Thermodynamic Properties of a Double Ring-Shaped Quantum Dot at Low and High Temperatures

In this work, we study thermodynamic properties of a GaAs double ring-shaped quantum dot under external magnetic and electric fields. To this end, we first solve the Schrodinger equation and obtain the energy levels and wave functions, analytically. Then, we calculate the entropy, heat capacity, average energy and magnetic susceptibility of the quantum dot in the presence of a magnetic field using the canonical ensemble approach. According to the results, it is found that the entropy is an increasing function of temperature. At low temperatures, the entropy increases monotonically with raising the temperature for all values of the magnetic fields and it is independent of the magnetic field. But, the entropy depends on the magnetic field at high temperatures. The entropy also decreases with increasing the magnetic field. The heat capacity and magnetic susceptibility show a peak structure. The heat capacity reduces with increasing the magnetic field at low temperatures. The magnetic susceptibility shows a transition between diamagnetic and paramagnetic below for . The transition temperature depends on the magnetic field.