Possible Broken Inversion and Time-Reversal Symmetry State of Electrons in Bilayer Graphene

TL;DR

This paper investigates a novel symmetry-broken state in bilayer graphene, revealing a gapped ground state whose energy gap increases with magnetic field, aligning with experimental findings and explaining the Landau level disappearance.

Contribution

It provides an analytical solution to the mean-field Hamiltonian for bilayer graphene, demonstrating the behavior of the energy gap under magnetic fields and resolving previous experimental puzzles.

Findings

The ground state in bilayer graphene is gapped.

The energy gap increases with magnetic field B.

Disappearance of Landau levels explains gap behavior.

Abstract

With the two-band continuum model, we study the broken inversion and time-reversal symmetry state of electrons with finite-range repulsive interactions in bilayer graphene. With the analytical solution to the mean-field Hamiltonian, we obtain the electronic spectra. The ground state is gapped. In the presence of the magnetic field $B$, the energy gap grows with increasing $B$, in excellently agreement with the experimental observation. Such an energy gap behavior originates from the disappearance of a Landau level of $n$ = 0 and 1 states. The present result resolves explicitly the puzzle of the gap dependence of $B$.