Persistent currents in mesoscopic rings and conformal invariance

TL;DR

This paper investigates how point defects and aperiodic modulations affect persistent currents in mesoscopic rings, employing conformal invariance techniques to derive exact flux dependence and compare different sequences.

Contribution

It introduces a novel application of conformal invariance to relate persistent current amplitude to the Hamiltonian spectrum in defective mesoscopic rings.

Findings

Current amplitude depends on defect number and type.

Flux dependence varies significantly with Fibonacci and Thue-Morse sequences.

Exact solutions for rings with one or two point defects are provided.

Abstract

The effect of point defects on persistent currents in mesoscopic systems is studied in a simple tight-binding model. Using an analogy with the treatment of the critical quantum Ising chain with defects, conformal invariance techniques are employed to relate the persitent current amplitude to the Hamiltonian spectrum jsut above the Fermi energy. From this, the dependence of the current on the magnetic flux is found exactly for a ring with one or two point defects. The effect of an aperiodic modulation of the ring, generated through a binary substitution sequence, on the persistent current is also studied. The flux-dependence of the current is found to vary remarkably between the Fibonacci and the Thue-Morse sequences.