Power-laws in one-dimensional transport: Luttinger liquid or disorder?

Matthew P. A. Fisher, L. I. Glazman

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.

Hans Peter Wächter

In a first part, I study the electronic transport through a one-dimensional, finite-length quantum wire of correlated electrons (Luttinger liquid) coupled at arbitrary position via tunnel barriers to two semi-infinite, one-dimensional as well as stripe-like (two-dimensional) leads, thereby bringing theory closer towards systems resembling setups realized in experiments. In particular, I compute the temperature dependence of the linear conductance of a system without bulk impurities. The appearance of new temperature scales introduced by the lengths of the overhanging parts of the leads and the wire implies a conductance function which is much more complex than the simple power-law behavior obtained in earlier approaches. My results can be used to optimize the experimental setups designed for a verification of Luttinger-liquid scaling. In a second part, I suggest a setup to study Luttinger-liquid behavior in quantum wires which allows to determine the Luttinger-liquid parameter from two independent measurements: transport through a quantum dot embedded in the wire and the charge on the dot. To this end, I identified novel Luttinger-liquid power-laws in the charging of the dot. In a more technical part, I extended an adaption of the functional renormalization group such that it can be used on correlated electrons in complex geometries like the wire-lead structures described above and arbitrary dot structures coupled to Luttinger-liquid leads.

V. Meden, Walter Metzner, Ulrich Schollwöck +3 more

Thierry Giamarchi, Thomas Nattermann, Pierre Le Doussal

Yen-Wen Lu, Michael Mulligan

Strange metals are highly entangled gapless states of matter that exhibit anomalous transport, such as linear in temperature resistivity, over more than a decade of temperature. Why a single power law should be so robust is an open question. We propose a scenario in which interactions enhance the domain of certain scattering regimes, effectively suppressing other ``would-be regimes." We test this proposal in a one-dimensional Luttinger liquid coupled to a one-dimensional acoustic phonon. We use the memory matrix formalism to calculate the dc electrical and thermal conductivities at low and high temperatures, relative to the Debye cutoff on phonon frequencies, in both the ``clean" (umklapp scattering) and ``dirty" (disorder scattering) limits. We find the crossover temperature separating the low and high temperature regimes to be interaction-dependent, with repulsive interactions substantially increasing it, generally by more than an order of magnitude. This provides a concrete illustration for how interactions can extend a single transport regime over a wider temperature range.