Nonlinear thermoelectricity in point contacts at pinch off: A catastrophe aids cooling

I consider refrigeration and heat engine circuits based on the nonlinear thermoelectric response of point contacts at pinch off, allowing for electrostatic interaction effects. I 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 backflow due to phonons and photons stops cooling at a temperature above absolute zero, and above a certain threshold turns the discontinuity into a sharp cusp. I 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.