Thermal and magnetic properties of cylindrical quantum dot with asymmetric confinement

Abstract

We studied the thermal and magnetic properties of a cylindrical quantum dot in the presence of external electric and magnetic fields. The energy spectrum and wave functions for the quantum dot of asymmetric confinement are obtained by solving the Schrödinger wave equation analytically. The energy levels are employed to calculate the canonical partition function, which in turn is used to obtain specific heat, entropy, magnetization, and susceptibility. These thermal and magnetic quantities are found to have direct dependence on confinement length, magnetic field, and temperature, thus the parameters of the system can be tuned to fit into more than one application. PACS Nos.: 78.40.Fy, 75.75.-c, 68.65.Hb. Résumé : Nous étudions ici les propriétés thermiques et magnétiques de points quantiques cylindriques en présence de champs électriques et magnétiques externes. Nous solutionnons analytiquement l'équation de Schrödinger pour le spectre en énergie et les fonctions d'ondes de ce point quantique de confinement asymétrique. Les énergies propres permettent de calculer la fonction de partition canonique qui nous donne la capacité calorifique, l'entropie, la magnétisation et la susceptibilité. Nous trouvons que ces quantités thermiques et magnétiques dépendent directement de la longueur de confinement, du champ magnétique et de la température et qu'ainsi les paramètres du système peuvent être accordés pour satisfaire plus d'une application. [Traduit par la Rédaction]

A comparative study on heat capacity, magnetization and magnetic susceptibility for a GaAs quantum dot with asymmetric confinement

“…It is also compared the specific heat at low temperatures as is shown in Fig. 2(b) and we found a significant deviation from our results in comparison with the results presented in the reference [35]. For example, if we turn-off the external magnetic field i.e B = 0T at temperature approximately of T = 4K our model behaves accordingly to the gas of noninteracting particles as is shown as a solid red line in the Fig.…”

“…The energy levels E 0,1,1 (solid red line), E 1,1,1 (solid black line), E 0,2,1 (blue solid line) and E 1,2,1 (solid green line) are computed from the perturbation theory (see Eq. (14)) and compared with the results (dashed lines) obtained by Gumber et al in Ref [35]. from the Eq (6)…”

“…We found that the authors in ref. [35] are erroneously concluding that this system has a paramagnetic behavior.…”

“…More recently, a variational method has applied for studying the magnetization and the singlet-triplet transition in the ground state of QD's [33,34]. Recently, Gumber et al have considered a 3D cylindrical QD in the presence of external electric and magnetic fields [35]. Particularly, the authors have found an exact solution for the canonical partition function by assuming a free particle solution for the Schrödinger equation along of the axial direction and consequently the thermal and magnetic properties of the system were computed.…”

Diamagnetic susceptibility of the electron gas in the cylindrical nanolayer

“…It was shown that the system is in a paramagnetic phase at low temperatures and weak magnetic fields, and at high temperatures and strong field the diamagnetic phase is dominating. The authors of [12] studied the thermodynamic and magnetic properties of the cylindrical QD with the asymmetrical confinement potential. In particular, it was shown that the magnetic properties of the system reveal the paramagnetic behavior of the electron gas in the QD.…”