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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Dynamics and transport near quantum-critical points,
S. Sachdev, Dynamical properties of unconventional magnetic systems,
A. Skjeltorp and D. Sherrington eds., NATO ASI Series E: Applied Sciences,
vol 349, Kluwer Academic, Dordrecht (1997); cond-mat/9705266.
Thermally fluctuating superconductors in two dimensions,
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S. Kravchenko, and A. Yazdani, Proceedings of the National Academy of Sciences
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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.
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