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arXiv:2410.17569 · Physical Review Letters

Quasi-1D Coulomb Drag in the Nonlinear Regime

Mingyang Zheng, Rebika Makaju, R. R. Gazizulin, Alex Levchenko, Sadhvikas Addamane, Dominique Laroche

Published May 15, 2025• 3 citations
arXivHTMLPDF

Abstract

One-dimensional Coulomb drag has been an essential tool to probe the physics of interacting Tomonaga-Luttinger liquids. To date, most experimental work has focused on the linear regime while the predictions for Luttinger liquids beyond the linear response theory remain largely untested. In this Letter, we report measurements of reciprocal momentum transfer induced Coulomb drag between vertically coupled quasi-one-dimensional quantum wires in the nonlinear regime. Measurements were performed at ultralow temperatures between wires only 15 nm apart. Our results reveal a nonlinear dependence of the drag voltage as a function of the drive current superimposed with an oscillatory contribution, in agreement with theoretical predictions for Coulomb drag between Tomonaga-Luttinger liquids. Additionally, the observed current-voltage characteristics exhibit a nonmonotonic temperature dependence, further corroborating the presence of non-Fermi-liquid behavior in our system. These findings are observed both in the single and in the multiple subband regimes and in the presence of disorder, extending the onset of this behavior beyond the clean single channel Tomonaga-Luttinger regime where the predictions were originally formulated.

DOI
10.1103/v3dn-bnrp

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cond-mat.mes-hallCross-listedarXiv:2608.02812•Aug 5, 2026
One-dimensional Coulomb drag has been an essential tool to probe the physics of interacting Tomonaga-Luttinger liquids. To date, most experimental work has focused on the linear regime while the predictions for Luttinger liquids beyond the linear response theory remain largely untested. In this Letter, we report measurements of reciprocal momentum transfer induced Coulomb drag between vertically coupled quasi-one-dimensional quantum wires in the nonlinear regime. Measurements were performed at ultralow temperatures between wires only 15 nm apart. Our results reveal a nonlinear dependence of the drag voltage as a function of the drive current superimposed with an oscillatory contribution, in agreement with theoretical predictions for Coulomb drag between Tomonaga-Luttinger liquids. Additionally, the observed current-voltage characteristics exhibit a nonmonotonic temperature dependence, further corroborating the presence of non-Fermi-liquid behavior in our system. These findings are observed both in the single and in the multiple subband regimes and in the presence of disorder, extending the onset of this behavior beyond the clean single channel Tomonaga-Luttinger regime where the predictions were originally formulated.
One-dimensional (1D) quantum wires provide a versatile platform for studying strong electron-electron interactions and collective excitations under confinement. Coulomb drag between 1D systems offers a powerful probe of Tomonaga-Luttinger liquid (TLL) physics, with theoretical predictions suggesting distinct power-law in temperature dependencies between the spin-full and the spin-polarized regimes. However, experimental verification has thus far remained limited. Here, we report measurements of reciprocal and nonreciprocal Coulomb drag between vertically coupled quasi-1D quantum wires in the spin-polarized regime. Clear signatures of spin splitting are observed in both the wires conductance and the drag signal. We observed a connection between electron-hole asymmetry and negative drag, and demonstrated different power-law behaviors in spin-full and spin-polarized regimes, yielding consistent TLL interaction parameters. These results validate the theoretical predictions for backscattering induced drag in the reciprocal regime and extend them to the nonreciprocal and the multiple subband regimes. Furthermore, the nonmonotonic density dependence of the reciprocal interaction parameter correlates with the subband occupation of the drag wire, revealing the complexity of the scattering mechanisms in multichannel systems.
We evaluate the Coulomb drag current in two finite-length Tomonaga-Luttinger-liquid wires coupled by an electrostatic backscattering interaction. The drag current in one wire shows oscillations as a function of the bias voltage applied to the other wire, reflecting interferences of the plasmon standing waves in the interacting wires. In agreement with this picture, the amplitude of the current oscillations is reduced with increasing temperature. This is a clear signature of non-Fermi-liquid physics because for coupled Fermi liquids the drag resistance is always expected to increase as the temperature is raised.
In a one-dimensional electron gas at low enough density, the magnetic (spin) exchange energy JJJ between neighboring electrons is exponentially suppressed relative to the characteristic charge energy, the Fermi energy EF{E}_{F}EF​. At nonzero temperature TTT, the energy hierarchy J⪡T⪡EFJ⪡T⪡{E}_{F}J⪡T⪡EF​ can be reached, and we refer to this as the spin-incoherent Luttinger liquid state. We discuss the Coulomb drag between two parallel quantum wires in the spin-incoherent regime, as well as the crossover to this state from the low-temperature regime by using a model of a fluctuating Wigner solid. As the temperature increases from zero to above JJJ for a fixed electron density, the 2kF2{k}_{F}2kF​ oscillations in the density-density correlations are lost. As a result, the temperature dependence of the Coulomb drag is dramatically altered and nonmonotonic dependence may result. Drag between wires of equal and unequal density are discussed, as well as the effects of weak disorder in the wires. We speculate that weak disorder may play an important role in extracting information about quantum wires in real drag experiments.
We study Coulomb drag in a pair of parallel one-dimensional electron systems within the framework of the Tomonaga-Luttinger model. We find that Coulomb coupling has a much stronger effect on one-dimensional wires than on two-dimensional layers: At zero temperature the transresistivity diverges, due to the formation of locked charge density waves. At temperature well above a crossover temperature T∗{T}^{*}T∗ the transresistivity follows a power law $\ensuremath{\rho}\ensuremath{\propto}{T}^{x},$ where the interaction-strength dependent exponent x is determined by the Luttinger liquid parameter ${K}_{c\ensuremath{-}}$ of the relative charge mode. At temperature below T∗{T}^{*}T∗ relative charge displacements are enabled by solitonic excitations, reflected by an exponential temperature dependence. The crossover temperature T∗{T}^{*}T∗ depends sensitively on the wire width, interwire distance, Fermi wavelength and the effective Bohr radius. For wire distances $\overline{d}\ensuremath{\gg}{k}_{F}^{\ensuremath{-}1}$ it is exponentially suppressed with ${T}^{*}{/E}_{F}\ensuremath{\sim}\mathrm{exp}[\ensuremath{-}\overline{d}{k}_{F}/(1\ensuremath{-}{K}_{c\ensuremath{-}})].$ The behavior changes drastically if each of the two wires develop spin gaps. In this case we find that the transresistivity vanishes at zero temperature. We discuss our results in view of possible experimental realizations in $\mathrm{GaAs}\ensuremath{-}{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ semiconductor structures.
The inhomogeneous Tomonaga-Luttinger liquid model describing an interacting quantum wire adiabatically coupled to noninteracting leads is analyzed in the presence of a weak impurity within the wire. Due to strong electronic correlations in the wire, the effects of impurity backscattering, finite bias, finite temperature, and finite length lead to characteristic nonmonotonic parameter dependencies of the average current. We discuss oscillations of the nonlinear current voltage characteristics that arise due to reflections of plasmon modes at the impurity and quasi-Andreev reflections at the contacts, and show how these oscillations are washed out by decoherence at finite temperature. Furthermore, the finite-frequency current noise is investigated in detail. We find that the effective charge extracted in the shot noise regime in the weak backscattering limit decisively depends on the noise frequency $\ensuremath{\omega}$ relative to vF∕gL{v}_{F}∕gLvF​∕gL, where vF{v}_{F}vF​ is the Fermi velocity, ggg the Tomonaga-Luttinger interaction parameter, and LLL the length of the wire. The interplay of finite bias, finite temperature, and finite length yields rich structure in the noise spectrum which crucially depends on the electron-electron interaction. In particular, the excess noise, defined as the change of the noise due to the applied voltage, can become negative and is nonvanishing even for noise frequencies larger than the applied voltage, which are signatures of correlation effects.
We consider the problem of Coulomb drag in interactively coupled quantum circuits built of adiabatic constrictions: quantum point contacts and short quantum-wire channels. The interplay of spatial confinement and magnetic field leads to a rich oscillatory response of the drag current as a function of gate voltage and magnetic field: drag peaks track the depopulation of magnetoelectric subbands, are asymptotically periodic in inverse field, and their visibility is controlled by the competition of temperature with the field-sharpened tunneling width of the constriction. We derive a closed expression for the linear drag conductance whose interaction kernel simplifies dramatically in the experimentally relevant limit of a long thermal length compared with the range of the interwire coupling, investigate the drag in the nonlinear regime, where the drag current measures the transconductance of the drive channel at any field, and discuss physically motivated models of dissipation-induced nonreciprocity of the drag signal. Extensions accounting for Zeeman splitting, interaction renormalization of the barrier transmission, backscattering at high field, and the frequency structure of the circuit coupling delineate how each mechanism imprints itself on the temperature dependence and lineshapes of the drag oscillations.