Ab initio Approach to Collective Excitations in Excitonic Insulators
Abstract
An ab initio approach is presented for studying the collective excitations in excitonic insulators, charge/spin density waves and superconductors. We derive the Bethe-Salpeter-Equation for the particle-hole excitations in the quasiparticle representation, from which the collective excited states are solved and the corresponding order parameter fluctuations are computed. This method is demonstrated numerically for the excitonic insulating phases of the biased WSe2-MoSe2 bilayer. It reveals the gapless phase-mode, the subgap Bardasis-Schrieffer modes and the above-gap scattering states. Our work paves the way for quantitative predictions of excited state phenomena from first-principles calculations in electronic systems with spontaneous symmetry breaking.
Summary
This paper introduces an ab initio approach to study collective excitations in excitonic insulators, charge/spin density waves, and superconductors. The core method involves deriving the Bethe-Salpeter Equation (BSE) for particle-hole excitations in the quasiparticle representation. By solving this equation, the authors compute collective excited states and corresponding order parameter fluctuations. The approach is numerically demonstrated on a biased WSe2-MoSe2 bilayer, revealing the presence of a gapless phase-mode, subgap Bardasis-Schrieffer (BaSh) modes, and above-gap scattering states. The significance of this work lies in providing a first-principles computational framework for investigating excited-state phenomena in electronic systems exhibiting spontaneous symmetry breaking. Previous analytical approaches relied on model Hamiltonians, limiting their applicability to real materials. This research fills this gap by offering a computational formalism compatible with existing first-principles packages, allowing for quantitative predictions of excited-state properties without resorting to Green's function techniques. The method is applicable to a range of systems with spontaneous symmetry breaking, including charge/spin density waves and BCS superconductors.
Key Insights
- •Novelty: The paper presents a new ab initio method for calculating collective excitations in excitonic insulators using the Bethe-Salpeter Equation (BSE) in the quasiparticle representation.
- •Application: The method is successfully applied to a biased WSe2-MoSe2 bilayer, revealing a gapless phase-mode and subgap Bardasis-Schrieffer (BaSh) modes.
- •Optical Activity: The study finds that p-wave BaSh modes are optically active, and the interaction between quasiparticles rearranges the optical spectra weight from continuous above-gap excitations to a single strong peak at the 2p-mode. This optical activity can serve as direct evidence for the presence of excitons.
- •Comparison to TDA: The authors show that the full BSE is necessary to capture collective modes, especially for c1-type excitations, because the particle-hole pair annihilation channel is an important portion of them. The Tamm-Dancoff Approximation (TDA) is a good approximation for c2-type excitations.
- •Limitations: The current approach is based on mean-field plus Gaussian fluctuations and works well for conventional systems in the BCS weak coupling regime. It may not be suitable for systems very close to the critical point or away from the BCS weak coupling regime.
- •Screening: The paper notes that a self-consistent calculation of the dielectric function with high numerical accuracy is needed for more accurate results in the BCS regime.
- •Future work: The authors plan to address the effects of intrinsic interband tunneling and electron-phonon coupling in future works.
Practical Implications
- •Real-world applications: The method can be used to predict the optical responses of materials with excitonic order, aiding in the design of novel optoelectronic devices.
- •Beneficiaries: This research benefits experimentalists searching for EI states by providing concrete guidance for interpreting experimental signatures and designing new experiments.
- •Practitioner use: Practitioners can implement this method in existing first-principles software packages to study excited-state properties in symmetry-broken systems with state-of-the-art accuracy.
- •Future research: The work opens up avenues for future research, including going beyond the instantaneous approximation to the interaction to account for retardation effects and incorporating strong fluctuation methods for materials outside the BCS weak coupling regime.