Skyrme crystal in bilayer and multilayer graphene

TL;DR

This paper investigates the ground states of bilayer and multilayer graphene under strong magnetic fields, revealing the formation of Skyrme crystals with unique properties due to localized wave functions.

Contribution

It introduces the phase diagram of charge density wave states, including Skyrme crystals, in multilayer graphene systems using Hartree-Fock approximation.

Findings

Skyrme crystals are energetically favorable in the first excited Landau level.

Localized wave functions lead to low-energy Skyrme crystals up to four layers.

Bubble crystals are suppressed in multilayer graphene, altering the phase diagram.

Abstract

The ground state of the two-dimensional electron systems in Bernal bilayer and ABC-stacked multilayer graphenes in the presence of a strong magnetic field is investigated with the Hartree-Fock approximation. Phase diagrams of the systems are obtained, focusing on charge density wave states including states with vortices of valley pseudospins (called a Skyrme crystal). The single-electron states in these stacked graphenes are given by two-component wave functions. That of the first excited Landau level has the same component as the lowest Landau level of the ordinary two-dimensional electrons. Because of this localized wave functions, the Skyrme crystal has low energy in this first excited level up to four layers of graphene, when the inter-layer distance is assumed to be infinitesimal. At the same time, bubble crystals are suppressed, so the phase diagram is different from that of a single-layer graphene.