Effect of flexural phonons on the hole states in single-layer black phosphorus

TL;DR

This paper provides a theoretical analysis of how flexural phonons influence the hole density-of-states in single-layer black phosphorus, highlighting the anisotropic effects and phonon wavevector contributions.

Contribution

It introduces a quantitative model for the impact of two-phonon flexural processes on hole states, considering anisotropic dispersion and anharmonic phonon behavior.

Findings

Flexural phonons cause an exponential tail in the hole DOS.

Anisotropic dispersion enhances Van Hove singularity effects.

Phonons with wavevectors around q* dominate the physics.

Abstract

Flexural thermal fluctuations in crystalline membranes affect the band structure of the carriers, which leads to an exponential density-of-states (DOS) tail beyond the unperturbed band edge. We present a theoretical description of this tail for a particular case of holes in single-layer black phosphorus, a material which exhibits an extremely anisotropic quasi-one-dimensional dispersion ($m_y/m_x\gg1$) and, as a result, an enhanced Van Hove singularity at the valence band top. The material parameters are determined by {\it ab initio} calculations and then are used for quantitative estimation of the effect of two-phonon (flexural) processes have on the charge carrier DOS. It is shown that unlike the isotropic case, the physics is determined by the phonons with wavevectors of the order of $q^*$, where $q^*$ determines the crossover between harmonic and anharmonic behavior of the flexural phonons. The spectral density of the holes in single-layer black phosphorus at finite temperatures is calculated.