Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2005-05-09
Phys. Rev. B 72, 115327 (2005)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
21 pages, RevTeX4, 8 eps figures; version of 10/2006 : eqs.(100-102) of section V.C corrected
Scientific paper
10.1103/PhysRevB.72.115327
We study the effect of the electron-electron interaction on the weak localization correction of a ring pierced by a magnetic flux. We compute exactly the path integral giving the magnetoconductivity for an isolated ring. The results are interpreted in a time representation. This allows to characterize the nature of the phase coherence relaxation in the ring. The nature of the relaxation depends on the time regime (diffusive or ergodic) but also on the harmonics $n$ of the magnetoconductivity. Whereas phase coherence relaxation is non exponential for the harmonic $n=0$, it is always exponential for harmonics $n\neq0$. Then we consider the case of a ring connected to reservoirs and discuss the effect of connecting wires. We recover the behaviour of the harmonics predicted recently by Ludwig & Mirlin for a large perimeter (compared to the Nyquist length). We also predict a new behaviour when the Nyquist length exceeds the perimeter.
Montambaux Gilles
Texier Christophe
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