Polaronic corrections on magnetization and thermodynamic properties of electron-electron in 2D systems with Rashba spin-orbit coupling

Magnetic and thermodynamic properties of two electron system confined in 2-D quantum structures submitted to an applied magnetic field are studied taking into account the spin-orbit and electron-phonon interactions. The confinement is considered as a harmonic potential and the electron-electron interaction is taken as coulombic. We have first solved the Schrodinger equation to obtain energy levels and then obtain all the thermodynamic functions using canonical ensemble. The numerical calculation of our formalism is applied essentially for the GaN and InAs which are (III-V) compounds. Our results show that even at B = 0 T, the susceptibility of GaN shows diamagnetic behavior for all temperatures. However, with an increase in the magnetic field, susceptibility increases and the system shows paramagnetic behavior for both cases associated with and without polaron effect. We demonstrate that taking into account the Rashba spin-orbit interaction leads to a shift of the cutoff magnetic field Bc (value of B for which the magnetic nature of the dot changes from diamagnetic to paramagnetic) to the higher magnetic field with an increase in temperature. We also show that by taking into account the polaronic effect, Rashba spin-orbit interaction lowers the mean energy of the system. The heat capacity curve shows a peak at a low temperature (Schottky anomaly) and shifts toward high temperature with an increase in confinement and magnetic field strength. The consideration of the polaron effect shifts the heat capacity curve to lower temperatures.