Signature of topological transition in persistent current in a Dirac Ring

We study the persistent current in a one dimensional Dirac ring and show that the change of spin current with respect to an applied perpendicular electric field can be used to identify the topological phases. We further study the effect of Rashba spin orbit coupling and show that the Aharonov-Casher phase appearing due to Rashba spin orbit coupling vanishes in topologically nontrivial regime and thus can identify the topological phases. This Aharonov-Casher phase causes a finite spin-valley current in presence of valley mixing perturbation and is thus useful to detect the topological phases even in presence of such impurity.