Abstract
The thermal and magnetic properties of a parabolic GaAs quantum dot for two-Harmonically interacting electrons when it exposed to an external magnetic field, taking into account the spin-Zeeman energy are investigated using the canonical ensemble approach. The effect of spin on these properties is also investigated. With the possibility of a basic and physically sensible model of electron-electron interaction, the issue is precisely soluble. We found a Schottky-like anomaly in the heat capacity at low temperature, while it saturates to the 4kB value as the temperature increases. Also it is noted that entropy enhances with temperature as expected. However as a function of a magnetic field, a peak structure is observed in heat capacity at very low values of magnetic field, while it saturates to the 2kB value as magnetic field increases. Also we noticed that these peaks are not presented in the spinless case. Moreover magnetic field does not show a significant effect on the entropy at high temperatures, but at relatively lower temperatures, the entropy shows a monotonic increase with magnetic field. As a function of the Lande g* factor, we found a local minima and a double peak-structure in the susceptibility and in the heat capacity at g*=0. It is demonstrated that the favored state for both magnetization and susceptibility is the diamagnetic state. The significant effect of the spin on the magnetic properties of quantum dot is seen at low values of temperature and magnetic field. Moreover, our results showed a very good agreement with reported previous works.
Highlights
For more than two decades the research area of quantum dots has attracted great attention (Ashoori, 1996; Johnson, 1995; Kastner, 1992; Woggon, 1997; Jacak, Hawrylack, & Wojs, 1998; Bimberg, Grundmann, & Ledentsov, 1998; Mukhopadhyay & Chatterjee, 2001; Kouwenhoven, Austing, & Tarucha, 2001; Haddad, Nammas, Al Shorman, & Shukri, 2017)
We obtained the energy spectrum of the system in closed form by solving Schrodinger equation analytically and we find heat capacity, entropy, magnetization and susceptibility using the canonical ensemble approach
As a function of temperature, it was demonstrated that the heat capacity exhibits a peak structure at a very low temperature, while at high temperature it saturates to the value of 4kB and it was noted that the spin increases heat capacity only at low temperature and at high magnetic field
Summary
For more than two decades the research area of quantum dots has attracted great attention (Ashoori, 1996; Johnson, 1995; Kastner, 1992; Woggon, 1997; Jacak, Hawrylack, & Wojs, 1998; Bimberg, Grundmann, & Ledentsov, 1998; Mukhopadhyay & Chatterjee, 2001; Kouwenhoven, Austing, & Tarucha, 2001; Haddad, Nammas, Al Shorman, & Shukri, 2017). The generalized Kohn theorem together with magneto-optical experiments (Sikorski & Merkt, 1989; Karrai, Drew, Lee, & Shayengan, 1989) have proposed that the confinement potential in a QD is less or pretty much parabolic (Peeters, 1990; Yip, 1991; Li, Karrai, Yip, Sarma, & Drew, 1991). This has leads to a hot pace action in the field of QD's (Maksym & Chakraborty, 1990; Gu & Guo, 1993; Johnson & Payne, 1992; Mukhopadhyay & Chatterjee, 1996; Mukhopadhyay & Chatterjee, 1997). Many analytical methods and numerical approximations have been adopted to explore and study a multi-electrons QD problem
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