Precursors of Mott insulator in modulated quantum wires

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 $ΔR = R - π\hbar/e^2$ of a modulated quantum wire of length $L$ changes from the interaction-dependent "bulk" power-law $ΔR \propto T^{4K_ρ-3}$ at high temperatures, $T \gg v_ρ/L$, to the universal $ΔR \propto T^2$ behavior at low temperatures, $T \ll v_ρ/L$. Away from half-filling the "bulk" results are qualitatively incorrect even at high temperatures $v_ρ/L \ll T \ll T^{*}$ despite the electron coherence in the wire is absent in this regime.