Theory of phonon spectroscopy with the quantum twisting microscope

TL;DR

This paper develops a theoretical framework for using the quantum twisting microscope to probe phonon modes and electron-phonon interactions in van-der-Waals materials, especially graphene, through inelastic tunneling measurements.

Contribution

It introduces a systematic theory linking tunneling current features to phonon dispersions and electron-phonon coupling strengths in twisted bilayer graphene.

Findings

Tunneling current reveals phonon dispersions along specific reciprocal space lines.

Electron-phonon coupling strengths can be extracted from tunneling data.

Dominant inelastic processes depend on the phonon mode considered.

Abstract

We develop a theory of probing phonon modes of van-der-Waals materials using the quantum twisting microscope. While elastic tunneling dominates the tunneling current at small twist angles, the momentum mismatch between the K-points of tip and sample at large twist angles can only be bridged by inelastic scattering. This allows for probing phonon dispersions along certain lines in reciprocal space by measuring the tunneling current as a function of twist angle and bias voltage. We illustrate this modality of the quantum twisting microscope by developing a systematic theory for graphene-graphene junctions. We show that beyond phonon dispersions, the tunneling current also encodes the strength of electron-phonon couplings. Extracting the coupling strengths for individual phonon modes requires careful consideration of various inelastic tunneling processes. These processes are associated with the intralayer and interlayer electron-phonon couplings and appear at different orders in a perturbative calculation of the tunneling current. We find that the dominant process depends on the particular phonon mode under consideration. Our results inform the quest to understand the origin of superconductivity in twisted bilayer graphene and provide a case study for quantum-twisting-microscope investigations of collective modes.