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Persistent currents on graphs

M. Pascaud·G. Montambaux
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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.

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M. Pascaud, G. Montambaux. 1999-04-08. Persistent currents on graphs. https://doi.org/10.1103/physrevlett.82.4512

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