Broken-symmetry $\nu=0$ quantum Hall states in bilayer graphene: Landau level mixing and dynamical screening

TL;DR

This paper investigates the $ u=0$ quantum Hall states in bilayer graphene, revealing how Landau level mixing and dynamical screening influence the phase transition between spin-polarized and layer-polarized states, with results aligning with experiments.

Contribution

It provides a comprehensive analysis including all Landau levels and dynamical screening, offering new insights into the phase transition and energy gaps in bilayer graphene under magnetic fields.

Findings

Two types of $ u=0$ solutions: spin-polarized and layer-polarized.

Critical electric field depends linearly on magnetic field.

Dynamical screening increases energy gaps and level reordering.

Abstract

For bilayer graphene in a magnetic field at the neutral point, we derive and solve a full set of gap equations including all Landau levels and taking into account the dynamically screened Coulomb interaction. There are two types of the solutions for the filling factor $\nu=0$: (i) a spin-polarized type solution, which is the ground state at small values of perpendicular electric field $E_{\perp}$, and (ii) a layer-polarized solution, which is the ground state at large values of $E_{\perp}$. The critical value of $E_{\perp}$ that determines the transition point is a linear function of the magnetic field, i.e., $E_{\perp,{\rm cr}}=E_{\perp}^{\rm off}+a B$, where $E_{\perp}^{\rm off}$ is the offset electric field and $a$ is the slope. The offset electric field and energy gaps substantially increase with the inclusion of dynamical screening compared to the case of static screening. The obtained values for the offset and the energy gaps are comparable with experimental ones. The interaction with dynamical screening can be strong enough for reordering the levels in the quasiparticle spectrum (the $n=2$ Landau level sinks below the $n=0$ and $n=1$ ones).