Persistent currents in one dimension: the other side of Leggett's theorem

Details Persistent currents in one dimension: the other side of Leggett's theorem Persistent currents in one dimension: the other side of Leggett's theorem

2008-04-10

arxiv.org/abs/0804.1689v1

Phys. Rev. Lett. 101, 106804 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.101.106804

We discuss the sign of the persistent current of N electrons in one dimensional rings. Using a topology argument, we establish lower bounds for the free energy in the presence of arbitrary electron-electron interactions and external potentials. Those bounds are the counterparts of upper bounds derived by Leggett. Rings with odd (even) numbers of polarized electrons are always diamagnetic (paramagnetic). We show that unpolarized electrons with N being a multiple of four exhibit either paramagnetic behavior or a superconductor-like current-phase relation.

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