Super-statistical description of thermo-magnetic properties of a system of 2D GaAs quantum dots with gaussian confinement and Rashba spin-orbit interaction

TL;DR

This paper uses superstatistics to analyze the thermo-magnetic properties of 2D GaAs quantum dots with Rashba spin-orbit interaction, revealing how non-equilibrium temperature fluctuations affect specific heat and magnetic susceptibility.

Contribution

It introduces a superstatistical framework to study thermo-magnetic properties of quantum dots, highlighting the effects of temperature fluctuations and subsystem number on physical observables.

Findings

Disappearance of Schottky anomaly with fewer subsystems

Suppression of paramagnetic phase transition due to temperature fluctuations

Recovery of standard properties when thermal distribution is sharply peaked

Abstract

We examine the effect of non-equilibrium processes modeled by the introduction of a generalized Boltzmann factor on the thermal and magnetic properties of an array of two-dimensional GaAs quantum dots in the presence of an external uniform and constant magnetic field. The model consists of a single-electron subject to a confining Gaussian potential with a spin-orbit interaction in the Rashba approach. We compute the specific heat and the magnetic susceptibility within the formalism of $\chi^2$-superstatistics from the exact solution of the Schr\"odinger equation. Furthermore, an analytic solution for the partition function allows a study of the impact of the number of subsystems on the superstatistical corrections and confirms that the ordinary thermo-magnetic properties are recovered whenever the thermal distribution can be approximated by a Dirac delta. Also, we found a progressive disappearance of the Schottky anomaly with decreasing number of subsystems, while the specific heat ceases to be a monotonically increasing function with respect to the average temperature when the $\chi^2$-distribution is spread over a large range of temperatures. Remarkably, the introduction of fluctuations in the temperature is found to suppress the paramagnetic phase transition that would otherwise appear at low temperatures. Finally, we emphasize that an appropriate construction of the definition of physical observables is crucial for obtaining a correct description of the physics derived from a non-extensive construction of the entropy.