Charge localization and isospin blockade in vertical double quantum dots

Charge localization seems unlikely to occur in two vertically coupled symmetric quantum dots even if a small bias voltage breaks the exact isospin-symmetry of the system. However, we find a strong localization of charges in one of the dots at certain vertically applied magnetic fields. The charge localization is directly connected to ground state transitions between eigenstates differing only in parity. The transitions are driven by magnetic-field-dependent Coulomb correlations between the electrons and give rise to strong isospin blockade signatures in transport through the double-dot system.

Figure 1

Energy difference of the lowest two eigenstates to $\widehat{\mathcal{H}}(M=-5\text{and}S=S_z=3∕2)$ as a function of the magnetic field $B$. $t=-0.059\mathrm{meV},\hslash {\omega }_0=2.96\mathrm{meV}$, and $d=19.6\mathrm{nm}$. The crossing takes place at $B=7.77\mathrm{T}$ (dashed vertical line).

Figure 2

Angular momentum $M$, total spin $S$, and expectation value of the $z$ component of isospin $⟨{\mathcal{I}}_z⟩$ for three electron GS to $\widehat{\mathcal{H}}+{\widehat{\mathcal{V}}}_z$. ${\widehat{\mathcal{V}}}_z=5.9\times {10}^{-4}{\widehat{\mathcal{I}}}_z\mathrm{meV}$. The peak in $⟨{\widehat{\mathcal{I}}}_z⟩$ illustrates the charge localization that corresponds to the parity crossing (see text). Other parameters are as in Fig. 1.

Figure 3

Dependence of parity $P$ for $M=-5$ and $S=3∕2$ on magnetic field $B$ and tunneling $t$. The solid line indicates where the crossing between the parity eigenstates takes place. Other parameters are as in Fig. 1.

Figure 4

Height of the third and fourth conductance peaks (transition from $N_e=2$ to $N_e=3$ or from $N_e=3$ to $N_e=4$) as a function of $B$ for two temperatures and $V_{sd}=12\mu \mathrm{V}$. $\Gamma =\mathrm{DOS}{\mid T\mid }^2(2\pi ∕\hslash )$ determines the coupling to the external reservoirs, where DOS is the density of states in the reservoirs and $T$ denotes the tunnel matrix elements to the reservoirs. Other parameters are as in Figs. 1, 2. In particular the asymmetry between the lower and upper dot $V_z={10}^{-2}\mid t\mid \approx 0.6\mu \mathrm{eV}$.