Collision-dominated spin transport in graphene and Fermi liquids

Abstract

In a clean Fermi liquid, due to spin up/spin down symmetry, the dc spin current driven by a magnetic field gradient is finite even in the absence of impurities. Hence, the spin conductivity σs assumes a well-defined collisiondominated value in the disorder-free limit, providing a direct measure of the inverse strength of electron-electron interactions. In neutral graphene, with Fermi energy at the Dirac point, the Coulomb interactions remain unusually strong, such that the inelastic scattering rate comes close to a conjectured upper bound Τ?1inel ≲ kBT/ℏ, similar to the case of strongly coupled quantum critical systems. The strong scattering is reflected by a minimum of spin conductivity at the Dirac point, where it reaches σ s = 0.121/α2 μ 2s ℏ at weak Coulomb coupling α μ ≈ μB being the magnetic moment of the electronic spins. Up to the replacement of quantum units, e2/ℏ → μs ℏ this result equals the collisiondominated electrical conductivity obtained previously. This accidental symmetry is, however, broken to higher orders in the interaction strength. For gated graphene and two-dimensional metals in general, we show that the transport time is parametrically smaller than the collision time. We exploit this fact to compute the collision-limited σs analytically as σs = 1/C(μ/T) 2 μ 2s/ℏ with C = 4π2α2[2/31n(1/2α-1) for weak Coulomb coupling α. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.