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Low Temperature Physics

Magnetic and electrostatic Aharonov–Bohm effects in a pure mesoscopic ring

Michael V. Moskalets

Published Apr 1, 1997• 3 citations
Publisher

Abstract

The effect of weak scalar potential on a persistent current in a one-dimensional ballistic ring is considered. It is shown that the current amplitude oscillates with a change in the potential.
DOI
10.1063/1.593401

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Physical review. B, Condensed matter•Oct 15, 1995•8 citations
Based upon a tight-binding model Hamiltonian and by applying the Jordan-Wigner transformation, the Aharonov-Bohm (AB) effect for charged hard-core bosons in one-dimensional (1D) mesoscopic rings is investigated for the first time. By introducing a specific unitary transformation, the energy spectrum and the persistent charge current are analytically derived for ID perfect lattices. Similar to electron systems, it has been found that the energy and persistent current are periodic in AB flux with the period Φ0=hc/q. More interestingly, we have exactly shown that, in the absence of the external AB flux, the charge current can be self-sustained via the AB effect, which is in fact the ground state of the system regardless of the number of hard-core bosons being even or odd.
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.
Charge persistent currents in single-channel ballistic rings are investigated in various models of strongly correlated electrons (Wigner crystal, Luttinger liquid, Hubbard model, t–J model, and the fermion representation of the Heisenberg–Ising model). The primary objective of the survey is to compare the properties of Aharonov–Bohm oscillations for weakly and strongly correlated electrons and to formulate a set of persistent current characteristics that will unambiguously support the anomalous (departing from a Fermi liquid) behavior of one-dimensional electron systems. For this purpose the onset of the parity effect (dependence of the system response on whether the number of particles in the ring is odd or even) and various properties of the persistent current are analyzed in detail for model spinless fermions and real electrons. The influence of solitary impurities on the value and temperature dependence of the amplitude of the Aharanov–Bohm oscillations is also investigated. It is shown that the formation of a Wigner crystal (which is possible for weakly shielded Coulomb interaction) leads to a very pronounced anomalous (nonmonotonic) temperature dependence of the current in a nonideal ring. The properties of the charge current near the Mott metal–insulator transition are altered to the greatest degree by local types of electron–electron interaction.
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.
The Aharonov-Bohm oscillations in the transmission probability of a one-dimensional mesoscopic ring between two electrodes are considered numerically where a time-periodical flux \ensuremath{\gamma}(t)=\ensuremath{\gamma}+\ensuremath{\lambda} cos\ensuremath{\omega}t is applied. Such a flux simulates a phase-coherent inelastic scattering due to the absorption/emission processes of modulation quanta. An increase of alternating flux amplitude \ensuremath{\lambda} drastically changes the Aharonov-Bohm oscillations of the transmission though the exact period remains ${\mathrm{\ensuremath{\varphi}}}_{0}$=hc/e. A frequency dependence of the transmission has abrupt steps at \ensuremath{\omega}=(E-EF{\mathit{E}}_{\mathit{F}}EF​)/n, caused by the locking of the transmission in the nth channel where EF{\mathit{E}}_{\mathit{F}}EF​ is the Fermi level. Moreover, for transmission of a narrow wave packet the time-periodical flux gives rise to two effects. The first is a fractioning of the input wave packet by the ring in such a way that the output wave function consists of a few separate wave packets. Their number, distance apart, and height essentially depend on the static flux \ensuremath{\gamma}. The second effect is a strong space squeezing of the output wave packet.