Long wavelength interdomain phonons and instability of dislocations in small-angle twisted bilayers

TL;DR

This paper develops a theory for long wavelength interdomain phonons in small-angle twisted bilayers of 2D materials, revealing instabilities in dislocation spectra and potential stabilization mechanisms, with implications for experimental detection.

Contribution

It introduces a novel theoretical framework for interdomain phonons in twisted bilayers, analyzing dislocation-induced phonon spectra and their stability, which was not previously understood.

Findings

Gapless phonon subband exhibits imaginary frequencies indicating instability.

Gapped subbands are detectable via optical and magnetotransport techniques.

Dislocation orientation affects the critical wave-number for phonon instability.

Abstract

We develop a theory for long wavelength phonons originating at dislocations separating domains in small-angle twisted homobilayers of 2D materials such as graphene and MX$_2$ transition metal dichalcogenides (M=Mo,W; X=S,Se). We find that both partial and perfect dislocations, forming due to lattice relaxation in the twisted bilayers with parallel and anti-parallel alignment of unit cells of the constituent layers, respectively, support several one-dimensional subbands of the {\it interdomain} phonons. We show that spectrum of the lowest gapless subband is characterized by imaginary frequencies, for wave-numbers below a critical value, dependent on the dislocation orientation, which indicates an instability for long enough straight partial and perfect dislocations. We argue that pinning potential and/or small deformations of the dislocations could stabilize the gapless phonon spectra. The other subbands are gapped, with subband bottoms lying below the frequency of interlayer shear mode in domains, which facilitates their detection with the help of optical and magnetotransport techniques.