Interference effects in the Coulomb blockade regime: Current blocking and spin preparation in symmetric nanojunctions

We consider nanojunctions in the single-electron tunneling regime which, due to a high degree of spatial symmetry, have a degenerate many-body spectrum. As a consequence, interference phenomena which cause a current blocking can occur at specific values of the bias and gate voltage. We present here a general formalism to give necessary and sufficient conditions for interference blockade also in the presence of spin-polarized leads. As an example we analyze a triple quantum-dot single-electron transistor. For a setup with parallel polarized leads, we show how to selectively prepare the system in each of the three states of an excited spin triplet without application of any external magnetic field.

Figure 1

(Color online) Interference in a SET. The dynamics is governed by equivalent paths in the many-body spectrum that involve two (or more) degenerate states.

Figure 2

(Color online) Energetically available transitions from an $N$-particle level. The patterned rectangles indicate the energy range of energetically available source (S) and drain (D) transitions both to states with $N+1$ and $N-1$ particles. The arrows show examples of both allowed and forbidden transitions.

Figure 3

(Color online) Schematic representation of a triple dot ISET.

Figure 4

(Color online) Spectrum of the triple dot system for the specific gate voltage $e{V}_g=4.8b$ chosen to favor a configuration with two electrons. The other parameters in the system are $U=5\left|b\right|$ and $V=2\left|b\right|$, where $b$ is the hopping integral between the different dots.

Figure 5

(Color online) Stationary current for the triple dot ISET. Coulomb blockade diamonds are visible at low biases. Ground-state and excited-state interference blockades are also highlighted. The temperature is $k_{b}T=0.002\left|b\right|$. The other parameters are the same as the ones in Fig. 4.

Figure 6

(Color online) Blow up of the stationary current through the triple dot ISET around the 2 to 1 particle degeneracy point. The black area sticking out of the 2 particle Coulomb diamond denotes the excited-state blocking.

Figure 7

(Color online) Current as a function of the polarization and of the bias voltage in proximity of the excited-state interference blocking. The white dashed lines are defined by the conditions ${\omega }_{S{S}_z}=0$ for $S_z=-\hslash$, 0, $\hslash$ from left to right, respectively.

Figure 8

(Color online) Spin projection $S_z$ as a function of the polarization and of the bias in proximity of the excited-state interference blocking. Notice by comparison with Fig. 7 the correspondence between current blocking and spin preparation.

Figure 9

(Color online) Renormalization frequencies as a function of the bias for different polarizations $P=0$, 0.25, 0.5, and 0.75 in the leads. The gate is $V_g=4.8b/e$. At $P=0$ all the renormalization frequencies coincide (full line). The $S_z=\hslash \left(-\hslash \right)$ frequency increases (decreases) monotonously with the polarization. The $S_z=0$ frequency is instead independent of it.