# Universal conductance fluctuations

Universal conductance fluctuations (UCF) in mesoscopic physics is a phenomenon encountered in electrical transport experiments in mesoscopic species. The measured electrical conductance will vary from sample to sample, mainly due to inhomogeneous scattering sites. Fluctuations originate from coherence effects for electronic wavefunctions and thus the phase-coherence length ${\displaystyle \textstyle l_{\phi }}$ needs be larger than the momentum relaxation length ${\displaystyle \textstyle l_{m}}$. UCF is more profound when electrical transport is in weak localization regime. ${\displaystyle \textstyle l_{\phi } where ${\displaystyle l_{c}=M\cdot l_{m}}$ , ${\displaystyle \textstyle M}$ is the number of conduction channels and ${\displaystyle \textstyle l_{m}}$is the momentum relaxation due to phonon scattering events length or mean free path. For weakly localized samples fluctuation in conductance is equal to fundamental conductance ${\displaystyle \textstyle G_{o}=2e^{2}/h}$ regardless of the number of channels.

Many factors will influence the amplitude of UCF. At zero temperature without decoherence, the UCF is influenced by mainly two factors, the symmetry and the shape of the sample. Recently, a third key factor, anisotropy of Fermi surface, is also found to fundamentally influence the amplitude of UCF.[1]