Persistent charge and spin currents due to Aharonov - Bohm and Aharonov - Casher interferences of correlated electrons moving along a mesoscopic ring are discussed at finite temperature. As a function of applied flux the ground-state persistent currents have the shape of a generalized saw-tooth, i.e. they consist of piecewise straight segments. The periods and amplitudes of the oscillations are associated with the properties of the Fermi surface of the elementary excitations (two Dirac seas), namely the group velocities and the matrix of dressed generalized charges (Luttinger parameters). The temperature reduces the amplitudes of oscillation by smearing the Fermi surface in a similar way to that for the de Haas - van Alphen effect in 3D metals. The amplitude of higher harmonics decreases more quickly with T than the fundamental one, changing the saw-tooth to a more sinusoidal form with much smaller amplitude. The controlling parameters are the ratios of the thermal energy to the level spacings in the ring. The results are discussed in the context of the exact Bethe ansatz solutions for the Hubbard chain and the supersymmetric t - J model.
Persistent charge and spin currents due to Aharonov - Bohm and Aharonov - Casher interferences of correlated electrons moving along a mesoscopic ring are discussed at finite temperature. As a function of applied flux the ground-state persistent currents have the shape of a generalized saw-tooth, i.e. they consist of piecewise straight segments. The periods and amplitudes of the oscillations are associated with the properties of the Fermi surface of the elementary excitations (two Dirac seas), namely the group velocities and the matrix of dressed generalized charges (Luttinger parameters). The temperature reduces the amplitudes of oscillation by smearing the Fermi surface in a similar way to that for the de Haas - van Alphen effect in 3D metals. The amplitude of higher harmonics decreases more quickly with T than the fundamental one, changing the saw-tooth to a more sinusoidal form with much smaller amplitude. The controlling parameters are the ratios of the thermal energy to the level spacings in the ring. The results are discussed in the context of the exact Bethe ansatz solutions for the Hubbard chain and the supersymmetric t - J model.
The Aharonov-Casher effect is a quantum interference arising in mesoscopic rings involving particles with magnetic moments. The wave function acquires a phase due to an electric-field flux F enclosed by the ring and gives rise to flux-dependent oscillations in persistent spin currents. In the ground state of the spin-1/2 Heisenberg chain the period and amplitude of the oscillations are associated with the properties of the Fermi surface of the elementary excitations of the spin chain (spinons). We consider an antiferromagnetic spin-1/2 Heisenberg ring with a concentration x of impurity spins S. The calculations are performed within the framework of Bethe's ansatz. Due to the finite concentration of impurities the ground state consists of two (rather than one) Dirac seas, corresponding to spinons and 2S strings of rapidities. The persistent spin current reveals two periods of oscillation associated with the properties of the two Fermi seas. The interference pattern as a function of F is discussed for several external magnetic fields.
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.
One-dimensional conductors are a long-standing topic of research with direct applications to organic conductors and mesoscopic rings. The discovery of the ceramic high-temperature superconductors has revitalized the interest in low-dimensional charge and spin fluctuations of highly correlated electron systems. Several mechanisms proposed to explain the high-T c superconductors invoke properties of the two-dimensional Hubbard model, but probably also some one-dimensional aspects are relevant. Numerous one-dimensional models for correlated electrons have been studied with various approximate, asymptotically exact and exact methods. These results lead to the concept of Luttinger liquid for interacting electron gases without excitation gaps (metallic systems). Characteristic of Luttinger liquids are the charge and spin separation, marginal Fermi liquid properties, e.g. the absence of quasiparticles in the vicinity of the Fermi surface, nonuniversal power-law singularities in the one-particle spectral function and the related absence of a discontinuity in the momentum distribution at the Fermi level, the power-law decay of correlation functions for long times and large distances, persistent currents in finite rings, etc. Due to the peculiarities of the phase space in one dimension some of the models have sufficient conserved currents to be completely integrable. We review exact results derived within the framework of Bethe's ansatz for integrable one-dimensional models of correlated electrons. The Bethe-ansatz method is presented by explicitly showing the steps leading to the solution of the N-component electron gas interacting via a δ-function potential (repulsive and attractive interaction), which is probably the simplest model of correlated electrons. Emphasis is given to the procedure to extract the groundstate properties, the classification of states, the excitation spectrum, the thermodynamics and finite size effects, such as critical exponents of correlation functions and persistent currents. The method is then applied to numerous other models, e.g. (i) a two-band model involving attractive and repulsive potentials and crystalline fields splitting the bands, (ii) the traditional Hubbard chain with attractive and repulsive U, (iii) the degenerate Hubbard model with repulsive U, which displays a metal–insulator transition at a finite U, (iv) a two-band Hubbard model with repulsive U, (v) the traditional supersymmetric t–J model (vi) a two-band supersymmetric t–J model with band-splitting and (vii) the N-component supersymmetric t–J model. Finally, results for models with long-range interactions, in particular r-2 and sinh -2(r) potentials, are briefly reviewed.
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 investigate anomalous oscillations due to the Aharonov-Bohm(AB) and Aharonov-Casher(AC) effects of the one-dimensional Hubbard ring with flux in the strong coupling limit. By using the exact diagonalization method and the Shiba transformation, we examine the energies of the ground state and few excited states in the presence of the flux producing the AB or AC effect, where the transformation not only reverses the sign of the interaction U, but also exchanges the role between the AB and AC effects in the model Hamiltonian. We classify the number of oscillation of the ground state as a function of the flux systematically and clarify the close relationship between the AB and AC effects. For example, it is shown that the number of the periods are given by N_L - N_e(N_L - N_↑ + N_↓) for the AB(AC) effect in the very strong attraction, where N_L, N_e, N_↑, and N_↓ are the system size, the number of the total electrons, the number of electrons with up-spin, and the number of electrons with down-spin, respectively, in the condition of N_L > N_e > N_↓ > N_↑. More special case, such as the half-filled band and spin balanced case (N_L = N_e and N_↓ = N_↑ ), we find the periodicity of the system to be 0(2) for the AB(AC) effect in the very strong repulsion. These results show us the nature of interesting phenomena originated by the interplay between the strong correlation and the quantum interference effect in the mesoscopic ring.
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.