Tunneling conductance of a mesoscopic ring with spin-orbit coupling and Tomonaga-Luttinger interaction

We study the tunneling current through a mesoscopic two-terminal ring with spin-orbit coupling, which is threaded by a magnetic flux. The electron-electron interaction in the ring is described in terms of a Tomonaga-Luttinger model which also allows us to account for a capacitive coupling between the ring and the gate electrode. In the regime of weak tunneling, we describe how, at temperatures lower than the mean level spacing, the peak positions of the conductance depend on magnetic flux, spin-orbit coupling strength, gate voltage, charging energy, and interaction parameters (charge and spin velocity and stiffness).

Figure 1

The ring threaded by a magnetic flux $\Phi$ is weakly coupled to the leads through the tunneling barriers $t_l$ and $t_r$ and capacitively coupled to the gate electrode $\left(V_g\right)$.

Figure 2

The lowest radial band of the quasi-1D mesoscopic ring SO-split into two subbands.

Figure 3

Splitting of the conductance peaks (solid lines) due to SO coupling. The dashed lines correspond to $k_R=0$.

Figure 4

Shift of the conductance peaks (solid lines) due to the charging energy. The dashed lines correspond to the noninteracting case $({\Delta }_c=0)$.

Figure 5

Conductance peaks for $k_R=0.1$ and different values of the charging energy $8E_c∕{\omega }_0=0.0$ (upper left), 0.5 (upper right), 1.0 (bottom left), 3.0 (bottom right). The TLL parameters are ${\nu }_{c,s}={\lambda }_{c,s}=1$.

Figure 6

Conductance peaks for $\kappa =1$ and different values of the charging energy $8E_c∕{\omega }_0=0.0$ (upper left), 0.5 (upper right), 1.0 (bottom left), 3.0 (bottom right).