Topological qubits in graphenelike systems

TL;DR

This paper explores how topological charges in graphene-like systems influence the existence of Majorana zero modes, addressing the fermion-doubling problem and proposing methods to manipulate topological states for quantum computing.

Contribution

It introduces a Z_2 x Z_2 topological charge framework for 2D fermionic models, linking fermion doubling, Chern number parity, and Majorana modes in graphene-like materials.

Findings

Topological charge determines Majorana zero mode count.

Graphene can host up to ten order parameters affecting topology.

Methods to switch topological states from even to odd parity.

Abstract

The fermion-doubling problem can be an obstacle to getting half-a-qubit in two-dimensional fermionic tight-binding models in the form of Majorana zero modes bound to the core of superconducting vortices. We argue that the number of such Majorana zero modes is determined by a Z_2 x Z_2 topological charge for a family of two-dimensional fermionic tight-binding models ranging from noncentrosymmetric materials to graphene. This charge depends on the dimension of the representation (i.e., the number of species of Dirac fermions -- where the doubling problem enters) and the parity of the Chern number induced by breaking time-reversal symmetry. We show that in graphene there are as many as ten order parameters that can be used in groups of four to change the topological number from even to odd.