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arXiv:0801.2324 · Physical Review B

Spin-drag relaxation time in one-dimensional spin-polarized Fermi gases

Diego Rainis, Marco Polini, Monica Tosi, Giovanni Vignale

Published Jan 11, 2008• 20 citations
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Abstract

Spin propagation in systems of one-dimensional interacting fermions at finite temperature is intrinsically diffusive. The spreading rate of a spin packet is controlled by a transport coefficient termed ``spin drag'' relaxation time ${\ensuremath{\tau}}_{\mathrm{sd}}$. In this paper we present both numerical and analytical calculations of ${\ensuremath{\tau}}_{\mathrm{sd}}$ for a two-component spin-polarized cold Fermi gas trapped inside a tight atomic waveguide. At low temperatures we find an activation law for ${\ensuremath{\tau}}_{\mathrm{sd}}$, in agreement with earlier calculations of Coulomb drag between slightly asymmetric quantum wires, but with a different and much stronger temperature dependence of the prefactor. Our results provide a fundamental input for microscopic time-dependent spin-density functional theory calculations of spin transport in one-dimensional inhomogeneous systems of interacting fermions.

DOI
10.1103/physrevb.77.035113

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Spin propagation in systems of one-dimensional interacting fermions at finite temperature is intrinsically diffusive. The spreading rate of a spin packet is controlled by a transport coefficient termed ``spin drag'' relaxation time \ensuremathτsd{\ensuremath{\tau}}_{\mathrm{sd}}\ensuremathτsd​. In this paper we present both numerical and analytical calculations of \ensuremathτsd{\ensuremath{\tau}}_{\mathrm{sd}}\ensuremathτsd​ for a two-component spin-polarized cold Fermi gas trapped inside a tight atomic waveguide. At low temperatures we find an activation law for \ensuremathτsd{\ensuremath{\tau}}_{\mathrm{sd}}\ensuremathτsd​, in agreement with earlier calculations of Coulomb drag between slightly asymmetric quantum wires, but with a different and much stronger temperature dependence of the prefactor. Our results provide a fundamental input for microscopic time-dependent spin-density functional theory calculations of spin transport in one-dimensional inhomogeneous systems of interacting fermions.
Low-energy spin and charge excitations of one-dimensional interacting fermions are completely decoupled and propagate with different velocities. These modes, however, can decay due to several possible mechanisms. In this Letter we expose a new facet of spin-charge separation: not only the speeds but also the damping rates of spin and charge excitations are different. While the propagation of long-wavelength charge excitations is essentially ballistic, spin propagation is intrinsically damped and diffusive. We suggest that cold Fermi gases trapped inside a tight atomic waveguide offer the opportunity to measure the spin-drag relaxation rate that controls the broadening of a spin packet.
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.
Spin drag, the friction between interacting atoms of opposite spin, is the single relaxation mechanism of spin currents in cold atomic gases. Experiments are ongoing and one of the quantities of interest is the spin drag relaxation rate in a two-component atomic Fermi gas. Motivated by these experiments, we use the Kubo formalism to obtain an expression for the spin drag conductivity. The sunset approximation to the selfenergy is considered and a T 2 dependence of the relaxation rate is found. The effect of the BCS phase transition is studied by taking into account pair correlations with a ladder summation. Preliminary results indicate a sudden increase of the spin drag relaxation rate close to but above the critical temperature.
We consider two parallel layers of two-dimensional spin-polarized dipolar Fermi gas without any tunneling between the layers. The effective interactions describing screening and correlation effects between the dipoles in a single layer (intra-layer) and across the layers (interlayer) are modeled within the Hubbard approximation. We calculate the rate of momentum transfer between the layers when the gas in one layer has a steady flow. The momentum transfer induces a steady flow in the second layer which is assumed initially at rest. This is the drag effect familiar from double-layer semiconductor and graphene structures. Our calculations show that the momentum relaxation time has temperature dependence similar to that in layers with charged particles which we think is related to the contributions from the collective modes of the system.
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.