Persistent currents on graphs

Details Persistent currents on graphs Persistent currents on graphs

1999-04-08

arxiv.org/abs/cond-mat/9904112v1

Phys. Rev. Lett. 83, 1076 (1999)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 3 figures, to appear in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.82.4512

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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