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arXiv:1912.10379 · Physical Review Research

Tunneling conductance of long-range Coulomb interacting Luttinger liquid

DinhDuy Vu, Aníbal Iucci, S. Das Sarma

Published May 28, 2020• 8 citations
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Abstract

This paper shows that tunneling measurements in a Luttinger liquid with long-range Coulomb interaction show a power law with an effective exponent that is scale-dependent and increases with decreasing energy. The authors provide a scheme to tunneling experiments that relies on measuring over a longer range of temperature/ voltage bias to fully characterize this dependence

DOI
10.1103/physrevresearch.2.023246

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This paper shows that tunneling measurements in a Luttinger liquid with long-range Coulomb interaction show a power law with an effective exponent that is scale-dependent and increases with decreasing energy. The authors provide a scheme to tunneling experiments that relies on measuring over a longer range of temperature/ voltage bias to fully characterize this dependence
The theoretical model of the short-range interacting Luttinger liquid predicts a power-law scaling of the density of states and the momentum distribution function around the Fermi surface, which can be readily tested through tunneling experiments. However, some physical systems have long-range interaction, most notably the Coulomb interaction, leading to significantly different behaviors from the short-range interacting system. In this paper, we revisit the tunneling theory for the one-dimensional electrons interacting via the long-range Coulomb force. We show that even though in a small dynamic range of temperature and bias voltage, the tunneling conductance may appear to have a power-law decay similar to short-range interacting systems, the effective exponent is scale-dependent and slowly increases with decreasing energy. This factor may lead to the sample-to-sample variation in the measured tunneling exponents. We also discuss the crossover to a free Fermi gas at high energy and the effect of the finite size. Our work demonstrates that experimental tunneling measurements in one-dimensional electron systems should be interpreted with great caution when the system is a Coulomb Luttinger liquid.
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.
The nonlinear charge transfer through a tunnel junction between two Luttinger systems is studied for repulsive, finite-range interaction between electrons on the same side, V11{\mathrm{V}}_{11}V11​, and on different sides, V12{\mathrm{V}}_{12}V12​, of a junction. Features of the Coulomb blockade effect are observed if V12{\mathrm{V}}_{12}V12​=0. We predict an interaction-induced enhancement of the current if V12{\mathrm{V}}_{12}V12​>0. When V12{\mathrm{V}}_{12}V12​=V11{\mathrm{V}}_{11}V11​, the current is suppressed at small bias, but the ``charging energy,'' obtained from the asymptotic behavior at high-bias voltage, vanishes.
Intermode electron transitions in a two-channel Luttinger liquid (LL) are considered. At first we study chiral LL and show that for a long-range Coulomb interaction even forward-scattering intermode electron transitions are strongly renormalized by interaction at low energies. For a short-range interaction the renormalization of the electron transition rates in a chiral LL do not depend on the energy (temperature, bias voltage) involved in the tunneling process. We show, however, that the interference effects are sensitive to the strength of electron interaction, and they are significantly enhanced for strongly correlated electrons. The analyses of the intermode electron transitions is generalized for a nonchiral two-channel LL. The forward- and the backward-scattering interchannel electron transition rates are calculated and their connection to the problem of x-ray singularity in a LL is elucidated.