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Non-zero temperature transport near quantum critical points | | Kedar Damle
; Subir Sachdev
; | | Date: |
21 May 1997 | | Journal: | Physical Review B 56, 8714 (1997). | | Subject: | Strongly Correlated Electrons; Statistical Mechanics; Superconductivity | cond-mat.str-el cond-mat.stat-mech cond-mat.supr-con | | Affiliation: | Yale University | | 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 $k_B T/hbar$. This implies that the transport at frequencies $omega ll k_B T/hbar$ is in the hydrodynamic, collision-dominated (or `incoherent’) regime, while $omega gg k_B T/hbar$ is the collisionless (or `phase-coherent’) regime. The conductivity is argued to be $e^2 / h$ times a non-trivial universal scaling function of $hbar omega / k_B T$, and not independent of $hbar omega/k_B T$, as has been previously claimed, or implicitly assumed. The experimentally measured d.c. conductivity is the hydrodynamic $hbar omega/k_B T o 0$ 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 $hbar omega/k_B T o infty$ 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 $epsilon=3-d$. 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. | | Source: | arXiv, cond-mat/9705206 | | Services: | Forum | Review | PDF | Favorites | |
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