A one-dimensional quantum waveguide theory is developed for a mesoscopic ring subject to the Aharonov–Casher(AC) effect based on the SU (2) spin gauge theory. The quantum interference by the AC effect is found to be equivalent to that by the Aharonov–Bohm(AB) effect. This indicates that AC effect can be utilized for device application in a very similar manner to the AB effect. The transmission probability induced by the AC effect is shown to be identical for the spin up and down components.
A one-dimensional quantum waveguide theory is developed for a mesoscopic ring subject to the Aharonov–Casher(AC) effect based on the SU (2) spin gauge theory. The quantum interference by the AC effect is found to be equivalent to that by the Aharonov–Bohm(AB) effect. This indicates that AC effect can be utilized for device application in a very similar manner to the AB effect. The transmission probability induced by the AC effect is shown to be identical for the spin up and down components.
Quantum interference effects for a mesoscopic loop with three leads are investigated by using a one-dimensional quantum waveguide theory. The transmission and reflection probabilities are analytically obtained in terms of the magnetic flux, arm length, and wave vector. Oscillation of the magnetoconductance is explicitly demonstrated. Magnetoconductance is found to be sharply peaked for certain localized values of flux and kl. In addition, it is noticed that the periodicity of the transmission probability with respect to kl depends more sensitively on the lead position, compared to the case of the two-lead loop.
We briefly review the theoretical formulations and applications of the Aharonov--Bohm effect and the Aharonov--Casher effect with emphasis on mesoscopic physics. Topics relating to the Aharonov--Bohm effect include: locality, periodicity, non-integrable phase factors, Abelian gauge theory, interference, the spectrum and persistent current of electrons on a ring pierced by a magnetic field, Onsager reciprocity relations, and Aharonov--Bohm interferometer. Topics relating to the Aharonov--Casher effect include: a magnetic dipole in an electric field, locality, periodicity, non-Abelian gauge invariance, SU(2) non-integrable phase factors, spin-orbit coupling, Pauli equation, Rashba Hamiltonian, Aharonov--Casher interferometer, conductance and polarization in two-channel systems due to the Aharonov--Casher effect.
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.
We show the existence of a nonadiabatic geometric phase, i.e., an Aharonov-Anandan (AA) phase, in the Aharonov-Casher (AC) topological interference effect in one-dimensional mesoscopic rings. We find the AC phase is the phase accumulated by the spin wave function during a cyclic evolution, and show it is the sum of a geometric AA phase and a dynamical phase. In the adiabatic limit, the AA phase becomes the spin-orbit Berry phase introduced by Aronov and Lyanda-Geller. By solving exactly the model of a quasi-one-dimensional ring formed by the 2DEG on a semiconductor heterostructure, we discuss the observability of the AA phase in the AC effect.
A one-dimensional quantum waveguide theory for mesoscopic structures is proposed, and the boundary conditions of the wave functions at an intersection are given. The Aharonov-Bohm effect is quantitatively discussed with use of this theory, and the reflection, transmission amplitudes, etc., are given as functions of the magnetic flux, the arm lengths, and the wave vector. It is found that the oscillating current consists of a significant component of the second harmonic. This theory is also applied to investigate quantum-interference devices. The results on the Aharonov-Bohm effect and the quantum-interference devices are found to be in agreement with previous theoretical results.
We have studied the quantum transport by nonadiabatic Aharonov-Casher phase in mesoscopic rings embedded in textured electric fields. The quantum transport of the electron is examined based on a one-dimensional quantum waveguide theory. Periodic behaviors of the transmission probability are found in the domain when the quantum phase approaches an adiabatic limit, whereas anomalous quantum transport is shown in the nonadiabatic domain. The difference between the angle of the spin and that of the electric field is found to determine the detailed characteristics of the nonadiabatic quantum phase and transport. The destructive pattern of the transmission probability is found to occur in accordance with the abrupt change of the persistent current in an isolated ring.