Measuring Phonon Dispersion and Electron-Phason Coupling in Twisted Bilayer Graphene with a Cryogenic Quantum Twisting Microscope

TL;DR

This paper introduces a cryogenic quantum twisting microscope technique to directly measure phonon dispersions and electron-phonon coupling in twisted bilayer graphene, revealing unique mode-dependent coupling behaviors.

Contribution

The work presents a novel method for directly mapping phonon and electron-phonon interactions in van der Waals materials at cryogenic temperatures.

Findings

Measured phonon spectrum and EPC in twisted bilayer graphene.

Discovered increasing EPC with decreasing twist angle for a low energy mode.

Identified a layer-antisymmetric 'phason' mode affecting inter-layer tunnelling.

Abstract

The coupling between electrons and phonons is one of the fundamental interactions in solids, underpinning a wide range of phenomena such as resistivity, heat conductivity, and superconductivity. However, direct measurements of this coupling for individual phonon modes remains a significant challenge. In this work, we introduce a novel technique for mapping phonon dispersions and electron phonon coupling (EPC) in van der Waals materials. By generalizing the quantum twisting microscope to cryogenic temperatures, we demonstrate its capability to map not only electronic dispersions via elastic momentum-conserving tunnelling, but also phononic dispersions through inelastic momentum-conserving tunnelling. Crucially, the inelastic tunnelling strength provides a direct and quantitative measure of the momentum and mode resolved EPC. We use this technique to measure the phonon spectrum and EPC of twisted bilayer graphene (TBG). Surprisingly, we find that unlike standard acoustic phonons, whose coupling to electrons diminishes as their momentum goes to zero, TBG exhibits a low energy mode whose coupling increases with decreasing twist angle. We show that this unusual coupling arises from the modulation of the inter-layer tunnelling by a layer-antisymmetric 'phason' mode of the moir\'e system. The technique demonstrated here opens the way for probing a large variety of other neutral collective modes that couple to electronic tunnelling, including plasmons, magnons and spinons in quantum materials.