Non-zero temperature transport near quantum critical points

الأصل · EN

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 kB T/ℏ. This implies that the transport at frequencies ω≪ kB T/ℏ is in the hydrodynamic, collision-dominated (or `incoherent') regime, while ω≫ kB T/ℏ is the collisionless (or `phase-coherent') regime. The conductivity is argued to be e² / h times a non-trivial universal scaling function of ℏ ω/ kB T, and not independent of ℏ ω/kB T, as has been previously claimed, or implicitly assumed. The experimentally measured d.c. conductivity is the hydrodynamic ℏ ω/kB T → 0 limit of this function, and is a universal number times e² / h, even though the transport is incoherent. Previous work determined the conductivity by incorrectly assuming it was also equal to the collisionless ℏ ω/kB T → ∞ limit of the scaling function, which actually describes phase-coherent transport with a conductivity given by a different universal number times e² / 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.