Two-dimensional pair-interacting hole gas thermodynamics: Exactly solvable Moshinsky model for lens-shaped quantum dots

The thermodynamic characteristics of a pair-interacting hole gas localized in a Ge/Si lens-shaped quantum dot are studied. The pair-interaction potential is modeled by the oscillator function, which depends on the distance between the particles. The analytical form of the spectra makes it possible to calculate the partition function in Boltzmann approximation. Based on the partition function mean and free energies, heat capacity and entropy of the interacting gas are calculated. Interaction between particles substantially changes the behavior of the thermodynamic properties in comparison with the non-interacting gas case. In particular, the gas undergoes a first-order phase transition driven by the height of the upper (or lower) section of QD, resulting in a changing symmetry of the lens-shaped QD. •The thermodynamic parameters of a pair-interacting holes gas in a Ge/Si lens-shaped quantum dot are studied.•An exact form of the partition function for the heavy holes gas in a quantum dot is obtained.•Entropy and heat capacity of the pair-interacting gas are calculated in Boltzmann approximation.•A first-order phase transition driven by the change of height of the upper (or lower) section of QD is found.