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arXiv:cond-mat/0510597 · Physical Review B

Thermoelectric transport near pair breaking quantum phase transition out of d -wave superconductivity

Daniel K. Podolsky, Ashvin Vishwanath, Joel E. Moore, Subir Sachdev A

Published Jan 16, 2007• 21 citations
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Abstract

We study electric, thermal, and thermoelectric conductivities in the vicinity of a $z=2$ superconductor-diffusive metal transition in two dimensions, both in the high- and low-frequency limits. We find violation of the Wiedemann-Franz law and a dc thermoelectric conductivity $\ensuremath{\alpha}$ that does not vanish at low temperatures, in contrast to Fermi liquids. We introduce a Langevin equation formalism to study critical dynamics over a broad region surrounding the quantum critical point.

DOI
10.1103/physrevb.75.014520

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We study electric, thermal, and thermoelectric conductivities in the vicinity of a z=2z=2z=2 superconductor-diffusive metal transition in two dimensions, both in the high- and low-frequency limits. We find violation of the Wiedemann-Franz law and a dc thermoelectric conductivity \ensuremathα\ensuremath{\alpha}\ensuremathα that does not vanish at low temperatures, in contrast to Fermi liquids. We introduce a Langevin equation formalism to study critical dynamics over a broad region surrounding the quantum critical point.
Department of Physics, Harvard University, Cambridge, MA 02138(Dated: Printed February 2, 2008)We study electric, thermal, and thermoelectric conductivities in the vicinity of a z = 2superconductor-diffusive metal transition in two dimensions, both in the high and low frequencylimits. We find violation of the Wiedemann-Franz law and a dc thermoelectric conductivity α thatdoes not vanish at low temperatures, in contrast to Fermi liquids. We introduce a Langevin equationformalism to study critical dynamics over a broad region surrounding the quantum critical point.INTRODUCTION
We describe a search for renormalization group fixed points which control a second-order quantum phase transition between a dx2-y2-superconductor and some other superconducting ground state. Only a few candidate fixed points are found. In the finite temperature (T) quantum-critical region of some of these fixed points, the fermion quasiparticle lifetime is very short and the spectral function has an energy width of order kBT near the Fermi points. Under the same conditions, the thermal conductivity is infinite in the scaling limit. We thus provide simple, explicit, examples of quantum theories in two dimensions for which a purely fermionic quasiparticle description of transport is badly violated.
We define a ``hyperconductor'' to be a material whose electrical and thermal dc conductivities are infinite at zero temperature and finite at any nonzero temperature. The low-temperature behavior of a hyperconductor is controlled by a quantum critical phase of interacting electrons that is stable to all potentially gap-generating interactions and potentially localizing disorder. In this paper, we compute the low-temperature dc and ac electrical and thermal conductivities in a one-dimensional hyperconductor, studied previously by the present authors, in the presence of both disorder and umklapp scattering. We identify the conditions under which the transport coefficients are finite, which allows us to exhibit examples of violations of the Wiedemann-Franz law. The temperature dependence of the electrical conductivity, which is characterized by the parameter ${\mathrm{\ensuremath{\Delta}}}_{X}$, is a power law, $\ensuremath{\sigma}\ensuremath{\propto}1/{T}^{1\ensuremath{-}2(2\ensuremath{-}{\mathrm{\ensuremath{\Delta}}}_{X})}$ when ${\mathrm{\ensuremath{\Delta}}}_{X}\ensuremath{\ge}2$, down to zero temperature when the Fermi surface is commensurate with the lattice. There is a surface in parameter space along which ${\mathrm{\ensuremath{\Delta}}}_{X}=2$ and ${\mathrm{\ensuremath{\Delta}}}_{X}\ensuremath{\approx}2$ for small deviations from this surface. In the generic (incommensurate) case with weak disorder, such scaling is seen at high temperatures, followed by an exponential increase of the conductivity $ln\ensuremath{\sigma}\ensuremath{\sim}1/T$ at intermediate temperatures and, finally, $\ensuremath{\sigma}\ensuremath{\propto}1/{T}^{2\ensuremath{-}2(2\ensuremath{-}{\mathrm{\ensuremath{\Delta}}}_{X})}$ at the lowest temperatures. In both cases, the thermal conductivity diverges at low temperatures.
The two-dimensional Hubbard model exhibits superconductivity with d-wave symmetry even at half-filling in the presence of a next-nearest neighbor hopping. Using plaquette cluster dynamical mean-field theory with a continuous-time quantum Monte Carlo impurity solver, we reveal the non-Fermi liquid character of the metallic phase in proximity to the superconducting state. Specifically, the low-frequency scattering rate for momenta near (π, 0) varies nonmonotonically at low temperatures, and the dc conductivity is T linear at elevated temperatures with an upturn upon cooling. Evidence is provided that pairing fluctuations dominate the normal-conducting state even considerably above the superconducting transition temperature.
We consider the fluctuation conductivity in the critical region of a disorder induced quantum phase transition in layered d-wave superconductors. We specifically address the fluctuation contribution to the system’s conductivity in the limit of large (quasi-two-dimensional system) and small (quasi-three-dimensional system) separation between adjacent layers of the system. Both in-plane and c-axis conductivities were discussed near the point of insulator-superconductor phase transition. The value of the dynamical critical exponent, z = 2, permits a perturbative treatment of this quantum phase transition under the renormalization group approach. We discuss our results for the system conductivities in the critical region as function of temperature and disorder.
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