Charge $2e$ Skyrmions in Bilayer Graphene

Quantum Hall states that result from interaction induced lifting of the eightfold degeneracy of the zeroth Landau level in bilayer graphene are considered. We show that at even filling factors electric charge is injected into the system in the form of charge $2e$ Skyrmions. This is a rare example of binding of charges in a system with purely repulsive interactions. We calculate the Skyrmion energy and size as a function of the effective Zeeman interaction and discuss the signatures of the charge $2e$ Skyrmions in the scanning probe experiments.

Figure 1

(a) Bilayer graphene lattice. Perpendicular electric field $E$ generates effective valley Zeeman interaction ${\Delta }_v=eEd$, where $d=0.34\mathrm{nm}$ is the separation between the layers. (b) The order of the zeroth LL splitting, assuming that effective valley Zeeman interaction ${\Delta }_v$ favors $K$ valley states and ${\Delta }_v<E_z$. (c) Texture corresponding to the charge $2e$ Skyrmion at $\nu =\pm 2$. Vectors illustrate the rotation of the order parameter in the valley space.