Zeeman coupling and screening corrections to skyrmion excitations in graphene

TL;DR

This paper investigates the energies of spin and valley skyrmion excitations in graphene's Landau levels, considering Zeeman coupling and screening effects, and compares theoretical predictions with experimental data.

Contribution

It provides a Hartree-Fock calculation of skyrmion excitation energies in graphene, incorporating screening corrections and analyzing their dependence on Landau level index and filling factors.

Findings

Skyrmion excitation energy is lower than electron-hole pair energy in a finite Zeeman range for |n|=1,2,3.

The Zeeman range for stable skyrmions decreases rapidly with increasing Landau level index.

Screening effects are more significant for valley skyrmions at 3/4 filling than at 1/4 filling.

Abstract

At half filling of the fourfold degenerate Landau levels |n| \geq 1 in graphene, the ground states are spin polarized quantum Hall states that support spin skyrmion excitations for |n| =1,2,3. Working in the Hartree-Fock approximation, we compute the excitation energy of an unbound spin skyrmion-antiskyrmion excitation as a function of the Zeeman coupling strength for these Landau levels. We find for both the bare and screened Coulomb interactions that the spin skyrmion-antiskyrmion excitation energy is lower than the excitation energy of an unbound spin 1/2 electron-hole pair in a finite range of Zeeman coupling in Landau levels |n| =1,2,3. This range decreases rapidly for increasing Landau level index and is extremely small for |n| =3. For valley skyrmions which should be present at 1/4 and 3/4 fillings of the Landau levels |n| =1,2,3, we show that screening corrections are more important in the latter case. It follows that an unbound valley skyrmion-antiskyrmion excitation has lower energy at 3/4 filling than at 1/4. We compare our results with recent experiments on spin and valley skyrmion excitations in graphene.