Energy Spectrum and Quantum Hall Effect in Twisted Bilayer Graphene

TL;DR

This paper explores the evolution of electronic spectra and quantum Hall effects in twisted bilayer graphene under magnetic fields, revealing transitions from Landau levels to fractal Hofstadter butterfly patterns.

Contribution

It provides a comprehensive model including interlayer interactions to describe spectral evolution and Hall conductivity in twisted bilayer graphene across various magnetic field regimes.

Findings

Landau levels in weak fields reflect Fermi surface topology change.

Hall conductivity sharply drops at the electron-hole transition.

Fractal Hofstadter spectrum emerges at high magnetic fields, especially in small rotation angles.

Abstract

We investigate the electronic spectra and quantum Hall effect in twisted bilayer graphenes with various rotation angles under magnetic fields, using a model rigorously including the interlayer interaction. We describe the spectral evolution from discrete Landau levels in the weak field regime to the fractal band structure in the strong field regime, and estimate the quantized Hall conductivity for each single gap. In weak magnetic fields, the low-energy conduction band of the twisted bilayer is quantized into electron-like Landau levels and hole-like Landau levels above and below the van Hove singularity, respectively, reflecting a topological change of the Fermi surface between electron pocket and hole pocket. Accordingly the Hall conductivity exhibits a sharp drop from positive to negative at the transition point. In increasing magnetic field, the spectrum gradually evolves into fractal band structure so-called Hofstadter's butterfly, where the Hall conductivity exhibits a nonmonotonic behavior varying from a minigap to a minigap. The magnetic field strength required to invoke the fractal band structure is more feasible in smaller rotating angle.