Orbital and interlayer Skyrmions crystals in bilayer graphene

TL;DR

This paper explores the formation and control of orbital and interlayer Skyrmion crystal phases in bilayer graphene under magnetic fields and electric gating, revealing their topological properties and experimental signatures.

Contribution

It introduces the concept of electrically controllable orbital Skyrmion crystals in bilayer graphene and analyzes their properties and experimental detection methods.

Findings

Orbital Skyrmions exhibit electric dipole textures controllable by in-plane electric fields.

Skyrme crystal phases show modulated electronic densities detectable via local density of states measurements.

Electric fields influence the stability and structure of Skyrmion crystal phases.

Abstract

A graphene bilayer in a transverse magnetic field has a set of Landau levels with energies $E=\pm \sqrt{N(N+1)}\hslash \omega_{c}^{\ast}$ where $\omega_{c}^{\ast}$ is the effective cyclotron frequency and $% N=0,1,2,...$ All Landau levels but N=0 are four times degenerate counting spin and valley degrees of freedom. The Landau level N=0 has an extra degeneracy due to the fact that orbitals $n=0$ and $n=1$ both have zero kinetic energies. At integer filling factors, Coulomb interactions produce a set of broken-symmetry states with partial or full alignement in space of the valley and orbital pseudospins. These quantum Hall pseudo-ferromagnetic states support topological charged excitations in the form of orbital and valley Skyrmions. Away from integer fillings, these topological excitations can condense to form a rich variety of Skyrme crystals with interesting properties. We study in this paper different crystal phases that occur when an electric field is applied between the layers. We show that orbital Skyrmions, in analogy with spin Skyrmions, have a texture of electrical dipoles that can be controlled by an in-plane electric field. Moreover, the modulation of electronic density in the crystalline phases are experimentally accessible through a measurement of their local density of states