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arXiv:cond-mat/9309012 · Physical review. B, Condensed matter

Persistent currents in mesoscopic Hubbard rings with spin-orbit interaction

Satoshi Fujimoto, Norio Kawakami

Published Dec 15, 1993• 44 citations
arXivHTMLPDF

Abstract

The effect of spin-orbit interaction on persistent currents in mesoscopic Hubbard rings threaded by an Aharonov-Bohm flux is investigated, with attention focused on orbital magnetism. The nonperturbative treatment of the spin-orbit interaction developed by Meir et al. is combined with the Bethe ansatz solution in order to deal with this problem exactly. We find that the interplay of spin-orbit interaction and electron-electron interaction plays a crucial role, bringing about some remarkable effects on orbital magnetism.

DOI
10.1103/physrevb.48.17406

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The effect of spin-orbit interaction on persistent currents in mesoscopic Hubbard rings threaded by an Aharonov-Bohm flux is investigated, with attention focused on orbital magnetism. The nonperturbative treatment of the spin-orbit interaction developed by Meir et al. is combined with the Bethe ansatz solution in order to deal with this problem exactly. We find that the interplay of spin-orbit interaction and electron-electron interaction plays a crucial role, bringing about some remarkable effects on orbital magnetism.
Abstract We study the persistent current in a chain of two coupled quantum rings threaded by an Aharonov-Bohm flux in the presence of electron-phonon and Rashba spin-orbit interactions. In the framework of the Holstein-Hubbard model, the equations for ground state energy, persistent current and Drude weight were derived. Obtaining of the expression for the ground state energy allowed us to obtain the persistent current by a conventional way (differentiating). The influence of the magnetic flux and the Rashba spin-orbit interaction on the ground state energy, persistent current and Drude weight was studied numerically.
Persistent currents flowing through disordered mesoscopic rings threaded by a magnetic flux are investigated. Models of fermions with on-site interactions (Hubbard model) or models of spinless fermions with nearest neighbor interactions are considered on 2D cylinders with twisted boundary conditions in one direction to account for a magnetic flux. Self-consistent Hartree-Fock methods are used to treat the electron-electron interaction beyond first order. We show that the second harmonic of the current (which is relevant in the diffusive regime) is strongly suppressed by the interaction in the case of spinless fermions while it is significantly enhanced in the Hubbard model. Our data also strongly suggest that the reduction (increase) of this harmonic is related to a strong increase (reduction) of the spatial fluctuations of the charge density.
The quantum orbital motion of electrons in mesoscopic normal-metal rings threaded by a magnetic flux produces striking interference phenomena such as persistent currents due to the Aharonov-Bohm effect. Similarly, when a quantum spin adiabatically follows a magnetic field that rotates slowly in time, the phase of its state vector acquires an additional contribution known as the Berry phase. We explore the combination of these two quantum phenomena by examining the interplay between orbital and spin degrees of freedom for a charged spin-1/2 particle moving in a mesoscopic ring embedded in a classical, static inhomogeneous magnetic field, i.e, a texture. As a consequence of its orbital motion through the texture, the spin experiences, via the Zeeman interaction, a varying magnetic field. This results in a Berry---or geometric---phase, leading to persistent (i.e., equilibrium) currents of charge and spin. These mesoscopic phenomena are related to (but should be distinguished from) the conventional persistent currents that result from magnetic flux through a ring. We develop a path-integral approach to decouple the orbital and spin motion and, by using an adiabatic approximation, we compute the equilibrium expectation values of the persistent charge and spin currents and the magnetization. We find that the persistent currents depend on the texture in a striking manner through a geometric phase (related to a surface area characterizing the texture) and a geometric vector (related to the projections of this area). In the special case of a cylindrically symmetric texture we use a spectrum obtained by Kuratsuji and Iida to obtain exact results that confirm, independently, the validity of the path-integral approach in the adiabatic limit. We discuss the connection between the geometric vector and quantum-mechanical correlations, and examine quantum fluctuations and the zero-point energy.
We study the effects of correlations on a one-dimensional ring threaded by a uniform magnetic flux. In order to describe the interaction between particles, we work in the framework of the Hubbard model and the t - and t - - models. We focus on the dilute limit. Our results suggest the possibility that the persistent current has an anomalous periodicity , where p is an integer in the range ( is the number of particles in the ring and is the flux quantum). We find that this result depends neither on disorder nor on the detailed form of the interaction, while there is still on-site infinite repulsion.
Persistent currents flowing through disordered mesoscopic rings threaded by a magnetic flux are investigated. Models of fermions with on-site interactions (Hubbard model) or models of spinless fermions with nearest neighbor interactions are considered on 2D cylinders with twisted boundary conditions in one direction to account for a magnetic flux. Self-consistent Hartree-Fock methods are used to treat the electron-electron interaction beyond first order. We show that the second harmonic of the current (which is relevant in the diffusive regime) is {\it strongly suppressed} by the interaction in the case of spinless fermions while it is {\it significantly enhanced} in the Hubbard model. Our data also strongly suggest that the reduction (increase) of this harmonic is related to a strong increase (reduction) of the spacial fluctuations of the charge density.