1306.0826 (Robert S. Whitney)

The best quantum thermoelectric at finite power output    [PDF]

Robert S. Whitney

A thermoelectric device (heat-engine or refrigerator) can have Carnot efficiency if it is reversible, however this means it has a vanishingly small power output. For finite power output, what is the optimal irreversible device? What is the maximum efficiency possible at given power output? Using a nonlinear scattering theory, we answer these questions for thermoelectric quantum systems - nanostructures or molecules exhibiting Peltier effects. Maximum efficiency at given power output occurs when the system's transmission distribution is a top-hat function of energy, whose position and width are given by self-consistency conditions. Unlike Carnot efficiency, this maximum finite-power efficiency is explicitly quantum (hbar-dependent). Quantum mechanics places an upper bound on power output, and the efficiency depends on the ratio of the power output to this quantum bound. For a small ratio, the efficiency is that of Carnot minus a term that goes like the square-root of the ratio. The suppression of efficiency by (nonlinear) phonon and photon effects is also calculated.

View original: http://arxiv.org/abs/1306.0826