Mesoscopic quantum ratchets and the thermodynamics of energy selective electron heat engines

A ratchet is an asymmetric, non-equilibrated system that can produce a directed current of particles without the need for macroscopic potential gradients. In rocked quantum electron ratchets, tunnelling and wave-reflection can induce reversals in the direction of the net current as a function of system parameters.An asymmetric quantum point contact in a GaAs/GaAlAs heterostructure has been studied experimentally as a realisation of a quantum electron ratchet. A Landauer model predicts reversals in the direction of the net current as a function of temperature, amplitude of the rocking voltage, and Fermi energy.Artifacts such as circuit-induced asymmetry, also known as self-gating, were carefully removed from the experimental data, which showed net current and net differential conductance reversals, as predicted by the model. The model also predicts the existence of a heat current where the net electron current changes sign, as equal numbers of high and low energy electrons are pumped in opposite directions.An idealised quantum electron ratchet is studied analytically as an energy selective electron heat engine and refrigerator. The hypothetical device considered consists of two electron reservoirs with different temperatures and Fermi energies. The reservoirs are linked via a resonant state in a quantum dot, which functions as an idealised energy filter for electrons. The efficiency of the device approaches the Carnot value when the energy transmitted by the filter is tuned to that where the Fermi distributions in the reservoirs are equal.The maximum power regime, where the filter transmits all electrons that contribute positively to the power, is also examined. Analytic expressions are obtained for the power and efficiency of the idealised device as both a heat engine and as a refrigerator in this regime of operation. The expressions depend on the ratio of the voltage to the difference in temperature of the reservoirs, and on the ratio of the reservoir temperatures. The energy selective electron heat engine is shown to be non-endoreversible, and to operate in an analogous manner to the three-level amplifier, a laser based quantum heat engine. Implications for improving the efficiency of thermionic refrigerators and power generators are discussed