Role of spin-orbit interactions on the entropy and heat capacity of a quantum dot helium placed in an external magnetic field

The effects of Rashba, Dresselhaus and Coulomb interactions on the entropy and heat capacity of a two-electron quantum dot placed in an external magnetic field are studied at finite temperature. The effect of electron-electron interaction is studied by using the Johnson-Payne harmonic model which is exactly soluble, while the Rashba and Dresselhus spin-orbit coupling effects are dealt with using unitary transformations. It is observed that as a function of the magnetic field, the heat capacity has a double peak structure with the minima between the peaks occurring at the singlet-triplet transition point and the e-e interaction shifts the peaks to lower magnetic fields. It is also observed that the coulomb correlation reduces the heat capacity in the low temperature regime while in the high temperature regime it enhances it. Interestingly, however, in the high field regime, the heat capacity does not seem to be influenced by the electron-electron interaction. The entropy is found to show a single peak as a function of magnetic field at the singlet-triplet transition point. The Rashba spin-orbit interaction reduces the heat capacity and the Dresselhaus interaction enhances it whereas the opposite effect is exhibited by the entropy. The temperature behaviour of both the entropy and heat capacity clearly demonstrates the effect of zero field spin-splitting.