Electric dipole moment oscillations in Aharonov-Bohm quantum rings

Magneto-oscillations of the electric dipole moment are predicted and analyzed for a single-electron nanoscale ring pierced by a magnetic flux (an Aharonov-Bohm ring) and subjected to an electric field in the ring's plane. These oscillations are accompanied by periodic changes in the selection rules for interlevel optical transitions in the ring allowing control of polarization properties of the associated terahertz radiation.

Figure 1

(a) The energy spectrum of an infinitely narrow quantum ring pierced by a magnetic flux $\Phi$. Each parabola corresponds to a particular value of the electron angular momentum $m$. The electron energies $\varepsilon$ are plotted vs the number of flux quanta $\Phi /{\Phi }_0$. (b) Expanded view on a smaller energy scale.

Figure 2

(a) The energy spectrum of an infinitely narrow quantum ring of radius $R$ pierced by a magnetic flux $\Phi$ and subjected to an in-plane electric field $E=0.2{\varepsilon }_1\left(0\right)/eR$. The electron energies $\varepsilon$ are plotted vs the number of flux quanta $\Phi /{\Phi }_0$. (b) Expanded view on a smaller energy scale.

Figure 3

A polar plot of the electron density distribution in a single-electron quantum ring pierced by a half of the flux quantum and subjected to a weak in-plane electric field, $E\ll {\varepsilon }_1\left(0\right)/eR$, applied at the zero angle: (a) for the electron ground state, and (b) for the first excited state.

Figure 4

Magneto-oscillations of the dipole moment of a ring at various temperatures for $E=0.2{\varepsilon }_1\left(0\right)/eR$. Different curves correspond to different temperatures in the range from $T=0.01{\varepsilon }_1\left(0\right)/k_B$ to $T=0.41{\varepsilon }_1\left(0\right)/k_B$ with the increment $0.1{\varepsilon }_1\left(0\right)/k_B$. The upper curve corresponds to $T=0.01{\varepsilon }_1\left(0\right)/k_B$.

Figure 5

Magneto-oscillations of the dipole moment of a ring at various magnitudes of the in-plane electric field for $T=0.01{\varepsilon }_1\left(0\right)/k_B$. Different curves correspond to different magnitudes of the electric field in the range from $E=0.2{\varepsilon }_1\left(0\right)/eR$ to $E=1.0{\varepsilon }_1\left(0\right)/eR$ with the increment $0.2{\varepsilon }_1\left(0\right)/eR$. The upper curve corresponds to $E=1.0{\varepsilon }_1\left(0\right)/eR$.

Figure 6

Relative directions of the external electric field $\mathbf{E}$ and the projection $\mathbf{e}$ of the THz radiation polarization vector onto the quantum ring's plane.

Figure 7

Magneto-oscillations of the degree of polarization for the transitions between the ground state and the first excited state. Here, $T_{\parallel }$ and $T_{\perp }$ are correspondingly the intensities of transitions polarized parallel ($\mathbf{e}\parallel \mathbf{E}$) and perpendicular ($\mathbf{e}\perp \mathbf{E}$) to the direction of the in-plane electric field.

Figure 8

The normalized energy spectrum as a function of dimensionless parameter $f$ for $\beta =0.1$. Dashed line: the result of analytical solution of the $3\times 3$ system. Solid line: the result of numerical diagonalization of the $23\times 23$ system. A horizontal line is shown to indicate $\lambda =0$ value.

Figure 9

The normalized energy spectrum as a function of dimensionless parameter $f$ for $\beta =0.1$. Dashed line: the result of analytical solution of the $2\times 2$ system. Solid line: the result of numerical diagonalization of the $23\times 23$ system. A horizontal line is shown to indicate $\lambda =0$ value.

Figure 10

Magnetic-flux dependence of the wave-function coefficients $|c_0{|}^2$ (solid line), $|c_{-1}{|}^2$ (dotted line), and $|c_{+1}{|}^2$ (dashed line): (a) for the ground state, (b) for the first excited state, and (c) for the second excited state.