Nonlinear thermoelectricity in point-contacts at pinch-off: a   catastrophe aids cooling
  We consider refrigeration and heat engine circuits based on the nonlinear thermoelectric response of point-contacts at pinch-off, allowing for electrostatic interaction effects. We show that a refrigerator can cool to much lower temperatures than predicted by the thermoelectric figure-of-merit ZT (which is based on linear-response arguments). The lowest achievable temperature has a discontinuity, called a fold catastrophe in mathematics, at a critical driving current I=I_c. For I >I_c one can in principle cool to absolute zero, when for I<I_c the lowest temperature is about half the ambient temperature. Heat back-flow due to phonons and photons stop cooling at a temperature above absolute zero, and above a certain threshold turns the discontinuity into a sharp cusp. We also give a heuristic condition for when an arbitrary system's nonlinear response means that its ZT ceases to indicate (even qualitatively) the lowest temperature to which the system can refrigerate. 
Robert S. Whitney
cond-mat.mes-hall