# Fractional Conductance in Strongly Interacting 1D Systems

## TL;DR

This paper investigates how strong electron interactions in one-dimensional systems can produce fractional conductance and shot noise, revealing conditions for these phenomena and connecting theory to recent experimental observations.

## Contribution

It demonstrates the emergence of fractional conductance in strongly interacting 1D systems under time reversal symmetry, using abelian bosonization and re-fermionization techniques, and relates findings to experiments.

## Key findings

- Fractional conductance plateaus at 2/5 e^2/h observed.
- Conditions for fractional quantization depend on Fermi momentum commensurability and interaction strength.
- Conductance reverts to integer values at very low energies, with disorder effects considered.

## Abstract

We study one dimensional clean systems with few channels and strong electron-electron interactions. We find that in several circumstances, even when time reversal symmetry holds, they may lead to two terminal fractional quantized conductance and fractional shot noise. The condition on the commensurability of the Fermi momenta of the different channels and the strength of interactions resulting in such remarkable phenomena are explored using abelian bosonization. Finite temperature and length effects are accounted for by a generalization of the Luther-Emery re-fermionization at specific values of the interaction strength. We discuss the connection of our model to recent experiments in confined 2DEG, featuring possible fractional conductance plateaus. One of the most dominant observed fractions, with two terminal conductance equals to $\frac{2}{5}\frac{e^{2}}{h}$, is found in several scenarios of our model. Finally, we discuss how at very small energy scales the conductance returns to an integer value and the role of disorder.