Non-zero temperature transport near quantum critical points

Kedar Damle; Subir Sachdev

doi:10.1103/PhysRevB.56.8714

paper

Non-zero temperature transport near quantum critical points

arXiv:cond-mat/9705206 · doi:10.1103/PhysRevB.56.8714

Abstract

We describe the nature of charge transport at non-zero temperatures ( $T$ ) above the two-dimensional ( $d$ ) superfluid-insulator quantum critical point. We argue that the transport is characterized by inelastic collisions among thermally excited carriers at a rate of order $k_{B} T /ℏ$ . This implies that the transport at frequencies $ω ≪ k_{B} T /ℏ$ is in the hydrodynamic, collision-dominated (or `incoherent') regime, while $ω ≫ k_{B} T /ℏ$ is the collisionless (or `phase-coherent') regime. The conductivity is argued to be $e^{2} / h$ times a non-trivial universal scaling function of $ℏ ω / k_{B} T$ , and not independent of $ℏ ω / k_{B} T$ , as has been previously claimed, or implicitly assumed. The experimentally measured d.c. conductivity is the hydrodynamic $ℏ ω / k_{B} T \to 0$ limit of this function, and is a universal number times $e^{2} / h$ , even though the transport is incoherent. Previous work determined the conductivity by incorrectly assuming it was also equal to the collisionless $ℏ ω / k_{B} T \to \infty$ limit of the scaling function, which actually describes phase-coherent transport with a conductivity given by a different universal number times $e^{2} / h$ . We provide the first computation of the universal d.c. conductivity in a disorder-free boson model, along with explicit crossover functions, using a quantum Boltzmann equation and an expansion in $ε = 3 - d$ . The case of spin transport near quantum critical points in antiferromagnets is also discussed. Similar ideas should apply to the transitions in quantum Hall systems and to metal-insulator transitions. We suggest experimental tests of our picture and speculate on a new route to self-duality at two-dimensional quantum critical points.

Feedback incorporated into numerous clarifying remarks; additional appendix discusses relationship to transport in dissipative quantum mechanics and quantum Hall edge state tunnelling problems, stimulated by discussions with E. Fradkin

Non-zero temperature transport near quantum critical points

Abstract

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