Magnetization of nanoscopic quantum rings and dots

The magnetization of one- and two-electron quantum dots and a series of quantum rings with increasingly larger inner radii is calculated using a three-dimensional model with realistic finite confining potential, including strain and Coulomb effects. A change in topology leads to a sharp response in the calculated magnetization. The magnetization is also extremely sensitive to changes in the length of the inner radius of the ring. These results suggest the use of magnetization as a tool, complementary to far-infrared spectroscopy, for probing the topology of nanocrystals. Our calculations also reveal that atomic Zeeman splitting and, more especially, electron-electron interaction induce significant changes in the magnetic moment of a quantum ring of nanoscopic size.

Figure 1

Energy levels vs magnetic field of one electron in a quantum dot (a) and in a quantum ring with $R_{\mathit{in}}=5\mathrm{nm}$ (b). Solid lines denote spin $\alpha$ levels, and dotted lines spin $\beta$ levels. The insets show the cross section of the investigated dot (upper panel) and ring (lower panel).

Figure 2

Magnetization of one-electron nanocrystals with increasing inner radius. From bottom to top the curves correspond to $R_{\mathit{in}}=0\mathrm{nm}$, $R_{\mathit{in}}=1\mathrm{nm}$, $R_{\mathit{in}}=2\mathrm{nm}$, $R_{\mathit{in}}=5\mathrm{nm}$ and $R_{\mathit{in}}=10\mathrm{nm}$. The curves are offset by $1.0\mathrm{meV}∕\mathrm{T}$.

Figure 3

Magnetization of two-electron nanocrystals with increasing inner radius. From bottom to top the curves correspond to $R_{\mathit{in}}=0\mathrm{nm}$, $R_{\mathit{in}}=1\mathrm{nm}$, $R_{\mathit{in}}=2\mathrm{nm}$, $R_{\mathit{in}}=5\mathrm{nm}$ and $R_{\mathit{in}}=10\mathrm{nm}$. The curves are offset by $1.0\mathrm{meV}∕\mathrm{T}$.

Figure 4

Magnetization of a one-electron quantum dot (a), a one-electron quantum ring with $R_{\mathit{in}}=5\mathrm{nm}$ (b), a two-electron quantum dot (c) and a two-electron quantum ring with $R_{\mathit{in}}=5\mathrm{nm}$ (d). In (c) and (d), solid lines represent interacting electrons and dashed lines non-interacting electrons.