Is Einstein's relation D = ukT always true?

[ppguo]

Hey,
I am trying to understand electron transport in 2D semiconductors. One question keeps lingering in my mind is whether the Einstein relation holds for these 2D materials. The only literature I can find is back to 1997 (http://arxiv.org/ftp/arxiv/papers/1004/1004.1717.pdf). The author proposed one situation that Einstein Relation may not hold: electron transport in fluid particles.
Any thought about this is appreciated!

 

[Henryk]

The Einstein relation holds true for non-degenerate charged gas system. By non-degenerate I mean system obeying Boltzmann distribution, that is n~ exp(-eV/kT). Combine that with the flux equation J = -e⋅n⋅∇V - D∇n and, in equilibrium, J =0. That gives you the Einstein relation.
If the system is degenerate (i.e. obeys Fermi-Dirac statistics), the relation may not hold true.