Energy Partitioning of Tunneling Currents into Luttinger Liquids

TL;DR

This paper investigates how energy from tunneling electrons in a Luttinger liquid is partitioned between excitations, revealing differences from charge partitioning and potential experimental signatures.

Contribution

It introduces a detailed analysis of energy partitioning in Luttinger liquids, highlighting its dependence on bias and interaction strength, distinct from charge partitioning.

Findings

Energy partition depends on excess energy and interaction strength.

Charge partitioning is solely determined by the Luttinger parameter.

Energy partitioning can be observed in dc experiments with Fermi-liquid leads.

Abstract

Tunneling of electrons of definite chirality into a quantum wire creates counterpropagating excitations, carrying both charge and energy. We find that the partitioning of energy is qualitatively different from that of charge. The partition ratio of energy depends on the excess energy of the tunneling electrons (controlled by the applied bias) and on the interaction strength within the wire (characterized by the Luttinger liquid parameter $\kappa$), while the partitioning of charge is fully determined by $\kappa$. Moreover, unlike for charge currents, the partitioning of energy current should manifest itself in $dc$ experiments on wires contacted by conventional (Fermi-liquid) leads.