Eur. Phys. J. B 5, 787-792 (1998)
https://doi.org/10.1007/s100510050503

Persistent currents in mesoscopic rings and conformal invariance^*

Laboratoire de Physique des Matériaux (Unité Mixte de Recherche CNRS No. 7556) , Université Henri Poincaré Nancy I, BP 239, 54506 Vandœuvre-lès-Nancy Cedex, France

Corresponding author: ^a henkel@lps.u-nancy.fr

Received: 4 March 1998
Revised: 20 April 1998
Accepted: 30 April 1998
Published online: 15 October 1998

Abstract

The effect of point defects on persistent currents in mesoscopic rings 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 persistent current amplitude to the Hamiltonian spectrum just 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.