Correlated Nanoscopic Josephson Junctions

TL;DR

This paper demonstrates how correlated nanoscopic lattice models can exhibit Josephson-junction-like behavior, including supercurrents and flux quantization, through time-dependent potentials and correlation effects in small quantum systems.

Contribution

It introduces a method to realize Josephson-like effects in minimal lattice models with correlation-enhanced pairing and provides explicit solutions and mappings for small clusters and ring systems.

Findings

Observation of Josephson-like supercurrents in small correlated systems

Evidence of flux quantization indicating effective superconductivity

Detection of inverse-Josephson (Shapiro) currents under AC bias

Abstract

We discuss correlated lattice models with a time-dependent potential across a barrier and show how to implement a Josephson-junction-like behavior. The pairing occurs by a correlation effect enhanced by the symmetry of the system. In order to produce the effect we need a mild distortion which causes avoided crossings in the many-body spectrum. The Josephson-like response involves a quasi-adiabatic evolution in the time-dependent field. Besides, we observe an inverse-Josephson (Shapiro) current by applying an AC bias; a supercurrent in the absence of electromotive force can also be excited. The qualitative arguments are supported by explicit exact solutions in prototype 5-atom clusters with on-site repulsion. These basic units are then combined in ring-shaped systems, where one of the units sits at a higher potential and works as a barrier. In this case the solution is found by mapping the low-energy Hamiltonian into an effective anisotropic Heisenberg chain. Once again, we present evidence for a superconducting flux quantization, i.e. a Josephson-junction-like behavior suggesting the build-up of an effective order parameter already in few-electron systems. Some general implications for the quantum theory of transport are also briefly discussed, stressing the nontrivial occurrence of asymptotic current oscillations for long times in the presence of bound states.