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.