Coulomb drag between quantum wires

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 ϰT x , where the interaction-strength dependent exponent x is determined by the Luttinger liquid parameter K cϪ 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 d ӷk FϪ1 it is exponentially suppressed with T*/E F ϳexp͓Ϫdk F /(1ϪK cϪ )͔. 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-Al x Ga 1Ϫx As semiconductor structures.

Coulomb drag

“…For short wires, Klesse and Stern (2000) report a qualitatively different behavior. Here the CDW in one wire may slip as a whole relative to the CDW in the other wire.…”

“…Then, from Eq. (128) one finds the values for the Luttinger parameter K 0.1 − 0.2 (for samples 3-R and 2-C) corresponding to very strong interaction that is beyond the applicability of the bosonization theory of Klesse and Stern (2000). On the other hand, fitting the high-temperature data to the power-law behavior (129) yields K 1.5.…”

“…Consequently, the vast majority of theoretical studies of Coulomb drag are devoted to the investigation of the lowest-order effect. Notable exceptions are given by the studies of the interlayer correlated states, either in the context of quantum Hall devices (Girvin and MacDonald, 1997;Kim et al, 2001;Stern and Halperin, 2002;Stern et al, 2000;Yang, 1998;Yang and MacDonald, 2001) or quantum wires (Klesse and Stern, 2000;Nazarov and Averin, 1998), as well as strongly correlated intralayer states, such as Wigner crystals (Baker and Rojo, 2001;Braude and Stern, 2001) or Anderson insulators (Raikh and von Oppen, 2002). The "single-particle" drag resistivity, Eqs.…”

“…Schlottmann (2004a,b) used Bethe-Ansatz methods to solve the problem of two wires coupled by a particular δ-function potential. Especially interesting is the prediction of the Mott-insulator-type state corresponding to formation of two interlocked charge density waves (CDW) in quantum wires (Fuchs et al, 2005;Klesse and Stern, 2000) [see also a recent preprint (Furuya et al, 2015)]. …”

“…Below a certain crossover scale T * , the drag resistivity between infinitely long quantum wires of equal electron density is predicted to increase exponentially with decreasing temperature (Klesse and Stern, 2000) ρ…”