Electronic Raman Scattering in Twistronic Few-Layer Graphene.

A García-Ruiz,M Mucha-Kruczyński,J J P Thompson,V I Fal’Ko

doi:10.1103/physrevlett.125.197401

A García-Ruiz, M Mucha-Kruczyński + Show 2 more

Open Access

https://doi.org/10.1103/physrevlett.125.197401

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Abstract

We study electronic contribution to the Raman scattering signals of two-, three- and four-layer graphene with layers at one of the interfaces twisted by a small angle with respect to each other. We find that the Raman spectra of these systems feature two peaks produced by van Hove singularities in moiré minibands of twistronic graphene, one related to direct hybridization of the Dirac states, and the other resulting from band folding caused by moiré superlattice. The positions of both peaks strongly depend on the twist angle, so that their detection can be used for noninvasive characterization of the twist, even in hBN-encapsulated structures.

Highlights

We study electronic contribution to the Raman scattering signals of two, three- and four-layer graphene with layers at one of the interfaces twisted by a small angle with respect to each other
We find that the Raman spectra of these systems feature two peaks produced by van Hove singularities in moireminibands of twistronic graphene, one related to direct hybridization of the Dirac states, and the other resulting from band folding caused by moiresuperlattice
We study the electronic minibands and electronic contributions to the Raman spectra for few-layer graphene stacks with one of the interfaces between the layers twisted by a small angle, θ < 2°, Fig. 1(a)

Summary

Published by the American Physical Society

[(1 þ 3) and (2 þ 2)] and show that these are formed by transitions from the nth valence to the nth conduction moiresuperlattice (mSL) miniband and feature two spectral peaks. At a lower Raman shift, is caused by the resonant hybridization of electronic states of the two few-layer graphene crystals separated by the twisted interface forming the lowest-energy minibands [51,52]. Another higher-energy peak is due to the anticrossing of bands, backfolded by mSL. We use a hybrid k · p theory-tight-binding model, where we describe electrons’ states in each flake using the k · p expansion around ÆK and ÆK0 Brillouin zone corners of the bottom and anticlockwise rotated (by angle θ) top crystal, respectively [see Fig. 1(b)], and the interlayer hybridization using tunneling Hamiltonian [52,55], H.

Interlayer couplings across the nontwisted interfaces are set using

In the carrying electronic Raman vector potential A