Magnetic-flux-driven topological quantum phase transition and manipulation of perfect edge states in graphene tube

TL;DR

This paper investigates how magnetic flux induces topological phase transitions in a graphene tube, revealing exact edge states and demonstrating flux-controlled manipulation of quantum states for potential quantum information applications.

Contribution

It provides an exact analysis of topological phases and edge states in a graphene tube model, introducing flux-controlled manipulation of boundary states.

Findings

Topological phases depend on magnetic flux and perimeter length.

Exact zero-energy edge states exist at the boundaries.

Flux can transfer and entangle boundary states.

Abstract

We study the tight-binding model for a graphene tube with perimeter N threaded by a magnetic field. We show exactly that this model has different nontrivial topological phases as the flux changes. The winding number, as an indicator of topological quantum phase transition (QPT) fixes at N/3 if N/3 equals to its integer part [N/3], otherwise it jumps between [N/3] and [N/3]+1 periodically as the flux varies a flux quantum. For an open tube with zigzag boundary condition, exact edge states are obtained. There exist two perfect midgap edge states, in which the particle is completely located at the boundary, even for a tube with finite length. The threading flux can be employed to control the quantum states: transferring the perfect edge state from one end to the other, or generating maximal entanglement between them.