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arXiv:1306.5078 · Physical Review B

Unified Boltzmann transport theory for the drag resistivity close to an interlayer-interaction-driven second-order phase transition

M. P. Mink, Henk T. C. Stoof, R. A. Duine, Marco Polini, Giovanni Vignale

Published Dec 19, 2013• 8 citations
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Abstract

We present a unified Boltzmann transport theory for the drag resistivity ${\ensuremath{\rho}}_{\mathrm{D}}$ in two-component systems close to a second-order phase transition. We find general expressions for ${\ensuremath{\rho}}_{\mathrm{D}}$ in two and three spatial dimensions, for arbitrary population and mass imbalance, for particle- and holelike bands, and show how to incorporate, at the Gaussian level, the effect of fluctuations close to a phase transition. We find that the proximity to the phase transition enhances the drag resistivity upon approaching the critical temperature from above, and we qualitatively derive the temperature dependence of this enhancement for various cases. In addition, we present numerical results for two concrete experimental systems: (i) three-dimensional cold atomic Fermi gases close to a Stoner transition and (ii) two-dimensional spatially separated electron and hole systems in semiconductor double quantum wells.

DOI
10.1103/physrevb.88.235311

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We present a unified Boltzmann transport theory for the drag resistivity \ensuremathρD{\ensuremath{\rho}}_{\mathrm{D}}\ensuremathρD​ in two-component systems close to a second-order phase transition. We find general expressions for \ensuremathρD{\ensuremath{\rho}}_{\mathrm{D}}\ensuremathρD​ in two and three spatial dimensions, for arbitrary population and mass imbalance, for particle- and holelike bands, and show how to incorporate, at the Gaussian level, the effect of fluctuations close to a phase transition. We find that the proximity to the phase transition enhances the drag resistivity upon approaching the critical temperature from above, and we qualitatively derive the temperature dependence of this enhancement for various cases. In addition, we present numerical results for two concrete experimental systems: (i) three-dimensional cold atomic Fermi gases close to a Stoner transition and (ii) two-dimensional spatially separated electron and hole systems in semiconductor double quantum wells.
We consider spin transport in a two-component atomic Bose gas in three dimensions, at temperatures just above the critical temperature for Bose-Einstein condensation. In these systems the spin conductivity is determined by spin drag, i.e., frictional drag between the two spin components due to interactions. We find that in the critical region the temperature dependence of the spin conductivity deviates qualitatively from the Boltzmann result and is fully determined by the critical exponents of the phase transition. We discuss the size of the critical region where these results may be observed experimentally.
In this Thesis we consider the behavior of the drag conductivity close to exciton condensation in bilayer systems and close to the superfluid transition in cold Fermi gases. In chapter 2 we calculate the transition temperature for exciton condensation in double-layer graphene, showing that the remote bands can play a supporting role in this transition. In chapter 3 we consider a topological insulator thin film and calculate the behavior of the drag resistivity close to the transition temperature. We find a strong enhancement which can be used as a precursor for the transition. In chapter 4 we discuss an ultracold Fermi gas close to the superconducting transition and compare two different methods to obtain the drag resistivity, each taking into account a different phenomenon which affects the drag resistivity close to the transition. Finally, in chapter 5, we present a uniform theoretical framework to determine the drag resistivity in all experimental systems considered in this Thesis.
Part of Focus on Bose Condensation Phenomena in Atomic and Solid State Physics We consider spin transport in a two-component atomic Bose gas in three dimensions, at temperatures just above the critical temperature for Bose–Einstein condensation. In these systems, the spin conductivity is determined by spin drag, i.e. frictional drag between the two spin components due to interactions. We find that in the critical region, the temperature dependence of the spin conductivity deviates qualitatively from the Boltzmann result and is fully determined by the critical exponents of the phase transition. We discuss the size of the critical region where these results may be observed experimentally.
We consider two-dimensional spin-polarized dipolar Fermi gases confined in a double-layer system and calculate the momentum transfer between the layers as a function of temperature to investigate the transport properties of the system. We use the Hubbard approximation to describe the correlation effects and the screening between the dipoles within a single layer. The effective interlayer interaction between the dipoles across the layers is obtained by the random-phase approximation. We calculate the interaction strength and the layer separation distance dependence of the drag rate, and we show that there is a critical distance below which the system is unstable. In addition, we calculate the typical behavior of the collective modes related to the density fluctuations.
Recent years have seen a surge of interest in studies of hydrodynamic transport in electronic systems. We investigate the electron viscosity of metals and find a component that is closely related to Coulomb drag. By using linear-response theory, viscosity, which is a transport coefficient for momentum, can be extracted from the retarded correlation function of the momentum flux, i.e., the stress tensor. There exists a previously overlooked contribution to the shear viscosity from the interacting part of the stress tensor which accounts for the momentum flow induced by interactions. This contribution, which we dub drag viscosity, is caused by the frictional drag force due to long-range interactions. It is therefore linked to Coulomb drag which also originates from the interaction-induced drag force. Starting from the Kubo formula and using the Keldysh technique, we compute the drag viscosity of two- and three-dimensional metals along with the drag resistivity of double-layer two-dimensional electronic systems. Both the drag resistivity and drag viscosity exhibit a crossover from quadratic-in-TTT behavior at low temperatures to a linear behavior at higher temperatures. Although the drag viscosity appears relatively small compared with the normal Drude component for the clean metals, it may dominate hydrodynamic transport in some systems, which are discussed in the conclusion.
We calculate the spin-drag relaxation rate for a two-component ultracold atomic Fermi gas with positive scattering length between the two-spin components. In one dimension, we find that it vanishes linearly with temperature. In three dimensions, the spin-drag relaxation rate vanishes quadratically with temperature for sufficiently weak interactions. This quadratic temperature dependence is present, up to logarithmic corrections, in the two-dimensional (2D) case as well. For stronger interaction, the system exhibits a Stoner ferromagnetic phase transition in two and three dimensions. We show that the spin-drag relaxation rate is enhanced by spin fluctuations as the temperature approaches the critical temperature of this transition from above.