Magnetoresistance and electric current oscillations induced by geometry in a two-dimensional quantum ring

TL;DR

This paper analyzes a GaAs two-dimensional quantum ring with conical geometry to understand how curvature modulates electric transport. By adapting the Landauer formalism for resonant tunneling and incorporating a curvature-induced geometric potential, the authors quantify changes in conductance, Van-Hove singularities, and AB oscillations as functions of the curvature parameter $\alpha$ and magnetic field $B$. Key findings include an increased AB period $p_0/\alpha^2$, reduced density of states per energy, and curvature-enhanced magnetoresistance oscillations, as well as voltage-driven current behaviors that exhibit Ohm's law at low bias and saturation at high bias with a curvature-dependent response. The results suggest that geometry alone can tune electron transport in mesoscopic rings, enabling geometry-based optimization of device performance in quantum circuits.

Abstract

In this work, we investigate the effects of a controlled conical geometry on the electric charge transport through a two-dimensional quantum ring weakly coupled to both the emitter and the collector. These mesoscopic systems are known for being able to confine highly mobile electrons in a defined region of matter. In particular, we consider a GaAs device having an average radius of $800\hspace{0.05cm}\text{nm}$ in different regimes of subband occupation at non-zero temperature and under the influence of a weak and uniform background magnetic field. Using the adapted Landauer formula for the resonant tunneling and the energy eigenvalues, we explore how the modified surface affects the Van-Hove conductance singularities, the magnetoresistance interference patterns resulting from the Aharonov-Bohm oscillations of different frequencies and the charge transport when an electric potential is applied in the terminals of the device. Magnetoresistance and charge current oscillations depending only on the curvature intensity are reported, providing a new feature that represents an alternative way to optimize the transport through the device by tuning its geometry.

Figures (16)

• Figure 1: (a) (Color online) Schematic illustration in an upper view of the weakly coupled ring model used in this work, adapted from PhysRevB.53.6947. (b) A side view of the model highlights the conical geometry of the ring surface for $\alpha<1$. The origin is set on the virtual apex of the conical surface defined by the ring.
• Figure 2: (Color online) Energy eigenvalues of the quantum ring near $\epsilon_{f}=0.5\space\text{meV}$ as a function of the magnetic field $B$ for flat (a) and curvature (b) cases. Each curve denotes a specific $\chi_{n,m}$ state, and each color represents different subbands. In Figs. \ref{['subband1']} and \ref{['subband07']}, we plotted the subbands $n=0$ (red) and $n=1$ (orange). The dashed line locates the Fermi level.
• Figure 3: (Color online) Energy eigenvalues of the quantum ring near $\epsilon_{f}=2\space\text{meV}$ as a function of the magnetic field $B$ for flat (a) and curvature (b) cases. We plotted the subbands $n=3$ (light blue) and $n=4$ (dark blue). We have omitted the states from the lower subbands ($n\le 2$) for better visualization.
• Figure 4: (Color online) Plot of the expression for the transmission coefficient per energy state given by Eqs. (\ref{['land02']}) and (\ref{['land06']}). We have set $\Gamma_{1}=\Gamma_{2}=0.005\space\text{meV}$ and $\Gamma_{\phi}=0.004\space\text{meV}$. The shaded area represents the Fermi-Dirac distribution at $40 \space\text{mK}$.
• Figure 5: (Color online) (a) Conductance as a function of the Fermi energy for flat and curvature regime. The peaks result from the density of states per unity of energy Kittel2004. (b) Enlarged plot of Fig. \ref{['vanhoove']} for the first subband.