Modifications of Electron States,Magnetization, and Persistent Current in a Quantum Dot by Controlled Curvature

The thin‐layer quantization procedure is used to study the physical implications due to curvature effects on a quantum dot in the presence of an external magnetic field. Among the various physical implications due to the curvature of the system, the absence of the $m=0$ state is the most relevant one. This absence affects the Fermi energy and consequently the thermodynamic properties of the system. In the absence of magnetic fields, it is verified that the rotational symmetry in the lateral confinement is preserved in the electronic states of the system and its degeneracy concerning the harmonicity of the confining potential is broken. In the presence of a magnetic field, however, the energies of the electronic states in a quantum dot with curvature are greater than those obtained for a quantum dot in a flat space, and the profile of degeneracy changes when the field is varied. It is shown that the curvature of the surface modifies the number of subbands occupied in the Fermi energy. In the study of both magnetization and persistent currents, it is observed that Aharonov–Bohm‐type oscillations are present, whereas de Haas–van Alphen‐type oscillations are not well defined.