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The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics

Coulomb-drag effect between two quantum wires: integrable models with long-range potentials

P. Schlottmann

Published Apr 10, 2006• 2 citations
Publisher

Abstract

The exact solution of the one-dimensional Calogero–Sutherland models with spin-exchange and sinh− 2(r) and r − 2 interactions, and the supersymmetric t–J-model with long-range exchange interaction is used to calculate the drag current between two parallel quantum wires. The critical exponent for the drag current at low temperatures is obtained by means of the mesoscopic energy spectrum and conformal field theory. Since the interaction in the above models is repulsive, the drag current is opposite to the driving current.

DOI
10.1080/14786430500229356

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The exact solution of the one-dimensional Calogero–Sutherland models with spin-exchange and sinh− 2(r) and r − 2 interactions, and the supersymmetric t–J-model with long-range exchange interaction is used to calculate the drag current between two parallel quantum wires. The critical exponent for the drag current at low temperatures is obtained by means of the mesoscopic energy spectrum and conformal field theory. Since the interaction in the above models is repulsive, the drag current is opposite to the driving current.
The exact solution of the one-dimensional Hubbard model, the supersymmetric $t\ensuremath{-}J$ model, and the gas of fermions interacting via a $\ensuremath{\delta}$-function potential is used to calculate the drag current between two parallel quantum wires. The critical exponent for the drag current at low temperatures is obtained by means of the mesoscopic energy spectrum and conformal field theory. For a repulsive interaction between the carriers the drag current is opposite to the driving current, while for attractive potentials the two currents are parallel.
We calculate the critical exponent of the temperature dependence of the drag current between two parallel quantum wires. The two wires have carriers with equal mass but they may have different electron density. The electrons interact via a $\ensuremath{\delta}$-function spin-exchange potential, which is attractive or repulsive depending on whether the interacting particles are in a spin-singlet or spin-triplet state. This interaction leads to the formation of spin-singlet or spin-triplet bound states of the Cooper type (preformed hard core bosons that do not condensate). Depending on the parameters, the drag current can be parallel or opposite to the driving current. The critical exponent of the drag current is calculated using the Bethe Ansatz solution of the model and conformal field theory.
Charge carriers moving in a quantum wire may induce, via the Coulomb interaction and momentum conservation, a drag current in another quantum wire located nearby. In addition, tunnelling of carriers between the two parallel wires is considered. For spinless carriers the problem can be mapped onto the one-dimensional Hubbard model. The exact solution of the Hubbard chain and conformal field theory are used to calculate the critical exponents for the temperature dependence of the drag current between the two wires. The exponents are non-universal and depend on the interaction strength, the band filling and the tunnelling amplitude. For a repulsive interaction the drag current is opposite to the driving current, while for an attractive interaction they are parallel.
We observed negative Coulomb drag for parallel coupled quantum wires, in which electrons flow in the opposite directions between the wires. This only occurred under the conditions of strong correlation in the wires, that is, low density, high magnetic field, and low temperature, and cannot be addressed by a standard theory of momentum transfer. We propose a Coulomb drag model in which formation of a Wigner crystal state in the drag wire and a particle-like state in the drive wire is taken into account.
The exact solution of the one-dimensional Hubbard model (for repulsive and attractive U)U)U) is used to calculate the tunneling rates of single electrons and Cooper pairs between two quantum wires. The critical exponents for the tunneling at small frequencies and low temperatures is obtained by means of the mesoscopic energy spectrum and conformal field theory. The situations of crossing wires, tunneling at a boundary, and resonant tunneling (through a bound state) are considered.
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.