Quantum Hall ferromagnetic phases in the Landau level N=0 of a graphene bilayer

TL;DR

This paper maps the phase diagram of quantum Hall ferromagnetic states in bilayer graphene's Landau level N=0, exploring how various external parameters influence spin, valley, and orbital orderings and their experimental signatures.

Contribution

It provides a comprehensive analysis of the phase diagram, collective excitations, and optical properties of quantum Hall ferromagnetic states in bilayer graphene at various filling factors.

Findings

Identification of multiple ferromagnetic phases with different coherence properties.

Dependence of transport gap on layer potential difference.

Control of spin polarization via external in-plane electric field.

Abstract

In a Bernal-stacked graphene bilayer, an electronic state in Landau level $% N=0$ is described by its guiding-center index $X$ (in the Landau gauge) and by its valley, spin, and orbital indices $\xi =\pm K,\sigma =\pm 1,$ and $% n=0,1.$ When Coulomb interaction is taken into account, the chiral two-dimensional electron gas (C2DEG) in this system can support a variety of quantum Hall ferromagnetic (QHF)\ ground states where the spins and/or valley pseudospins and/or orbital pseudospins collectively align in space. In this work, we give a comprehensive account of the phase diagram of the C2DEG at integer filling factors $\nu \in [-3,3] $ in Landau level N=0 when an electrical potential difference $\Delta_{B}$ between the two layers is varied. We consider states with or without layer, spin, or orbital coherence. For each phase, we discuss the behavior of the transport gap as a function of $\Delta_{B},$ the spectrum of collective excitations and the optical absorption due to orbital pseudospin-wave modes. We also study the effect of an external in-plane electric field on a coherent state that has both valley and spin coherence and show that it is possible, in such a state, to control the spin polarization by varying the strength of the external in-plane electric field.