Accurate prediction of Hall mobilities in two-dimensional materials through gauge-covariant quadrupolar contributions

TL;DR

This paper introduces a gauge-invariant method for calculating electron-phonon interactions in 2D materials, significantly improving the accuracy of mobility predictions by including quadrupolar effects.

Contribution

It develops a general approach incorporating gauge-covariant quadrupolar contributions, enabling precise first-principles calculations of electron-phonon couplings in 2D materials.

Findings

Quadrupolar contributions are crucial for accurate mobility calculations.

Neglecting dynamical quadrupoles causes significant errors in mobility predictions.

The method achieves precise Wannier interpolations for MoS2 monolayers.

Abstract

Despite considerable efforts, accurate computations of electron-phonon and carrier transport properties of low-dimensional materials from first principles have remained elusive. By building on recent advances in the description of long-range electrostatics, we develop a general approach to the calculation of electron-phonon couplings in two-dimensional materials. We show that the nonanalytic behavior of the electron-phonon matrix elements depends on the Wannier gauge, but that a missing Berry connection restores invariance to quadrupolar order. We showcase these contributions in a MoS$_2$ monolayer, calculating intrinsic drift and Hall mobilities with precise Wannier interpolations. We also find that the contributions of dynamical quadrupoles to the scattering potential are essential, and that their neglect leads to errors of 23% and 76% in the room temperature electron and hole Hall mobilities, respectively.