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arXiv:cond-mat/9912371 · Physical review. B, Condensed matter

Coulomb drag between quantum wires

Rochus Klesse, Ady Stern

Published Dec 15, 2000• 59 citations
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Abstract

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 ${T}^{*}$ 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 ${T}^{*}$ relative charge displacements are enabled by solitonic excitations, reflected by an exponential temperature dependence. The crossover temperature ${T}^{*}$ 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.

DOI
10.1103/physrevb.62.16912

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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 \ensuremathρ\ensuremath∝Tx,\ensuremath{\rho}\ensuremath{\propto}{T}^{x},\ensuremathρ\ensuremath∝Tx, where the interaction-strength dependent exponent x is determined by the Luttinger liquid parameter Kc\ensuremath−{K}_{c\ensuremath{-}}Kc\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 d‾\ensuremath≫kF\ensuremath−1\overline{d}\ensuremath{\gg}{k}_{F}^{\ensuremath{-}1}d\ensuremath≫kF\ensuremath−1​ it is exponentially suppressed with T∗/EF\ensuremath∼exp[\ensuremath−d‾kF/(1\ensuremath−Kc\ensuremath−)].{T}^{*}{/E}_{F}\ensuremath{\sim}\mathrm{exp}[\ensuremath{-}\overline{d}{k}_{F}/(1\ensuremath{-}{K}_{c\ensuremath{-}})].T∗/EF​\ensuremath∼exp[\ensuremath−dkF​/(1\ensuremath−Kc\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 GaAs\ensuremath−AlxGa1\ensuremath−xAs\mathrm{GaAs}\ensuremath{-}{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}GaAs\ensuremath−Alx​Ga1\ensuremath−x​As semiconductor structures.
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.
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.
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.
We study the transconductance for two coupled one-dimensional wires or edge states described by Luttinger liquid models. The wires are assumed to interact over a finite segment. We find for the interaction parameter g=1/2g\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2g=1/2 that the drag rate is finite at zero temperature, which cannot occur in a Fermi-liquid system. The zero temperature drag is, however, cut off at low temperature due to the finite length of the wires. We also consider edge states in the fractional quantum Hall regime, and suggest that low temperature enhancement of the drag effect might be seen in this regime.
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.
We consider the effect of the curvature in fermionic dispersion on the observable properties of Luttinger liquid (LL). We use the bosonization technique where the curvature is irrelevant perturbation, describing the decay of LL bosons (plasmon modes). When possible, we establish the correspondence between the bosonization and the fermionic approach. We analyze modifications in density correlation functions due to curvature at finite temperatures, TTT. The most important application of our approach is the analysis of the Coulomb drag by small momentum transfer between two LLs, which is only possible due to curvature. Analyzing the ac transconductivity in the one-dimensional drag setup, we confirm the results by Pustilnik et al. for TTT dependence of drag resistivity, ${R}_{12}\ensuremath{\sim}{T}^{2}$ at high and ${R}_{12}\ensuremath{\sim}{T}^{5}$ at low temperatures. The bosonization allows for treating both intra- and interwire electron-electron interactions in all orders, and we calculate exact prefactors in the low-TTT drag regime. The crossover temperature between the two regimes is ${T}_{1}\ensuremath{\sim}{E}_{F}\ensuremath{\Delta}$, with $\ensuremath{\Delta}$ relative difference in plasmon velocities. We show that $\ensuremath{\Delta}\ensuremath{\ne}0$ even for identical wires, due to lifting of degeneracy by interwire interaction, U12{U}_{12}U12​, leading to crossover from ${R}_{12}\ensuremath{\sim}{U}_{12}^{2}{T}^{2}$ to ${R}_{12}\ensuremath{\sim}{T}^{5}∕{U}_{12}$ at $T\ensuremath{\sim}{U}_{12}$.