Persistent currents in Dirac fermion rings

TL;DR

This paper investigates persistent currents in one-dimensional Dirac fermion rings, analyzing the effects of magnetic and nonmagnetic impurities through continuum and lattice models, and extends findings to finite temperatures.

Contribution

It provides analytical and numerical analysis of impurity effects on persistent currents in Dirac systems, including the impact of temperature and impurity type.

Findings

Persistent current decay matches between continuum and lattice models.

Magnetic impurities cause decay of persistent current in both models.

Nonmagnetic impurities affect the current only in the lattice model.

Abstract

The persistent current in strictly one-dimensional Dirac systems is investigated within two different models, defined in the continuum and on a lattice, respectively. The object of the study is the effect of a single magnetic or nonmagnetic impurity in the two systems. In the continuum Dirac model, an analytical expression for the persistent current flowing along a ring with a single delta-like magnetic impurity is obtained after regularization of the unbounded negative energy states. The predicted decay of the persistent agrees with the lattice simulations. The results are generalized to finite temperatures. To realize a single Dirac massless fermion, the lattice model breaks the time-reversal symmetry, and, in contrast with the continuum model, a pointlike nonmagnetic impurity can lead to a decay in the persistent current.