Heat capacity and entropy of a GaAs quantum dot with Gaussian confinement

The heat capacity and entropy effects in a GaAs quantum dot with Gaussian confinement are calculated in the presence of a magnetic field and its interaction with the electron spin using the canonical ensemble approach. It is shown that the heat capacity shows a Schottky-like anomaly at a low temperature, while it approaches a saturation value 2k(B) as the temperature increases. As a function of the magnetic field, the heat capacity shows a maximum and then reduces to zero. Also the width of the maximum becomes wider with temperature. It is also shown that the heat capacity remains constant up to a certain value of the confinement length beyond which it displays a monotonic increase. However as a function of the confinement strength, though the heat capacity initially shows a significant drop, it remains constant thereafter. At low temperatures like T = 10 and 20 K, the entropy is found to decrease with increasing magnetic field, but at higher temperatures, it remains almost independent of the magnetic field. At high temperatures, entropy shows a monotonic increase with temperature, but at a sufficiently low temperature as the magnetic field decreases, the entropy is found to develop a shoulder which becomes more and more pronounced with decreasing magnetic field.