Dominant end-tunneling effect in two distinct Luttinger liquids coexisting in one quantum wire

TL;DR

This study combines tunneling spectroscopy and transport measurements in quantum wires to observe how the coexistence of two Luttinger liquids affects conductance, revealing the importance of mode-specific parameters for understanding quantum many-body systems.

Contribution

It demonstrates the coexistence of two Luttinger liquids in a single quantum wire and highlights the necessity of mode-specific measurements for accurate characterization.

Findings

Different power-law exponents observed in conductance with temperature.

Finite-size effects dominate the end-tunneling process.

Measurement of Luttinger parameters and modes is crucial for interpretation.

Abstract

Luttinger liquids occupy a special place in physics as the most understood case of essentially quantum many-body systems. The experimental mission of measuring its main prediction, power laws in observable quantities, has already produced a body of exponents in different semiconductor and metallic structures. Here, we combine tunneling spectroscopy with density-dependent transport measurements in the same quantum wires over more than two orders of magnitude in temperature to very low electron temperatures down to $\sim$40 mK. This reveals that, when the second 1D subband becomes populated, the temperature dependence splits into two ranges with different exponents in the power-law dependence of the conductance, both dominated by the finite-size effect of the end-tunneling process. This result demonstrates the importance of measuring the Luttinger parameters as well as the number of modes independently through spectroscopy in addition to the transport exponent in the characterization of Luttinger liquids. This opens a new pathway to unambiguous interpretation of the exponents observed in quantum wires.