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The low-frequency ac conductivity, σ , is evaluated numerically with use of the Kubo formula with inelastic lifetimes for a small one-dimensional (1D) closed metallic ring with random potentials. The effects of thermal excitations at finite temperatures and of increasing inelastic scattering are considered. It is found that energy averaging over a range larger than the typical level spacing (in 1D) markedly reduces the fundamental ( hc/e ) and odd harmonic periodicities of σ as a function of the Aharonov-Bohm flux, φ , through the ring. Thus, energy averaging makes the lowest even harmonic ( hc/2e ) appear to be the fundamental period.
Physical Review B – American Physical Society (APS)
Published: Jun 15, 1986
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