Effects of geometry and impurities on quantum rings in magnetic fields

We investigate the effects of impurities and changing ring geometry on the energetics of quantum rings under different magnetic field strengths. We show that as the magnetic field and/or the electron number are/is increased, both the quasiperiodic Aharonov-Bohm oscillations and various magnetic phases become insensitive to whether the ring is circular or square in shape. This is in qualitative agreement with experiments. However, we also find that the Aharonov-Bohm oscillation can be greatly phase shifted by only a few impurities and can be completely obliterated by a high level of impurity density. In the many-electron calculations we use a recently developed fourth-order imaginary time projection algorithm that can exactly compute the density matrix of a free electron in a uniform magnetic field.

Figure 1

Shapes of the external confinement potentials determining circular and square quantum rings with $\alpha =0$ and $0.2$ in Eq. (2), respectively.

Figure 2

Single-electron spectra in circular (a) and square (b) quantum rings as a function of the magnetic field. The Zeeman splitting is omitted.

Figure 3

Level-spacing distributions of noninteracting electrons at $B=10\mathrm{T}$ in impurity-affected quantum rings. The level spacings are calculated from 1000 random impurity configurations for $5$ (upper panel) and $30$ impurities (lower panel).

Figure 4

(Color online) Chemical potentials for $N=10,\dots ,17$ in circular (upper blue lines) and square (lower red lines) quantum rings. The filled circles, open circles, and crosses correspond to the spin changes $S\to S+1$, $S\to S-1$, and $S\to S+2$, respectively.

Figure 5

(Color online) Addition energies [light shade (yellow), low; black, high] as a function of the magnetic field and up to 16 electrons in circular (a) and square (b) quantum rings. The open and filled circles mark the first and final full spin polarizations, respectively. The dashed lines are plotted to guide the eye.

Figure 6

Magnetization of a 24-electron circular quantum ring. Different magnetic phases characteristic of finite Fermion systems are marked in the figure.

Figure 7

Addition-energy distributions of a 12-electron quantum ring having 5 (a), 10 (b), 20 (c), and 30 (d) impurities. The magnetic field is set to $B=10\mathrm{T}$ corresponding to the fully polarized regime.