Symmetries in zero and finite center-of-mass momenta excitons

Abstract

We present a symmetry-based framework for the analysis of excitonic states, incorporating both time-reversal and space-group symmetries. We demonstrate the use of time-reversal and space-group symmetries to obtain exciton eigenstates at symmetry-related center-of-mass momenta in the entire Brillouin zone from eigenstates calculated for center-of-mass momenta in the irreducible Brillouin zone. Furthermore, by explicitly calculating the irreducible representations of the little groups, we classify excitons according to their symmetry properties across the Brillouin zone. Using projection operators, we construct symmetry-adapted linear combinations of electron-hole product states, which block diagonalize the Bethe-Salpeter equation (BSE) Hamiltonian at both zero and finite exciton center-of-mass momenta. This enables a transparent organization of excitonic states and provides direct access to their degeneracies, selection rules, and symmetry-protected features. As a demonstration, we apply this formalism to monolayer MoS${}_2$, where the classification of excitonic irreducible representations and the block structure of the BSE Hamiltonian show excellent agreement with compatibility relations derived from group theory. Beyond this material-specific example, the framework offers a general and conceptually rigorous approach to the symmetry classification of excitons, enabling significant reductions in computational cost for optical spectra, exciton-phonon interactions, and excitonic band structure calculations across a wide range of materials.

arXiv comment18 pages, 2 figures, 2 Tables

References in corpus (27)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Atomically thin MoS2: A new direct-gap semiconductor
• Advanced capabilities for materials modelling with Quantum ESPRESSO
• Optimized norm-conserving Vanderbilt pseudopotentials
• Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer WS2
• The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table
• Optical Spectrum of MoS${}_2$: Many-body Effects and Diversity of Exciton States
• Phonons in single and few-layer MoS2 and WS2
• Measurement of the optical dielectric function of transition metal dichalcogenide monolayers: MoS2, MoSe2, WS2 and WSe2
• Yambo: an \textit{ab initio} tool for excited state calculations
• BerkeleyGW: A Massively Parallel Computer Package for the Calculation of the Quasiparticle and Optical Properties of Materials and Nanostructures
• Ab initio calculation of excitonic effects in the optical spectra of semiconductors
• Truncation of Periodic Image Interactions for Confined Systems
• Exciton band structure of monolayer MoS2
• Nonanalyticity, Valley Quantum Phases, and Light-like Exciton Dispersion in Monolayer TMDs: Theory and First-Principles Calculations
• Phonon-assisted optical absorption in silicon from first principles
• Measurement of the Spin-Forbidden Dark Excitons in MoS2 and MoSe2 monolayers
• Exciton-Phonon Interaction and Relaxation Times from First Principles
• Non-uniform sampling schemes of the Brillouin zone for many-electron perturbation-theory calculations in reduced dimensionality
• Excitons in boron nitride single layer
• Newly observed first-order resonant Raman modes in few-layer MoS${}_2$
• Exciton-phonon coupling in the UV absorption and emission spectra of bulk hexagonal boron nitride
• Exciton lifetime and optical linewidth profile via exciton-phonon interactions: Theory and first-principles calculations for monolayer MoS${}_2$
• Fully relativistic $GW$/Bethe-Salpeter calculations in BerkeleyGW: implementation, symmetries, benchmarking, and performance
• Interaction-induced crystalline topology of excitons
• Optical absorption and photoluminescence of single layer boron nitride from a first principles cumulant approach
• Origin of interlayer exciton-phonon coupling in 2D heterostructures