Supercurrent States in 1D Finite-Size Rings

TL;DR

This paper investigates topological supercurrent excitations in 1D mesoscopic rings, analyzing their stability, decay mechanisms, and scaling behavior under various conditions, with implications for experimental detection in related systems.

Contribution

It provides a detailed analysis of the macroscopic scaling of supercurrent excitations in 1D rings, including effects of impurities and disorder, supported by exact-diagonalization results.

Findings

Scaling of supercurrent amplitude $\Delta$ varies with system conditions.

Disorder and impurities significantly affect supercurrent stability.

Results align well with boson Hubbard model spectra.

Abstract

We consider topological supercurrent excitations (SC) in 1D mesoscopic rings. Under certain conditions such excitations are well-defined except for (i) a tunneling between resonating states with clockwise and anti-clockwise currents, which may be characterized by the amplitude $\Delta$, and (ii) a decay of SC assisted by phonons of the substrate, both effects being macroscopically small. Most attention is paid to the calculation of the macroscopic scaling of $\Delta$ (the main superfluid characteristic of a mesoscopic system) under different conditions: a commensurate system, a system with single impurity, and a disordered system. The results are in a very good agreement with the exact-diagonalization spectra of the boson Hubbard models. Apart from really 1D electron wires we discuss two other important experimental systems: the 2D electron gas in the FQHE state and quasi-1D superconducting rings. We suggest some experimental setups for studying SC, e.g., via persistent current measurements, resonant electro-magnetic absorption or echo signals, and relaxation of the metastable current states.