Magnetic Breakdown in Twisted Bilayer Graphene

TL;DR

This paper models magnetic breakdown in twisted bilayer graphene using a network of semiclassical trajectories and S-matrices, revealing how Landau levels evolve across saddle points and suggesting experimental signatures.

Contribution

It introduces a network-based semiclassical model with S-matrices to analyze magnetic breakdown and Landau level evolution in twisted bilayer graphene.

Findings

Landau levels evolve from Dirac points into electron- and hole-like levels

The network model predicts specific energy spectrum features

Possible experimental signatures of magnetic breakdown are discussed

Abstract

We consider magnetic breakdown in twisted bilayer graphene where electrons may hop between semiclassical $k$-space trajectories in different layers. These trajectories within a doubled Brillouin zone constitute a network in which an $S$-matrix at each saddle point is used to model tunneling between different layers. Matching of the semiclassical wavefunctions throughout the network determines the energy spectrum. Semiclassical orbits with energies well below that of the saddle points are Landau levels of the Dirac points in each layer. These continuously evolve into {\it both} electron-like and hole-like levels above the saddle point energy. Possible experimental signatures are discussed.