Fractional charge in transport through a 1D correlated insulator of finite length

TL;DR

This paper investigates charge transport in a finite 1D correlated insulator, revealing a crossover from Fermi liquid to fractional charge insulator behavior influenced by interactions and system size.

Contribution

It introduces a detailed analysis of fractional charge transport in finite 1D insulators, including a crossover energy scale and implications for conductance and shot noise.

Findings

Identification of a crossover energy scale T_x for transport behavior

Prediction of fractional charge signatures in conductance and noise

Extension of results to Mott insulators at specific fillings

Abstract

Transport through a one channel wire of length $L$ confined between two leads is examined when the 1D electron system has an energy gap $2M$: $M > T_L \equiv v_c/L$ induced by the interaction in charge mode ($v_c$: charge velocity in the wire). In spinless case the transformation of the leads electrons into the charge density wave solitons of fractional charge $q$ entails a non-trivial low energy crossover from the Fermi liquid behavior below the crossover energy $T_x \propto \sqrt{T_L M} e^{-M /[T_L(1-q^2)]}$ to the insulator one with the fractional charge in current vs. voltage, conductance vs. temperature, and in shot noise. Similar behavior is predicted for the Mott insulator of filling factor $\nu = integer/(2 m')$.