We study the model of a noninteracting spinless electron gas confined to the two-dimensional localized surface of a cone in the presence of external magnetic fields. The localized region is characterized by an annular radial potential. We write the Schrödinger equation and use the thin-layer quantization procedure to calculate the wavefunctions and the energy spectrum. In such a procedure, it arises a geometry induced potential, which depends on both the mean and the Gaussian curvatures. Nevertheless, since we consider a ring with a mesoscopic size, the effects of the Gaussian curvature on the energy spectrum are negligible. The magnetization and the persistent current are analyzed. In the former, we observed the Aharonov-Bohm (AB) and de Haas-van Alphen (dHvA) types oscillations. In the latter, it is observed only the AB type oscillations. In both cases, the curvature increases the amplitude of the oscillations.

我们研究了在存在外部磁场的情况下，局限于锥的二维局部表面的非相互作用的无旋转电子气体的模型。局部区域的特征在于环形的径向电势。我们编写薛定ding方程，并使用薄层量化程序来计算波函数和能谱。在这种过程中，产生了几何感应电势，该电势既取决于均值曲率，也取决于高斯曲率。然而，由于我们考虑了具有介观尺寸的环，因此高斯曲率对能谱的影响可以忽略不计。分析了磁化强度和持续电流。在前者中，我们观察到了Aharonov-Bohm（AB）和de Haas-van Alphen（dHvA）类型的振荡。在后者中，仅观察到AB型振荡。