Effects of external radiation on biased Aharonov-Bohm rings

We consider the currents flowing in a solid-state interferometer under the effect of both an Aharonov-Bohm phase and a bias potential. Expressions are obtained for these currents, allowing for electronic or electron-boson interactions, which may take place solely on a quantum dot placed on one of the interferometer arms. The boson system can be out of equilibrium. The results are used to obtain the transport current through the interferometer, and the current circulating around it under the effect of the Aharonov-Bohm flux. The modifications of both currents, brought about by coupling the quantum dot to an incoherent sonic or electromagnetic source, are then analyzed. By choosing the appropriate range of the boson source intensity and its frequency, the magnitude of the interference-related terms of both currents can be controlled.

Figure 1

An Aharonov-Bohm interferometer, containing a quantum dot (QD) on its upper arm and threaded by a magnetic flux $\Phi$. The lower arm of the interferometer contains a “reference” site (RS). The ring is connected to two electronic reservoirs whose chemical potentials are either equal or have a small difference, allowing a current $I$ to flow from the left to the right. The wavy vectors denote the external beam radiated on the dot.

Figure 2

The total transmission of the interferometer, under the effect of the radiation (thick line), and in the interaction-free case (dashed line), as function of the localized energy on the dot, at zero flux and for $T_B=0.4$, ${\Gamma }_0=0.3$, and radiation intensity scaled by 0.3 (see the text). The phonon frequency is $\Omega =3$ (energies are measured in meV).

Figure 3

The same as in Fig. 2, when the radiation intensity is doubled.

Figure 4

The transmission as function of the magnetic flux (in units of the flux quantum). The thin dashed line presents the interaction-free case, the thick line pertains to the same beam intensity as in Fig. 2, while the thick dashed line is for the intensity as in Fig. 3. The parameters are as in those figures, with ${ϵ}_d=-1$.

Figure 5

The persistent current as function of ${ϵ}_d$. The thin dashed line shows $I_{\mathit{pc}}^0$, the thick line is for beam intensity 0.3, and the thick dashed line for 0.6. The flux is taken at $\pi ∕2$, and the other parameters are as in Fig. 2.

Figure 6

The persistent current as function of the Aharonov-Bohm flux. Parameters are as in the previous figures, with ${ϵ}_d=-1$. The thin dashed line portrays $I_{\mathit{pc}}^0$, the thick line is for beam intensity 0.3, and the thick dashed line is for beam intensity 2; see the text.