Topological insulator in the core of the superconducting vortex in graphene

TL;DR

This paper explores the emergence of topological insulator states within the vortex cores of superconducting graphene, revealing universal behaviors and proposing experimental methods to observe competing orders.

Contribution

It introduces a universal framework for the order parameters in vortex cores of superconducting graphene and discusses the effects of Zeeman coupling on core states.

Findings

Zeeman coupling favors anomalous quantum Hall state in vortex cores

Universal algebraic structure of order parameters in vortex cores

Proposed experimental detection of competing orders

Abstract

The core of the vortex in a general superconducting order parameter in graphene is argued to be ordered, with the possible order parameters forming the algebra U(1) X Cl(3), where Cl(3) is the three dimensional Clifford algebra. A sufficiently strong Zeeman coupling of the magnetic field of the vortex to the electron spin breaks the degeneracy in the core in favor of the anomalous quantum Hall state. I consider a variety of superconducting condensates on the honeycomb lattice and demonstrate the surprising universality of this result. A way to experimentally determine the outcome of the possible competition between different types of orders in the core is proposed.