Abstract
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.
Highlights
Luttinger liquids emerge from interacting one-dimensional many-electron systems where the Fermi surface is two discrete points rather than a connected surface as in higherdimensional cases
The logarithmic divergence of the long-range Coulomb interaction gives rise to a scale-dependent effective exponent which increases at lower energy
We believe that the clear theoretical difference between short- and long-range Luttinger liquids established in this paper should be experimentally observable provided that the experimental tuning variables are varied over a large dynamical range
Summary
Luttinger liquids emerge from interacting one-dimensional many-electron systems where the Fermi surface is two discrete points rather than a connected surface as in higherdimensional cases. Since the Coulomb Luttinger liquid by definition does not have a constant exponent (i.e., the exponent varies slowly over the energy scale of measurements), it is important to analyze the tunneling experiment in depth using the long-range interaction model to figure out how this scale dependence might manifest in the tunneling spectroscopy. This is the main goal of the current work. IV summarizing our main findings and discussing possible experimental implications of our results
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