For background:

In a $D=2+1$ state with edge modes described by a chiral $( c_L \neq c_R )$ CFT there is a predicted thermal Hall conductance associated with the gravitational anomaly at the edge. This is the case for integer and some fractional quantum hall systems. For just free bosons on the edge the conductance is proportional to the difference in number between left and right movers as well as the temperature: $K_H \propto (c_L - c_R) T$

This seems like the sort of thing someone with a lab and a fancy set of probes might be able to measure. What's the state of experimental progress in this direction?

I'm familiar with a paper by Kane and Fisher which describes the difficulty a bit and proposes an experimental set-up but since the paper is almost 20 years old I was curious about the modern state of things. A review of some of the physics that goes into making this measurement would be appreciated!


1 Answer 1


The experiment on kxy has not been done yet, to my knowledge, but there are several (recent) experiments which are closely related and probe the heat flow through the edge channels of a Hall bar in the fractional regime: http://www.nature.com/nature/journal/v466/n7306/abs/nature09277.html or http://www.nature.com/nphys/journal/v8/n9/full/nphys2384.html?WT.ec_id=NPHYS-201209 are two examples. Measuring temperatures on a 2D sheet of material embedded in a substrate (as in GaAs/GaAlAs heterostructures) is a challenging task, and the signals for kxy are usually smaller than the ones for "simple" kxx measurements.

  • $\begingroup$ Hi user56622, can you say what "kxy" and "kxx" is in your answer? $\endgroup$ Aug 4, 2014 at 6:56
  • $\begingroup$ thermal conductivity kxx, thermal hall conductivity kxy. for temperature gradient del T and heat current density j_Q, the (tensor) relation is j_Q = k del T with k = (kxx kxy // kyx kxx) the conductivity matrix. $\endgroup$
    – user56622
    Aug 4, 2014 at 7:03

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