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, e^{2}/h. This is usually associated
with a nearby quantumcritical 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,
k_{B}T/h. As discussed in paper 1, the conventional perturbative computation
of the conductance holds only in the phasecoherent regime, hw
>> k_{B}T. In the experimentally more relevant low frequency regime
hw << k_{B}T, 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 quantumcritical point, the collision crosssection is universally
determined by the only available energy scale, k_{B}T, as is the density of excitations.
Consequently the solution of the quantum Boltzmann equation leads to a conductance which is
a universal number times e^{2}/h.
A series of recent experiments have explored the crossovers as a function of frequency and temperature
near the metalinsulator transition in an amorphous threedimensional semiconductor:
H.L. Lee et al., Physical Review Letters 80, 4261 (1998) and Science 287, 633 (2000).
PAPERS

Nonzero temperature transport near quantum critical
points, K. Damle and S. Sachdev, Physical Review B 56, 8714
(1997); condmat/9705206.

Nonzero temperature transport near fractional quantum
Hall critical points, S. Sachdev, Physical Review B 57, 7157
(1998); condmat/9709243.

Dynamics and transport near quantumcritical 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); condmat/9705266.

Thermally fluctuating superconductors in two dimensions,
S. Sachdev and O. Starykh, Nature 405, 322 (2000); condmat/9904354.

Quantum conductors in a plane, P. Phillips, S. Sachdev,
S. Kravchenko, and A. Yazdani, Proceedings of the National Academy of Sciences
96,
9983 (1999); condmat/9902025.

Quantum phase transitions in antiferromagnets and
superfluids, S. Sachdev and M. Vojta, Physica B 280, 333
(2000); condmat/9908008.

Quantum criticality: competing ground states in low
dimensions, S. Sachdev, Science 288, 475 (2000); condmat/0009456.

Comment on "Critical spin dynamics of the 2D quantum Heisenberg antiferromagnets: Sr_{2}CuO_{2}Cl_{2} and Sr_{2}Cu_{3}O_{4}Cl_{2}", S. Sachdev and O.A. Starykh, condmat/0101394.

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 2530 (2003), Physica 408410C, 218 (2004); condmat/0308063.
 Thermoelectric transport near pair breaking quantum phase transition out of dwave superconductivity , D. Podolsky, A. Vishwanath, J. Moore, and S. Sachdev,
condmat/0510597.
 Quantum critical transport, duality, and Mtheory,
C. P. Herzog, P. Kovtun. S. Sachdev, and D. T. Son, Physical Review D 75, 085020 (2007);
hepth/0701036.
 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
 Quantum criticality and black holes,
S. Sachdev and M. Müller, Journal of Physics: Condensed Matter 21, 164216 (2009);
arXiv:0810.3005.
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