Arbitrary mixture of two charged interacting particles in a magnetic Aharonov-Bohm ring: persistent currents and Berry's phases

TL;DR

This paper provides an exact analytical study of two interacting charged particles in an Aharonov-Bohm ring, revealing how flux, interactions, and topology influence persistent currents and Berry's phases in a nanoscopic quantum system.

Contribution

It introduces a solvable model for two charged particles in a magnetic ring, deriving explicit expressions for spectra, currents, and Berry's phases, highlighting their universal relationships and the role of particle distinguishability.

Findings

Analytical expressions for energy spectra and wavefunctions are derived.

Persistent currents and Berry's phases are shown to be universally linked.

The charge mixture nature is crucial for the observed universal behaviors.

Abstract

Aharonov-Bohm Physics at the two-particle level is investigated for distinguishable interacting charged particles through the exact solution of a toy model with confined states. The effect of the inaccessible magnetic flux is distributed between the center-of-mass and the internal pair level, and the nontrivial manner in which the two levels are mutually affecting each other demonstrates the interplay between interactions, nontrivial topology, the Aharonov-Bohm flux and the characteristics of a charged quantal mixture. Analytical expressions for energy spectra, wavefunctions, (flux-dependent) critical interactions for binding and current densities are derived, and these offer the rare possibility to study persistent currents from the point of view of an interacting nanoscopic system. Two cyclic adiabatic processes are identified, one coupled to the center-of-mass behavior and the other defined on the two-body interaction potential, with the associated Berry's phases also analytically determined; these are found to be directly linked to the electric and probability (persistent) currents in nontrivial ways that are shown to be universal (independent of the actual form of the interaction). The direct connection of the two-body Berry's phase to the electric current for a neutral system is found to disappear in case of identical particles - hence revealing the character of a charged mixture as being crucial for exhibiting these universal behaviors.