Eur. Phys. J. B 51, 5-15 (2006)
https://doi.org/10.1140/epjb/e2006-00184-y

Cyclic hydrocarbons: nanoscopic (π)-SQUIDs?

¹ Institut für Physik, Johannes Gutenberg-Universität, Staudingerweg 7, 55099,  Mainz, Germany
² Fachbereich Physik, Philipps-Universität Marburg, 35032 Marburg, Germany

Corresponding author: ^a Peter.vanDongen@uni-mainz.de

Received: 21 October 2004
Revised: 13 December 2005
Published online: 31 May 2006

Abstract

A nonperturbative method for calculating persistent currents in molecules and nanoscopic quantum rings is presented. Starting from the extended Hubbard model on a ring threaded by an Aharonov-Bohm flux, a feedback term through which the current can generate magnetic flux is added. Another extension of the Hamiltonian describes the energy stored in the internally generated field. This model is evaluated using exact diagonalization and an iterative scheme to find the minima of the free energy with respect to the current. The magnetic properties due to electron delocalization of conjugated hydrocarbons like benzene [magnetic anisotropy, magnetic susceptibility exaltation, nucleus-independent chemical shift (NICS)] — that have become important criteria for aromaticity — can be examined using this model. A possible novel mechanism for a permanent orbital magnetic moment in quantum rings analogous to the one in π-SQUIDs is found in the framework of the proposed model. The quantum rings must satisfy two conditions to exhibit this kind of permanent orbital magnetic moment: a negative Drude weight and an inductivity above the critical level.