Solvable Model of the Thermal Persistent Current at Low Temperatures of Two-Electron Parabolic GaAs Quantum Dot

Abstract

We have studied analytically the persistent current and the magnetization of two electrons trapped by a circular parabolic GaAs quantum dot using the canonical ensemble approach. We have investigated their behavior as a function of the dot size and magnetic field in the presence and the absence of the harmonic e-e interaction at high and low temperatures. Our investigations reveal that the diamagnetic state is the preferred state for the persistent current and magnetization. As a function of the dot size, initially the current is entirely independent of the interaction and it remains constant up to a certain value of the dot size beyond which it increases significantly and the effect of the harmonic interaction becomes tangible in the low-temperature limit. However as a function of the magnetic field at high temperatures, the current takes a diminishing linear form and this decrease is noticeable for narrower dots, but at extremely low temperatures, the current becomes insensitive to the interaction for a dot with small size. As a function of temperature, the current increases sharply with temperature and then tends to saturate as the temperature becomes slightly larger. This study demonstrates a comparison between the current and the magnetization. Our results show that, as a function of temperature, they qualitatively exhibit the same behavior and they are proportional to each other in the presence of weak magnetic field, while as a function of the magnetic field, they display non-similar behavior at low temperatures.

Modification of Landau Levels in a 2D Ring Due to Rotation Effects and Edge States

“…For states located far from the edges, that is, those with large values of r a − r m compared to the magnetic length 𝜆 1 , Equation (23) provides sin 𝜋𝜈 = 0 (24) which means that 𝜈 = n = 0, 1, 2 …. In this way, we recover the result obtained at the beginning of this section, namely that states located inside the ring but far from the edges, where the confinement potential does not influence the electronic states, the energy eigenvalues are given by Equation ( 16).…”

“…[12,13] Persistent currents have been detected on metallic rings [14,15] and in experiments on a semiconductor ring in the GaAs/GaAIAs system. [16] Here, we are interested in magnetization, [17][18][19][20][21][22][23] which is proportional to the persistent current in a single-isolated ring. [14][15][16][17]24] In the 2DEG bulk case Landau, and at zero temperature, the magnetization has sharp saw-tooth oscillations with a constant amplitude.…”

Structural modifications of two-electron systems under isotropic harmonic confinement

“…This idea was first exploited in the two-electron systems by Kestner and Sinanoglu [16] as an attempt to understand the electron correlation. Since then several studies are carried out on various aspects of such systems [11][12][13][14][17][18][19][20][21][22][23][24][25][26][27]. Taut [18] obtained an analytic solution of two electrons in harmonic-oscillator potential that can lead to the analytical solution of the two-electron quantum dot for some specific cases with a discrete frequency.…”

“…A useful list of references on such systems is also given there [14]. The application of harmonic-oscillator potential in quantum dots has also gained considerable attention among researchers [24][25][26]. Hartree-Fock and configuration interaction approaches were adopted by Olav et al [24] for two-electron systems trapped in a harmonic quantum dot with different confinement conditions.…”

“…Caicedo-Ortiz et al [25] studied the effects of pressure on the energy levels of a single-electron quantum dot which is modeled using an infinite potential well and a two-dimensional harmonic oscillator and solved using the second quantization formalism. Nammas [26] carried out analytical calculation of the persistent current and the magnetization of two electrons trapped by a circular parabolic GaAs quantum dot using canonical ensemble approach. Optical atom trapping potentials may be periodic or arbitrarily shaped in optical lattices but the bottom of such potential wells can be approximated by a harmonic potential [28].…”