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

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.

💡 Research Summary

In this paper the authors theoretically investigate how a controlled conical curvature influences charge transport in a two‑dimensional GaAs quantum ring weakly coupled to source and drain leads. The ring has an average radius of 800 nm and is subjected to a weak, uniform magnetic field perpendicular to the plane. The geometry of the ring surface is described by a curvature parameter α (0 < α ≤ 1); α = 1 corresponds to a flat ring, while smaller α values generate a conical shape with the apex located virtually beneath the ring.

Using the da Costa formalism for particles constrained to a curved surface, a purely geometric potential V_S = −ℏ²(1−α²)/(8μ α² r²) + δ‑term arises. This potential attracts electrons toward the cone apex and creates a strong repulsive core at r → 0. Adding the radial confinement potential V(r)=a₁r² + a₂r²−2√(a₁a₂) and the vector potential of the magnetic field (A = ½Bαr e_φ), the Schrödinger equation separates into an angular part (quantum number m) and a radial part. The radial equation can be solved analytically in terms of confluent hypergeometric functions, yielding energy eigenvalues

E_{n,m}=ℏω (n+½+L²) − mℏω_c − μω₀²r₀²/4,

where ω = √(ω₀²+α²ω_c²), ω_c = eB/μ, ω₀ is the confinement frequency, and L depends on m and α. The curvature parameter therefore modifies both the effective cyclotron frequency (scaled by α²) and the angular momentum contribution.

The authors compute the spectrum for two Fermi‑energy regimes: (i) ε_F ≈ 0.5 meV (single subband occupied) and (ii) ε_F ≈ 2 meV (four subbands occupied). Plots of E versus B show that decreasing α lengthens the Aharonov‑Bohm (AB) oscillation period as p₀ ∝ α⁻², because the magnetic flux threading the effective ring area π(αr_{n,m})² is reduced. Simultaneously, the spacing between adjacent energy levels grows, leading to a lower density of states per unit energy. In the higher‑subband case the increase of the subband minimum with B is also attenuated, reflecting the weakened magnetic coupling for curved geometries.

Transport is treated with the Landauer‑Büttiker formalism. The double‑barrier coupling to the leads is modeled by elastic broadenings Γ₁, Γ₂ (proportional to the individual barrier transmission probabilities) and an inelastic broadening Γ_φ that accounts for phase‑breaking processes (phonons, impurities, etc.). Near a resonance (E≈E_{n,m}) the coherent transmission is

T_c(E)=Γ₁Γ₂ /