Solving the Bethe-Salpeter Equation on a Subspace: Approximations and Consequences for Low-dimensional Materials

Abstract

It is well known that the ambient environment can dramatically renormalize the quasiparticle gap and exciton binding energies in low-dimensional materials, but the effect of the environment on the energy splitting of the spin-singlet and spin-triplet exciton states is less understood. A prominent effect is the renormalization of the exciton binding energy and optical strength (and hence the optical spectrum) through additional screening of the direct Coulomb term describing the attractive electron-hole interaction in the kernel of the Bethe-Salpeter equation (BSE). The repulsive exchange interaction responsible for the singlet-triplet slitting, on the other hand, is unscreened within formal many-body perturbation theory. However, Loren Benedict argued that in practical calculations restricted to a subspace of the full Hilbert space, the exchange interaction should be appropriately screened by states outside of the subspace, the so-called $S$ approximation \cite{Benedict2002}. Here, we systematically explore the accuracy of the $S$ approximation for different confined systems, including a molecule and heterostructures of semiconducting and metallic layered materials. We show that the $S$ approximation is actually exact in the limit of small exciton binding energies (i.e., small direct term) and can be used to significantly accelerate convergence of the exciton energies with respect to the number of empty states, provided that a particular effective screening consistent with the conventional Tamm-Dancoff approximation is employed. We further find that the singlet-triplet splitting in the energy of the excitons is largely unaffected by the external dielectric environment for most quasi-two-dimensional materials.

References in corpus (25)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Observation of tightly bound trions in monolayer MoS2
• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer WS2
• Observation of giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor
• Optical Spectrum of MoS${}_2$: Many-body Effects and Diversity of Exciton States
• Probing Excitonic Dark States in Single-layer Tungsten Disulfide
• BerkeleyGW: A Massively Parallel Computer Package for the Calculation of the Quasiparticle and Optical Properties of Materials and Nanostructures
• Excitonic Effects and Optical Spectra of Single-Walled Carbon Nanotubes
• Exciton Binding Energy of Monolayer WS2
• Exciton binding energies in carbon nanotubes from two-photon photoluminescence
• Calculations of Hubbard U from first-principles
• Theory and it ab initio calculation of radiative lifetime of excitons in semiconducting carbon nanotubes
• Nonanalyticity, Valley Quantum Phases, and Light-like Exciton Dispersion in Monolayer TMDs: Theory and First-Principles Calculations
• Coulomb-hole summations and energies for GW calculations with limited number of empty orbitals: a modified static remainder approach
• Electron localization in the insulating state: application to crystalline semiconductors
• Probing the Role of Interlayer Coupling and Coulomb Interactions on Electronic Structure in Few-Layer MoSe2 Nanostructures
• Structural and excited-state properties of oligoacene crystals from first principles
• Efficient many-body calculations of 2D materials using exact limits for the screened potential: Band gaps of MoS${}_2$, hBN, and phosphorene
• Finite temperature quantum embedding theories for correlated systems
• Origins of singlet fission in solid pentacene from an ab initio Green's-function approach
• Optical transitions and nature of Stokes shift in spherical CdS quantum dots
• Electronic and optical gap renormalization in carbon nanotubes near a metallic surface
• Dynamical configuration interaction: Quantum embedding that combines wave functions and Green's functions
• A quantum embedding theory in the screened Coulomb interaction: Combining configuration interaction with GW/BSE

Cited by in corpus (6)

• Many-Body Effects in the X-ray Absorption Spectra of Liquid Water
• Optical Emission from Light-like and Particle-like Excitons in Monolayer Transition Metal Dichalcogenides
• Chiral excitonics in monolayer semiconductors on patterned dielectric
• Exciton absorption, band structure, and optical emission in biased bilayer graphene
• Imaging Nanoscale Carrier, Thermal, and Structural Dynamics with Time-Resolved and Ultrafast Electron Energy-Loss Spectroscopy
• How to choose efficiently the size of the Bethe-Salpeter Equation Hamiltonian for accurate exciton calculations on supercells