  We study a 2D mesoscopic ring with an anisotropic effective mass considering
surface quantum confinement effects. Consider that the ring is defined on the
surface of a cone, which can be controlled topologically and mapped to the 2D
ring in flat space. We demonstrate through numerical analysis that the
electronic properties, the magnetization, and the persistent current undergo
significant changes due to quantum confinement and non-isotropic mass. We
investigate these changes in the direct band gap semiconductors SiC, ZnO, GaN,
and AlN. There is a plus (or minus) shift in the energy sub-bands for different
values of curvature parameter and anisotropy. Manifestations of this nature are
also seen in the Fermi energy profile as a function of the magnetic field and
in the ring width as a function of the curvature parameter. Aharonov-Bohm (AB)
and de Haas van-Alphen (dHvA) oscillations are also studied, and we find that
they are sensitive to variations in curvature and anisotropy.
