Spin-orbit interaction and asymmetry effects on Kondo ridges at finite magnetic field

We study electron transport through a serial double quantum dot with Rashba spin-orbit interaction (SOI) and Zeeman field of amplitude $B$ in the presence of local Coulomb repulsion. The linear conductance as a function of a gate voltage $V_g$ equally shifting the levels on both dots shows two $B=0$ Kondo ridges, which are robust against SOI as time-reversal symmetry is preserved. As a result of the crossing of a spin-up and a spin-down level at vanishing SOI, two additional Kondo plateaus appear at finite $B$. They are not protected by symmetry and rapidly vanish if the SOI is turned on. Left-right asymmetric level-lead couplings and detuned on-site energies lead to a simultaneous breaking of left-right and bonding-antibonding state symmetry. In this case, the finite-$B$ Kondo ridges in the $V_g$-$B$ plane are bent with respect to the $V_g$ axis. For the Kondo ridge to develop, different level renormalizations must be compensated by adjusting $B$.

Figure 1

The considered setup consists of a serial double quantum dot with energies ${\epsilon }_{1/2}=V_g\pm \delta$ coupled by a hopping amplitude $t$ and a SOI of strength $\alpha$. The levels are split by an external Zeeman field $B$. The local Coulomb interaction is $U$ and the interaction between electrons on the two sites is $U^{\prime }$. The system is coupled to noninteracting leads by hopping amplitudes $t_{L/R}$.

Figure 2

Conductance $G(V_g,B)$ for $t=1$,  $U=U^{\prime }=1$,  $t_{L/R}=0.3$, and $\delta =0$ in the absence of SOI ($\alpha =0$).

Figure 3

Gate-voltage dependence of the conductance $G$ and dot occupation $\langle n_1+n_2\rangle$ for different values of $B$, and the same parameters as in Fig. 2.

Figure 4

Conductance $G(V_g,B)$ for $t=1$,  $U=U^{\prime }=1$, and $\alpha =0$ with asymmetric couplings to the leads $t_L=0.3$,  $t_R=0.5$, and finite level-splitting $\delta =-0.3$.

Figure 5

Conductance $G(V_g,B)$ for $t=1$,  $U=U^{\prime }=1$,  $t_{L/R}=0.3$, and $\delta =0$ with $\theta =1.56$ and finite SOI $\alpha =0.6$. Inset: Conductance $G(\theta ,B)$ at $V_g=0$.