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Physica E Low-dimensional Systems and Nanostructures

Persistent current and the existence of a metallic phase flanked by two insulating phases in a quantum ring with both electron–electron and electron–phonon interactions

I. V. Sankar, P. J. Monisha, Shreekantha Sil, Ashok Chatterjee

Published May 29, 2015• 3 citations
Publisher
DOI
10.1016/j.physe.2015.05.029

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We present an exact calculation of the persistent current in interacting disordered 1D rings. This system exhibits a variety of interesting behaviors depending on the disorder and the strength of electron-electron interactions. We find that even for the disordered case the current at high values of interactions is strongly suppressed due to the Mott-Hubbard metal-insulator transition. We observe that no dramatic increase of the averaged current or its rms value as a result of interactions is possible for these systems.

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A perturbative approach for large (in comparison with electron overlap and onsite disorder) long-range Coulomb interaction is developed for a 1D ring model. The explicit expression for low-lying energy levels has been obtained. It is shown that in the case of strong repulsive long-range interaction persistent current does not depend exclusively on the filling factor nu =p/q but is extremely sensitive to its denominator q. It also depends on the common factor M of electrons and sites number. In the absence of a common factor (M=1) there exists only one quasiparticle that experiences no strong Coulomb interaction, thus moving freely with bare electron overlap, which provides an unexpectedly large persistent current. For the case of an arbitrary M and a large enough q a system of M weakly interacting quasiparticles has been introduced, which undergoes a metal-insulator transition at unusually small overlap even for a filling factor close to one half. Suppression of the persistent current by disorder is taken into account. Comparison of analytically obtained expressions with the results of numerical calculations shows a reasonable agreement.
Persistent current is a small but perpetual electric current that flows in metallic rings in the absence of any applied source. We compute the persistent currents of one-dimensional disordered metallic rings of interacting electrons in the presence of impurity on lattices up to 8-sites at half-filling and also away from half-filling using the Lanczos algorithm. For the case of half-filling, we observe that both interaction and disorder suppress the amplitude of the persistent currents by localizing the electrons. However, in the presence of disorder and away from half-filling, the Coulomb interaction is observed to enhance the persistent current. Furthermore, in the half-filled case, there is a transition from metal to insulator as U is increased significantly. In addition, shifting away from half-filling, the system is observed to remain in the metallic state irrespective of the value of the Coulomb repulsion (U). The observations are quite in agreement with the results from other techniques.
We present an exact calculation of the persistent current in interacting disordered 1D rings. This system exhibits a variety of interesting behaviors depending on the disorder and the strength of electron-electron interactions. We find that even for the disordered case the current at high values of interactions is strongly suppressed due to the Mott-Hubbard metal-insulator transition. We observe that no dramatic increase of the averaged current or its rms value as a result of interactions is possible for these systems.