Enhancement of persistent current in mesoscopic rings $&$ cylinders : shortest $&$ next possible shortest higher order hopping

TL;DR

This paper investigates how higher order hopping integrals in the tight-binding model significantly enhance persistent currents in mesoscopic rings and cylinders, with detailed analysis of disorder effects and current sign predictions.

Contribution

It introduces the impact of higher order hopping integrals on persistent current enhancement and provides exact predictions of current sign in disordered rings.

Findings

Higher order hopping integrals lead to an order of magnitude increase in persistent current.

In perfect rings, the current sign can be exactly predicted, showing diamagnetic behavior.

Disordered rings exhibit diamagnetic currents with odd electrons and paramagnetic with even electrons.

Abstract

We present a detailed study of persistent current and low-field magnetic susceptibility in single isolated normal metal mesoscopic rings and cylinders in the tight-binding model with higher order hopping integral in the Hamiltonian. Our exact calculations show that order of magnitude enhancement of persistent current takes place even in presence of disorder if we include higher order hopping integral in the Hamiltonian. In strictly one-channel mesoscopic rings the sign of the low-field currents can be predicted exactly even in presence of impurity. We observe that perfect rings with both odd and even number of electrons support only diamagnetic currents. On the other hand in the disordered rings, irrespective of realization of the disordered configurations of the ring, we always get diamagnetic currents with odd number of electrons and paramagnetic currents with even number of electrons. In mesoscopic cylinders the sign of the low-field currents can't be predicted exactly since it strongly depends on the total number of electrons, $N_e$, and also on the disordered configurations of the system. From the variation of persistent current amplitude with system size for constant electron density, we conclude that the enhancement of persistent current due to additional higher order hopping integrals are visible only in the mesoscopic regime.