Aharonov–Bohm effect in one-dimensional systems

Kazuhiro Sano, Yoshiaki Ōno

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.

Donald H. Kobe

Jian‐Xin Zhu, Z. D. Wang

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.

De‐Hone Lin

Van-Hoang Le, Ly Xuan Hai, L I Komarov +1 more

The authors establish the exact solution of the Dirac equation for a charged particle moving in the Coulomb field plus Aharonov-Bohm field plus Dirac monopole field by using the equation in two-dimensional complex space. On the basis of the found solution, the relativistic analogy of the Aharonov-Bohm effect for the system of a diogen atom existing in an infinite cylindrical solenoid is studied. In this case the authors obtain some surprising results. One of them is that the Aharonov-Bohm effect is absent for certain states.

Ghislain Golse, Hamza Jirari, H. Kröger +1 more