Persistent currents in one dimension: the counterpart of Leggett's theorem.
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 superconductorlike current-phase relation.
Waintal
Xavier
X
Nanoelectronics group, Service de Physique de l'Etat Condensé, CEA Saclay F-91191 Gif-sur-Yvette Cedex, France.
Fleury
Geneviève
G
Kazymyrenko
Kyryl
K
Houzet
Manuel
M
Schmitteckert
Peter
P
Weinmann
Dietmar
D