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arXiv:2501.13549 · Nature Communications

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, María Moreno, C. P. Scheller, Jonathan P. Griffiths, Ian A. Farrer, D. A. Ritchie, Dominik M. Zumbühl, Christopher J. B. Ford, Oleksandr Tsyplyatyev

Published Jul 30, 2025• 1 citation

Abstract

Luttinger liquids occupy a notable place in physics as one of the most understood classes of 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 ∼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 pathway to unambiguous interpretation of the exponents observed in quantum wires.

DOI: 10.1038/s41467-025-62325-5

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We study electronic transport through a one-dimensional, finite-length quantum wire of correlated electrons (Luttinger liquid) coupled at arbitrary position via tunnel barriers to two semi-infinite, one-dimensional as well as stripe-like (two-dimensional) leads, thereby bringing theory closer towards systems resembling set-ups realized in experiments. In particular, we compute the temperature dependence of the linear conductance G of a system without bulk impurities on the temperature T. The appearance of new temperature scales introduced by the lengths of overhanging parts of the leads and the wire implies a G(T) which is much more complex than the power-law behavior described so far for end-coupled wires. Depending on the precise set-up the wide temperature regime of power-law scaling found in the end-coupled case is broken up into up to five fairly narrow regimes interrupted by extended crossover regions. Our results can be used to optimize the experimental set-ups designed for a verification of Luttinger liquid power-law scaling.

Luttinger-liquid behavior of one-dimensional correlated electron systems is characterized by power-law scaling of a variety of physical observables with exponents determined by a single interaction dependent parameter

K

. We suggest a setup to study Luttinger-liquid behavior in quantum wires which allows us to determine

K

from two independent measurements: transport through a quantum dot embedded in the wire and the charge on the dot. Consistency of the two

K

's for a single probe would provide strong experimental evidence for the Luttinger-liquid paradigm.

Power laws in physics have until now always been associated with a scale invariance originating from the absence of a length scale. Recently, an emergent invariance even in the presence of a length scale has been predicted by the newly-developed nonlinear-Luttinger-liquid theory for a one-dimensional (1D) quantum fluid at finite energy and momentum, at which the particle's wavelength provides the length scale. We present experimental evidence for this new type of power law in the spectral function of interacting electrons in a quantum wire using a transport-spectroscopy technique. The observed momentum dependence of the power law in the high-energy region matches the theoretical predictions, supporting not only the 1D theory of interacting particles beyond the linear regime but also the existence of a new type of universality that emerges at finite energy and momentum.