Study on the effects of anisotropic effective mass on electronic properties, magnetization and persistent current in semiconductor quantum ring with conical geometry

TL;DR

This work addresses how curvature and anisotropic effective mass influence the electronic, magnetic, and transport properties of semiconductor quantum rings. By modeling a 2D ring on a conical surface with a geometric potential $V_S$ and solving the Schrödinger equation with an AB flux and a confining radial potential, the authors obtain structured energy spectra $E_{n,m}$ and wavefunctions $\chi_{n,m}$ and compute thermodynamic and transport quantities including the Fermi energy, magnetization, and persistent current. They show that the curvature parameter $\alpha$ and the mass anisotropy ratio $R$ shift subband bottoms, modulate the subband spacing via $\omega=\sqrt{\omega_0^2+(\alpha\omega_c)^2}$, and suppress AB and dHvA oscillations while enabling tunable ring width $\Delta r$ and orbital gaps. The results highlight design knobs for tailoring mesoscopic ring properties and offer insights for spin qubit robustness in curved semiconductor nanostructures, using materials with known $R$ values such as SiC, ZnO, GaN, and AlN.

Abstract

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.

Figures (13)

• Figure 1: Representation of the Fermi surfaces for different values of $R$ parameter. Spherical ($R=1$), oblate spheroid ($R>1$), prolate spheroid ($R<1$).
• Figure 2: Plot of the parametric equation (\ref{['conic01']}). Representation of a flat surface ($\alpha=1$) being transformed into a conical one by decreasing the $\alpha$ parameter to $0.9$, $0.7$ and $0.5$.
• Figure 3: Conical ring-shaped with a superconducting solenoid passing through its center and immersed in a uniform magnetic field $\mathbf{B}=B\hat{z}$. Because of the conical shape of the surface, the magnetic field $B$ is no longer parallel to the vector $\mathbf{N}$. $r_{-}$ and $r_{+}$ are the internal and external radius of the ring, respectively, and are measured from the idealized apex of the cone.
• Figure 4: Subbands of the system as a function of the $m$ quantum number for different magnetic field strength and curvature values cases. According to Table 1, we apply the anisotropic ratios $R$ corresponding to the SiC and AlN semiconductors.
• Figure 5: Energy of the states as a function of $B$. Frontiers between two color regions outline a subband minimum: for instance, the subband minimum for $n=1$ is the frontier between green and red regions.