BSE approach beyond the linear regime.[1,2] Using this approach, I’ll address the importance of many-body effects and in particular of excitonic effects for nonlinear optical properties.[3] For example, I’ll look at the case of single-layer monochalcogenide whose strong Second Harmonic Generation cannot be reproduced within the independent-particle approximation.[4] In the second part of the talk, I’ll then discuss the possibility of a real-time approach based on time-dependent density-functional theory, that can describe excitonic effects.[5]

[1] Attaccalite, C., Grüning, M. & Marini, A., (2011) Physical Review B 84, 24, 245110
[2] Attaccalite, C. & Grüning, M., (2013) Physical Review B 88, 235113
[3] Grüning, M. & Attaccalite, C., (2014) Physical Review B 89,081102
[4] Claudio Attaccalite, Maurizia Palummo, Elena Cannuccia, Myrta Grüning, (2019) Phys Rev Mat 3, 074003
[5] Grüning, M., Sangalli, D. & Attaccalite, C., (2016) Physical Review B 94, 035149   

Exciton bandstructure in carbon nanotubes from many-body perturbation theory

Understanding exciton decay processes and lifetimes in solid-state materials is of great interest, with emerging applications such as material characterization and energy conversion and storage. A predictive theoretical assessment of the involved underlying interaction mechanisms is, however, highly challenging. A computational scheme that supplies reliable excited-state properties in crystals is many-body perturbation theory within the GW approximation and the Bethe-Salpeter equation (BSE) approach (GW-BSE). This method allows a predictive evaluation of exciton wavefunctions and excitation energies, and recently also exciton bandstructures. In this study, we explore the excitonic bandstructure of a quasi 1D system – single wall carbon nanotubes (SWCNTs), a well-examined material due to its unique electronic properties and application in optoelectronic devices. We further explore the relation of the exciton dispersion to excitonic decay processes.   

Exciton and Spin Dynamics for Quantum Defects in Two-dimensional Materials from First-principles

Spin defects in 2D materials such as ultrathin hexagonal boron nitride (hBN) have been found to be promising single-photon emitters and potential candidates for qubits. However, first-principles prediction of accurate defect properties in 2D materials remains challenging, mainly because of the highly anisotropic dielectric screening in 2D materials and strong many body interactions. This work shows how we solve the numerical convergence issues for charged defect properties in 2D materials at both the DFT and many body perturbation theory (GW/Bethe-Salpeter equation), and how we tackle the complex many body interactions including electron-electron, electron-phonon and defect-excitons for the excited state dynamics of spin defects in 2D materials. We are also developing first-principles spin dynamics through Lindblad dynamics for open quantum systems. With our methods, we will design spin defects that have deep defect levels, weak electron-phonon coupling, high radiative recombination rates, and long spin relaxation and coherence time as future materials platforms for quantum information technologies.
  

Local Field Effect on Non-local Dielectric Screening of Two-Dimensional Interface Systems: A First-principles Study

Two-dimensional (2D) materials have provided platforms for exotic physics and emerging applications by forming van-der Waals interfaces. Non-local dielectric screening by substrates play an important role in modifying the quasiparticle properties of these interface systems. While several studies have been performed for the substrate screening of 2D materials, the underlying approximations and the connection between different methods have not been investigated in detail. We derived the effective polarizability of the interfaces from each monolayer sub-system, and showed its equivalence to sum over irreducible polarizability at the Random Phase Approximation level. We used this method to calculate prototypical 2D interface systems (heterojunctions and bilayers) and compared with explicit calculations. We compared different existing methods and discussed the local field effect on quasiparticle energies and absorption spectra. Our study shows good consistency between single layer calculations with effective interface screening and explicit interface calculations, and provides careful evaluation of approximations involved in studying substrate screening and interface quasiparticle properties.   

Microscopic Theory of Plasmons in Substrate-supported Borophene

Two-dimensional boron, or borophene, is a metallic monolayer material which hosts
low-loss, high-confinement, visible light plasmons, with possible applications in
nanoplasmonic devices. In contrast with graphene, borophene cannot be exfoliated
and has been synthesized on a variety of metallic substrates. In this talk, we
present first-principles density functional theory calculations of the dielectric and
plasmonic properties of borophene grown on Ag(111). We systematically investigate
the linear response and the momentum-dependent polarizability of borophene as a
function of its proximity to the metallic substrate. Our calculations indicate that the
plasmons in borophene are damped by the substrate, which we explain via a simple
electrodynamic model of coupled polarizabilities between the monolayer and
substrate. Using this model, we predict the plasmonic properties of borophene on a
variety of substrates that minimize plasmon damping.   

Impact of Defects on Electronic and Optical Properties of 2D Germanium Selenide

Germanium Selenide (GeSe) and other Group IV monochalcogenides are van der Waals-bonded layered materials with potential applications in sensing, solar energy and spintronics. Importantly, their band gaps can be tuned via strain, doping, and chemical modification. Due to the reduced dimensionality and reduced screening environment in the monolayer, these modifications have a significant impact on the optoelectronic properties. We apply density functional theory (DFT) and many-body perturbation theory to understand the electronic and optical properties of point vacancies in monolayer GeSe. We find that a Selenium vacancy in the -2 charge state induces mid-gap “trap states,” which strongly localize the electron and hole density. These trap states result in a sharp optical absorption peak below the predicted pristine optical gap and a localized exciton wavefunction around the defect. Overall, these results suggest that the vacancy is a strong perturbation to the system, demonstrating the importance of considering defects in the context of materials discovery and device design.   

Investigating the Role of Electron-Phonon Interactions and Reduced Dimensionality on Optical Excitations in Monolayer GeSe

Two-dimensional (2D) van der Waals-bonded layered materials are promising as inexpensive, light-weight solar energy conversion materials. Better understanding the role of electron-phonon interactions in 2D will be necessary for understanding the optical properties of this class of materials. Here, we use first-principles theory to investigate, the role of electron-phonon interactions on the optical absorption spectrum of monolayer germanium selenide GeSe, a direct gap 2D semiconductor with promising optoelectronic properties. We utilize density functional theory, density functional perturbation theory, and many-body perturbation theory to study both bulk and monolayer GeSe. We determine that the optical gap at room temperature is lower than that of the zero temperature for both systems. For the bulk, an indirect gap semiconductor, this reduction is mainly due to phonon-assisted transitions. For the monolayer, we attribute the reduced gap to the localization of the excited-state in the presence of phonons. The significant influence of electron-phonon interactions in the monolayer suggests that this phenomenon should be better understood for 2D material technology.   

Dielectric embedding GW for weakly coupled molecule-substrate interfaces

Molecule-substrate interfaces are ubiquitous in many areas of nanoscale materials science. Accurate characterization of their electronic structure from first principles is key in understanding material properties. Although the first-principles GW approach is state-of-the-art and can yield accurate quasiparticle energy levels and interfacial level alignments that are in agreement with experiments, it is computationally challenging for large-scale interfaces. In this work, we develop a dielectric embedding approach based on GW, which significantly reduces the computational cost of direct GW for interfaces without sacrificing accuracy. We perform explicit GW calculations only in the simulation cell containing the molecular adsorbate, in which the dielectric effect of the substrate is effectively embedded. The embedding of the dielectric environment is made possible via a real-space truncation of the Kohn-Sham polarizability. Here, we focus on the interfacial level alignments, i.e., relative positions between molecular frontier orbital resonances and the Fermi level of the substrate, at weakly coupled molecule-substrate interfaces. We demonstrate our approach using a few interfaces of experimental interest.   

Energy-level Alignments and Schottky Barrier Heights of Metal-2D Material Interfaces

As the technological applications of 2D material-based electronics continue to rise, an understanding of the physical underpinnings of the energy barriers between metal-2D material contacts becomes critically important. Experimentally, these interfaces are often found to be controlled by Fermi-level pinning, which prevents the tuning of Schottky barrier heights by the modification of the contact metal work function.
Theoretically, the high computational cost of these systems has largely restricted first principles studies to DFT-level calculations. The effects of dielectric screening, which are important even in atomically thin 2D materials¹, are therefore also ignored. Moreover, the small unit cells considered do not allow for the inclusion of defects, which can affect the energy-level alignment at the interface.
In this work we use the newly-developed XAF-GW approach² to study large supercells at the many-body GW level, thus including the full effects of dielectric screening. We examine the origin of the Schottky barrier heights of metal-2D material interfaces, including the effects of dielectric screening, structural reconstruction, and defects.

(1) Noori; Cheng; Xuan; Quek 2D Mater. 2019, 6 (3), 035036
(2) Xuan.; Chen.; Quek J. Chem. Theory Comput. 2019, 15 (6), 3824   

Dependence of 2D nitride electronic and optical properties on heterostructure stacking orientation

Given the successful synthesis of 2D GaN and investigations into the properties of freestanding 2D nitrides, heterostructures of these materials are now of particular interest. Extreme quantum confinement is a viable method to shift light emission to shorter wavelengths, but in 2D nitrides this is counteracted by the quantum-confined Stark shift due to the strong inherent polarization perpendicular to the 2D plane. We report the electronic and optical properties of 2D BN, GaN, AlN, and InN in various stacking orientations, such that the electric fields are either aligned or anti-parallel in two possible configurations. We employ density functional theory and quasiparticle corrections with the GW method, as well as the Bethe-Salpeter Equation, to derive accurate band structures, exciton binding energies, and luminescence energies. Through understanding how the stacking arrangement influences the underlying electronic and optical properties, critical insight will be gained in how to improve 2D III-nitride-based optoelectronics through accessing the additional degree of freedom provided by polarization.   

Optical trap for two-dimensional excitons

For its potential optical controllability as quantum degrees of freedom, the exciton in two-dimensional system has attracted much attentions. In this presentation, we propose an optical trapping technique for the exciton. Exploiting the energy shift mechanism of excitonic system coupled to the electromagnetic field, spatial confinement potential can be implemented. The dimensionality and symmetry of the potential can be dynamically tunable. We performed an ab initio calculation of the excitonic states in graphane, a two-dimensional wide gap semiconductor with D_3d symmetry, based on GW+BSE method by using BerkeleyGW package. The lowest excitonic state belongs to E_u representation, followed by E_g and A_2g excitons of which energy levels are 500meV and 650meV apart from E_u exciton, respectively. Two- and three-level systems can be implemented by coupling these levels with optical fields. We will report the possible depth and polarization dependency of the potential by applying nearly infrared laser light.   

Accurate and approximative many-body methods for optical gap of semiconducting 2D materials

Many-body GW approximation and Bethe-Salpeter equation (BSE) are considered as state-of-the-art methods for reliable prediction of quasiparticle (QP) and optical gaps of bulk materials, respectively. On the other hand, GW and BSE methods are still computationally challenging and its usage for a larger supercell is almost unfeasible. We show which factors are important to obtain accurate QP and optical gaps by GW+BSE approach and we evaluate the magnitudes of such factors [1-3]. We also show that several computationally cheap approximations based on time-dependent DFT can be used as accurate alternative to GW+BSE approach and promising applications on selected vdW heterostructures are demonstrated [3-4].

[1] F. Karlicky, J. Turon, Carbon 135, 134 (2018).
[2] F. Karlicky, M. Otyepka, Ann. Phys. 526, 408 (2014).
[3] M. Kolos, F. Karlicky, Phys. Chem. Chem. Phys. 21, 3999 (2019).
[4] T. Ketolainen, N. Machacova, F. Karlicky, to be submitted (2019).   

Valley Zeeman Effect in 2D Transition Metal Dichalcogenides from First Principles

The Zeeman effect of excitons in two-dimensional transition metal dichalcogenides (TMDs) has attracted much recent attention. A g-factor can be associated with the valley splitting of the band structure in the presence of a weak out-of-plane magnetic field. Experimentalists have measured g-factors of -4 and -16 for excitons in monolayer and twisted bilayer TMDs. Theoretical interpretations of the g-factors have largely focused on monolayer TMDs, relying on a phenomenological model or a k.p model. The phenomenological model assumes that the g-factor is a sum of orbital, spin and valley terms, while the k.p model uses effective masses extracted from tight-binding calculations. Here, we start from the Luttinger-Kohn approximation to treat the magnetic field as a perturbation in a periodic system, and show that the g-factor cannot be written as a sum of only orbital, spin and valley terms. We compute the g-factors for TMD materials using density functional theory (DFT) and include self-energy corrections within many-body perturbation theory (MBPT). Using these results, we comment on the exciton g-factors measured in both monolayer and twisted bilayer TMDs, and show that the MBPT results agree better with experiment than DFT. The effects of spin-orbit coupling are also discussed.