Persistent currents on graphs

TL;DR

This paper introduces a method to compute persistent currents and their spatial distribution on graphs of quasi-1D diffusive wires, linking them to graph topology and extending to disordered and clean systems.

Contribution

The authors develop a novel approach to calculate persistent currents on complex graphs, relating them to the graph's topology and extending understanding to disordered and interacting systems.

Findings

Currents are related to the determinant of a matrix describing the graph.

In certain limits, currents can be obtained by counting nodes and connectivity.

A relation is established between disordered and clean graph currents.

Abstract

We develop a method to calculate the persistent currents and their spatial distribution (and transport properties) on graphs made of quasi-1D diffusive wires. They are directly related to the field derivatives of the determinant of a matrix which describes the topology of the graph. In certain limits, they are obtained by simple counting of the nodes and their connectivity. We relate the average current of a disordered graph with interactions and the non-interacting current of the same graph with clean 1D wires. A similar relation exists for orbital magnetism in general.