Persistent current magnification in a double quantum-ring system

The electronic transport in a system of two quantum rings side-coupled to a quantum wire is studied via a single-band tunneling tight-binding Hamiltonian. We derived analytical expressions for the conductance, density of states, and the persistent current when the rings are threaded by magnetic fluxes. We found a clear manifestation of the presence of bound states in each one of those physical quantities when either the flux difference or the sum of the fluxes are zero or integer multiples of a quantum of flux. These bound states play an important role in the magnification of the persistent current in the rings. We also found that the persistent current keeps a large amplitude even for strong ring-wire coupling.

Figure 1

Schematic view of the two quantum rings attached to quantum wire.

Figure 2

Linear conductance as a function of Fermi energy measured in units of the hoping parameter $v$, for $\gamma =0.5v$, $\tilde{\phi }=0.6$, and for a difference of fluxes between both rings of $\delta \phi =0.1$ (top) and $\delta \phi =0.2$ (bottom).

Figure 3

Density of states (top) and persistent density current (in units of $v$), for $\tilde{\phi }=0.6$, $\delta \phi =0.1$, and $\gamma =0.5$. The solid and dotted lines indicate upper and lower rings, respectively.

Figure 4

Density of states as a function of energy (in units of $v$), for $\tilde{\phi }=0.6$, $\delta \phi =0.0$ and $\gamma =0.5$.

Figure 5

Persistent current, in units of the persistent current of an isolated ring $I_0$, as a function of $\tilde{\phi }$ for different values of ring-wire coupling, $\gamma =0.001$ (solid line), $\gamma =0.1$ (dashed line), $\gamma =1$ (dotted line), and $\gamma =100$ (dashed-dotted line).

Figure 6

Amplitude of the persistent current (solid line) and $I_s$ (dashed line) and $I_b$ (dotted line) as a function of $\gamma$ measured in units of $v$.

Figure 7

Linear conductance as a function of ${\epsilon }_F$ (in units of $v$) for $\delta \phi =0.01$ (solid line) and $\delta \phi =1.99$ (dashed line).

Figure 8

(a) DOS and (b) current density in the upper ring (solid line) and lower ring (dashed line) for $\delta \phi =0.01$ as a function of the energy (in units of $v$).

Figure 9

Persistent current as a function of the magnetic flux for $\delta \phi =0.001$ for different values of coupling parameter, $\gamma =0.0001$ (solid line), $\gamma =0.001$ (dashed line), $\gamma =0.5$ (dotted line), $\gamma =1$ (dashed-dotted line).