Asymptotic tunneling conductance in Luttinger liquids

TL;DR

This paper analyzes how the conductance in Luttinger liquids diminishes with frequency, revealing different dominant behaviors depending on the interaction parameter g, and provides explicit asymptotic formulas.

Contribution

It derives the asymptotic frequency dependence of tunneling conductance in Luttinger liquids, highlighting the crossover behavior based on the interaction parameter g.

Findings

Conductance vanishes as a sum of two power laws in frequency.

Different dominant terms depending on the value of g.

Explicit formulas for conductance behavior at low frequencies.

Abstract

Conductance through weak constrictions in Luttinger liquids is shown to vanish with frequency $\omega$ as $c_1 \omega^2 + c_2 \omega^{2/g - 2}$, where $g$ is a dimensionless parameter characterizing the Luttinger liquid phase, and $c_1$ and $c_2$ are nonuniversal constants. The first term arises from the ^^ Coulomb blockade' effect and dominates for $g < 1/2$, whereas the second results from eliminating high-energy modes and dominates for $g > 1/2$.