We explore 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 TPT is investigated in two types of thermodynamic cycles, with and without adiabatic stages. We examine a quantum Otto cycle for the adiabatic and an idealized Stirling cycle for the non-adiabatic case. In both cycles, investigations are done for high and low temperatures. It is found that 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. 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 towards the room temperature 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.

In this study, we have explored new structures which are derived from stanene. In these new proposed structures, half of the Sn atoms, every other Sn atom in two-dimensional (2D) buckled hexagonal stanene structure, are replaced with a group-IV atom, namely C, Si or Ge. So, we investigate the structural, electronic and optical properties of SnC, SnGe and SnSi by means of density functional theory based firstprinciples calculations. Based on our structure optimization calculations, we conclude that while SnC assumes almost flat structure, the other ones have buckled geometry like stanene. In terms of the cohesive energy, SnC is the most stable structure among them. The electronic properties of these structures strongly depend on the substituted atom. We found that SnC is a large indirect band gap semiconductor, but SnSi and SnGe are direct band gap ones. Optical properties are investigated for two different polarization of light. In all structures considered in this study, the optical properties are anisotropic with respect to the polarization of light. While optical properties exhibit features at low energies for parallel polarization, there is sort of broad band at higher energies after 5 eV for perpendicular polarization of the light. This anisotropy is due to the 2D nature of the structures.

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We investigate a heat engine with a finite-length Kitaev chain in an ideal Otto cycle. It is found that the critical point of the topological phase transition coincides with the maxima of the efficiency and work output of the total Otto engine. Finite-size effects are taken into account using the method of Hill's nanothermodynamics, as well as using the method of temperature-dependent energy levels. We identify the bulk and boundary thermal cycles of the Kitaev chain engine and find that they are nonideal Otto cycles. The physics of deviation from ideal Otto cycle is identified as a finite-size effect, which we dub as "internal geometric friction," leading to heat transfer from the bulk to the boundary during the adiabatic transformation of the whole system. In addition, we determine the regimes allowing for independently running an ideal Otto refrigerator at the boundary and ideal Otto engines in the bulk and in the whole system. Furthermore, we show that the first-order phase transition in the boundary and the second-order phase transition in the bulk can be identified through their respective contributions to the engine work output.