Topological phase transition in quantum-heat-engine cycles

We explore the signatures of a topological phase transition (TPT) in the work and efficiency of a quantum heat engine, which uses a single-layer topological insulator, stanene, in an external electric field as a working substance. The magnitude of the electric field controls the trivial and topological insulator phases of the stanene. The effect of the TPT is investigated in two types of thermodynamic cycles, with and without adiabatic stages. We examine a quantum Otto cycle for the adiabatic case and an idealized Stirling cycle for the nonadiabatic case. In both cycles, investigations are done for high and low temperatures. It is found that the Otto cycle can distinguish the critical point of the TPT as an extremum point in the work output with respect to applied fields at all temperatures. The Stirling cycle can identify the critical point of the TPT as the maximum work point with respect to the applied fields only at relatively lower temperatures. As temperatures increase toward room temperature, the maximum work point of the Stirling cycle shifts away from the critical point of the TPT. In both cycles, increasing the temperature causes considerable enhancement in work and efficiency from the order of meV to eV.