Precursors of Mott insulator in modulated quantum wires

TL;DR

This paper studies how electron transport in modulated quantum wires shows precursors to Mott insulator behavior, revealing temperature-dependent resistance changes near half-filling and highlighting limitations of bulk models.

Contribution

It introduces a non-uniform sine-Gordon model for weak Umklapp scattering in modulated quantum wires, analyzing temperature-dependent resistance behavior near the Mott transition.

Findings

At half-filling, resistance changes from a power-law to quadratic temperature dependence.

The bulk model predictions fail away from half-filling at high temperatures.

Resistance behavior is sensitive to electron filling and temperature regimes.

Abstract

We investigate the transport of interacting electrons through single-mode quantum wires whose parameters are periodically modulated on the scale of the electronic Fermi wave length. The Umklapp and backscattering of electrons can be described in terms of non-uniform quantum sine-Gordon-like models which also incorporate the effects of electronic reservoirs (electrodes) adiabatically coupled to the wire. We concentrate on weak Umklapp scattering and analyze the precursors of the Mott transition. At half-filling the temperature dependence of the extra resistance $\Delta R = R - \pi \hbar/e^2$ of a modulated quantum wire of length $L$ changes from the interaction-dependent "bulk" power-law $\Delta R \propto T^{4K_\rho-3}$ at high temperatures, $T \gg v_\rho/L$, to the universal $\Delta R \propto T^2$ behavior at low temperatures, $T \ll v_\rho/L$. Away from half-filling the "bulk" results are qualitatively incorrect even at high temperatures $v_\rho/L \ll T \ll T^{*}$ despite the electron coherence in the wire is absent in this regime.