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 temperatures down to ∼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 demonstrates 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, thus opening a new pathway to unambiguous interpretation of the exponents observed in quantum wires.

Infrastructure access project of the Cambridge Univerisity team on the H2020 European Microkelvin Platform (EMP) carried out at the University of Basel and theorecital work of University of Frankfurt supported in Basel by the Swiss NSF, FET TopSquad, and the Georg. H. Endress foundation.

Dominant end-tunneling effect in two distinct Luttinger liquids coexisting in one quantum wire 
Henok Weldeyesus, Pedro M.T. Vianez, Omid Sharifi Sedeh, Wooi Kiat Tan, Yiqing Jin, Maria Moreno, Christian P. Scheller, Jonathan P. Griffiths, Ian Farrer, David A. Ritchie, Dominik M. Zumbühl, Christopher J.B. Ford, Oleksandr Tsyplyatyev, Nature Communications 16, 6997 (Jul 30, 2025), manuscript pdf