Bilayer graphene as an helical quantum Hall ferromagnet

TL;DR

This paper explores how bilayer graphene exhibits complex quantum Hall ferromagnetic states, including Skyrmion crystals and helical phases, driven by electric bias and pseudospin interactions, revealing rich topological textures and excitations.

Contribution

It demonstrates the emergence of helical and Skyrmion crystal states in bilayer graphene under bias, highlighting the role of Dzyaloshinskii-Moriya interactions in pseudospin textures.

Findings

Identification of a transition from interlayer coherence to orbital coherence with increasing bias.

Discovery of a helical pseudospin state induced by Dzyaloshinskii-Moriya interactions.

Analysis of collective excitations and electromagnetic absorption in these states.

Abstract

The two-dimensional electron gas in a bilayer graphene in the Bernal stacking supports a variety of uniform broken-symmetry ground states in Landau level N=0 at integer filling factors $\nu \in [-3,4].$ When an electric potential difference (or bias) is applied between the layers at filling factors $\nu =-1,3$, the ground state evolves from an interlayer coherent state at small bias to a state with orbital coherence at higher bias where \textit{electric} dipoles associated with the orbital pseudospins order spontaneously in the plane of the layers. In this paper, we show that by further increasing the bias at these two filling factors, the two-dimensional electron gas goes first through a Skyrmion crystal state and then into an helical state where the pseudospins rotate in space. The pseudospin textures in both the Skyrmion and helical states are due to the presence of a Dzyaloshinskii-Moriya interaction in the effective pseudospin Hamiltonian when orbital coherence is present in the ground state. We study in detail the electronic structure of the helical and Skyrmion crystal states as well as their collective excitations and then compute their electromagnetic absorption.