Flux quantization due to monopole and dipole currents

By discussing field-induced quantum interference effects due to monopole moments and those due to dipole moments on equal footing, their similarities and differences are clarified. First, we demonstrate the general principle for flux quantization. For particles carrying a monopole moment, the interference causes the monopole current to oscillate periodically, with the flux defined as the inner product of the field and area, whereas for particles carrying a fixed dipole moment the dipole current oscillates periodically, with the flux vector defined as the cross product of the field and trajectory. Our analysis unifies the oscillation of monopole or dipole currents in various devices, such as the superconducting quantum interference device and spin field-effect transistor, into the same physical picture. Second, we show that interference effects can also happen in open trajectory devices that transport dipole currents, such as the spin Josephson effect, based on the non-gauge-field nature of the interference effects of dipole moments. In addition, we propose that the interference effect of electric dipoles, known as the He-McKellar-Wilkens effect, can be realized by the bilayer exciton condensates observed in semiconductor heterostructures and bilayer graphene.

Figure 1

(a) Generic setup that manifests oscillation of monopole or dipole currents due to AB, DAB, AC, and HMW effects, which consists of $q/q_m/\mu /\mathbf{d}$ in a mesoscopic ring that experiences the field from uniformly distributed $\mu /\mathbf{d}/q/q_m$ on a line pierced through the ring, respectively. (b) Schematics of the open trajectory devices in which AC and HMW effects can take place.

Figure 2

(a) Proposed 2DFMM-2DEG-2DFMM junction as a realization of the open trajectory device sketched in Fig. 1b. Magnetization $\langle {\mathbf{S}}_R\rangle$ and $\langle {\mathbf{S}}_L\rangle$ (blue arrows) yield the Josephson spin current $J_s$ (polarization $\mu \parallel \langle {\mathbf{S}}_R\times {\mathbf{S}}_L\rangle$) described by Eq. (15). The magnetization profile induced at the 2DEG interface (green arrows) gradually rotates from $\langle {\mathbf{S}}_R\rangle$ to $\langle {\mathbf{S}}_L\rangle$. (b) Applying a gate voltage yields a phase shift in the Josephson spin current. The induced magnetization profile (red arrows) changes accordingly, which should be visible as a certain fringe pattern by polarization-sensitive probes.

Figure 3

(a) Proposed dc SQUID-like device that uses the HMW effect to create interference of bilayer exciton condensates. The green and blue sheets indicate the bilayer. The two oppositely placed magnets create a magnetic field that passes the space between the two layers and cause a flux difference in the blue and green trajectories. $\pm I_J$ indicates the counterflow experiment to measure the current. (b) Schematics of the two equivalent descriptions of the exciton condensate, one carrying $+\mathbf{d}$ and the other $-\mathbf{d}$, in a quantum Hall bilayer at ${\nu }_T=1$. The HMW effect causes the two condensates to have opposite Josephson currents, but the net dipole current is the same.