In this Letter, the mesoscopic voltage and conductance fluctuations of a Luttinger liquid are examined. For quasiballistic wires, one finds that the amplitude of conductance fluctuations, i.e., $\mathrm{Var}(G)$ , is proportional to ${T}^{4g\ensuremath{-}5}$ where $g\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\pi}\ensuremath{\Elzxh}v(\ensuremath{\partial}n/\ensuremath{\partial}\ensuremath{\mu})$ is a dimensionless measure of compressibility. For macroscopic wires, one finds resistance fluctuations of the form $\mathrm{Var}(R)\ensuremath{\sim}{T}^{4g\ensuremath{-}5}$. We also investigate the voltage distribution function and the length scale over which self-averaging occurs.In this Letter, the mesoscopic voltage and conductance fluctuations of a Luttinger liquid are examined. For quasiballistic wires, one finds that the amplitude of conductance fluctuations, i.e., $\mathrm{Var}(G)$, is proportional to ${T}^{4g\ensuremath{-}5}$ where $g\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\pi}\ensuremath{\Elzxh}v(\ensuremath{\partial}n/\ensuremath{\partial}\ensuremath{\mu})$ is a dimensionless measure of compressibility. For macroscopic wires, one finds resistance fluctuations of the form $\mathrm{Var}(R)\ensuremath{\sim}{T}^{4g\ensuremath{-}5}$. We also investigate the voltage distribution function and the length scale over which self-averaging occurs.

Physical Review LettersMay 26, 19973 citations

NonlinearI(V) characteristics of Luttinger liquids and gated Hall bars

Scot R. Renn, Daniel P. Arovas

Nonlinear current voltage characteristics of a disordered Luttinger liquid are calculated using a perturbative formalism. One finds the nonuniversal power-law characteristics of the form I(V)\ensuremath{\sim}${\mathit{V}}^{1/(2\mathit{g}\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}\mathrm{\ensuremath{-}}1)}$, which is valid both in the superfluid phase when I is small and also in the insulator phase when I is large. Mesoscopic voltage fluctuations are also calculated. One finds Var(\ensuremath{\Delta}V)\ensuremath{\sim}${\mathit{I}}^{4\mathit{g}\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}\mathrm{\ensuremath{-}}3}$. Both the I(V) characteristic and the voltage fluctuations exhibit universal power-law behavior at the superfluid insulator transition where g\ifmmode \tilde{}\else \~{}\fi{}=3/2. The possible application of these results to the nonlinear transport properties of gated Hall bars is discussed.Nonlinear current voltage characteristics of a disordered Luttinger liquid are calculated using a perturbative formalism. One finds the nonuniversal power-law characteristics of the form I(V)\ensuremath{\sim}${\mathit{V}}^{1/(2\mathit{g}\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}\mathrm{\ensuremath{-}}1)}$, which is valid both in the superfluid phase when I is small and also in the insulator phase when I is large. Mesoscopic voltage fluctuations are also calculated. One finds Var(\ensuremath{\Delta}V)\ensuremath{\sim}${\mathit{I}}^{4\mathit{g}\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}\mathrm{\ensuremath{-}}3}$. Both the I(V) characteristic and the voltage fluctuations exhibit universal power-law behavior at the superfluid insulator transition where g\ifmmode \tilde{}\else \~{}\fi{}=3/2. The possible application of these results to the nonlinear transport properties of gated Hall bars is discussed.

arXiv:cond-mat/9501134Physical review. B, Condensed matterJun 15, 199525 citations

In this Letter, the mesoscopic voltage and conductance fluctuations of a Luttinger liquid are examined. For quasiballistic wires, one finds that the amplitude of conductance fluctuations, i.e.,

\mathrm{Var}(G)

, is proportional to ${T}^{4g\ensuremath{-}5}$ where $g\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\pi}\ensuremath{\Elzxh}v(\ensuremath{\partial}n/\ensuremath{\partial}\ensuremath{\mu})$ is a dimensionless measure of compressibility. For macroscopic wires, one finds resistance fluctuations of the form $\mathrm{Var}(R)\ensuremath{\sim}{T}^{4g\ensuremath{-}5}$. We also investigate the voltage distribution function and the length scale over which self-averaging occurs.