Magnetocaloric Effect in Non-Interactive Electron Systems: “The Landau Problem” and Its Extension to Quantum Dots

Abstract

Abstract:In this work, we report the magnetocaloric effect (MCE) in two systems of non-interactive particles: the first corresponds to the Landau problem case and the second the case of an electron in a quantum dot subjected to a parabolic confinement potential. In the first scenario, we realize that the effect is totally different from what happens when the degeneracy of a single electron confined in a magnetic field is not taken into account. In particular, when the degeneracy of the system is negligible, the magnetocaloric effect cools the system, while in the other case, when the degeneracy is strong, the system heats up. For the second case, we study the competition between the characteristic frequency of the potential trap and the cyclotron frequency to find the optimal region that maximizes the ∆T of the magnetocaloric effect, and due to the strong degeneracy of this problem, the results are in coherence with those obtained for the Landau problem. Finally, we consider the case of a transition from a normal MCE to an inverse one and back to normal as a function of temperature. This is due to the competition between the diamagnetic and paramagnetic response when the electron spin in the formulation is included.

Magnetocaloric Effect in an Antidot: The Effect of the Aharonov-Bohm Flux and Antidot Radius

“…Therefore, this result allows to control the size of the magnetocaloric response (i.e., the peak) with the parameter of the present model. For the case of the quantum dot with spin, in reference [ 41 ], the oscillation of the MCE is destroyed for higher values of and only direct MCE is obtained. Here, we find that the peak of the direct MCE increases without suppressing the oscillations of the MCE.…”

“… Upper row: Specific heat, magnetization and entropy for a quantum dot without intrinsic spin for our numerical calculations using the parameters and in Equation ( 6 ). The inset images correspond to the exact calculations obtained in the Reference [ 41 ] for the same observables. We clearly observe a very good convergence of numerical results.…”

“…Lower row: Specific heat, magnetization and entropy for the case of antidot with and . The inset images correspond to the exact calculations obtained in the Reference [ 41 ] for the case of an electron in a dot with an intrinsic spin. We observe here similar behaviour at low temperatures for the thermodynamics observables displayed.…”

“…We can see in the lower row of Figure 2 similar behaviour for the thermodynamics observables displayed for the cases of an electron in a dot with an intrinsic spin and an antidot with the presence of Aharonov-Bohm flux. The MCE effect of the dots with intrinsic spin is fully treated in the Reference [ 41 ] and shows that the inclusion of Zeeman term in the formulation produces an oscillatory response of the magnetocaloric observables. Therefore, similar behaviour in the principal thermodynamics quantities for the Bogachek and Landman model is found in our work, making the antidot an interesting candidate for the study of the MCE effect of oscillatory type.…”

“…Therefore, electrons are trapped in 2D space, where a magnetic field along z -axis can be applied [ 40 ]. A natural extension of the work [ 41 ] corresponds to the study of the magnetocaloric response for an ensemble of antidots. In simple words, an antidot is a potential hill inaccessible to 2D electrons [ 42 , 43 , 44 , 45 , 46 , 47 ].…”