Transport near quantum critical points

A large number of experimental systems in two dimensions display strong crossovers in their transport properties when their conductance is close to the quantum unit of conductance, e2/h. This is usually associated with a nearby quantum-critical point. In a theoretical description of such transport, it is crucial to pay attention to the relative values of the measurement frequency, w, and the absolute temperature, kBT/h. As discussed in paper 1, the conventional perturbative computation of the conductance holds only in the phase-coherent regime, hw >> kBT. In the experimentally more relevant low frequency regime hw << kBT, the transport is dominated by collisions between the thermally excited particles, and is described by a solution of the quantum Boltzmann equation. Because of the vicinity of a quantum-critical point, the collision cross-section is universally determined by the only available energy scale, kBT, as is the density of excitations. Consequently the solution of the quantum Boltzmann equation leads to a conductance which is a universal number times e2/h.

A series of recent experiments have explored the crossovers as a function of frequency and temperature near the metal-insulator transition in an amorphous three-dimensional semiconductor: H.-L. Lee et al., Physical Review Letters 80, 4261 (1998) and Science 287, 633 (2000).


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  5. Quantum conductors in a plane, P. Phillips, S. Sachdev, S. Kravchenko, and A. Yazdani, Proceedings of the National Academy of Sciences 96, 9983 (1999); cond-mat/9902025.
  6. Quantum phase transitions in antiferromagnets and superfluids, S. Sachdev and M. Vojta, Physica B 280, 333 (2000); cond-mat/9908008.
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  8. Comment on "Critical spin dynamics of the 2D quantum Heisenberg antiferromagnets: Sr2CuO2Cl2 and Sr2Cu3O4Cl2", S. Sachdev and O.A. Starykh, cond-mat/0101394.
  9. Conductivity of thermally fluctuating superconductors in two dimensions, S. Sachdev, Proceedings of 7th International Conference on Materials and Mechanisms of Superconductivity and High Temperature Superconductors, Rio de Janeiro, May 25-30 (2003), Physica 408-410C, 218 (2004); cond-mat/0308063.
  10. Thermoelectric transport near pair breaking quantum phase transition out of d-wave superconductivity , D. Podolsky, A. Vishwanath, J. Moore, and S. Sachdev, cond-mat/0510597.
  11. Quantum critical transport, duality, and M-theory, C. P. Herzog, P. Kovtun. S. Sachdev, and D. T. Son, Physical Review D 75, 085020 (2007); hep-th/0701036.
  12. Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes, S. A. Hartnoll, P. K. Kovtun, M. Mueller, and S. Sachdev, Physical Review B 76, 144502 (2007); arXiv:0706.3215
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