Pauli spin blockade in cotunneling transport through a double quantum dot

We study spin correlation in a double quantum dot containing a few electrons in each dot (around 10). Clear current rectification with negative differential conductance is observed in the cotunneling regime, which is well explained by a Pauli spin blockade. The current feature is discussed in connection with exchange singlet-triplet splitting based on two simple models, one of which takes coherent interdot coupling and the other incoherent interdot coupling into account.

Figure 1

(Color online) Current $I$ as a function of gate voltages $V_{GL}$ and $V_{GR}$ at $V_{\mathrm{SD}}=110\mu \mathrm{V}$. Hexagonal domains are accentuated by solid lines, where charge states $(n,m)$ denote the effective electron numbers in dots $L\left(n\right)$ and $R\left(m\right)$. The inset shows a scanning electron microscopy image of our double quantum dot device.

Figure 2

(Color online) (a) Schematic charge diagram in the $V_{GL}\text{−}{V}_{GR}$ plane. Sequential and charge-conserved cotunneling regions are shown by hatched and dotted patterns, respectively. (b)–(e) Absolute current $\mid I\mid$ in the $V_{GL}\text{−}{V}_{GR}$ plane in regions I (b) and (c) and II (d) and (e) of Fig. 1 at positive and negative $V_{\mathrm{SD}}$. The dashed lines trace the charge domains described in (a). Two sweeping voltages $V_{\delta }$ and $V_{\epsilon }$ are introduced for convenient operation (see text).

Figure 3

(Color) (a) Current $I$ as a function of $V_{\epsilon }$ and $V_{\mathrm{SD}}$ at $\delta =0$. Note that the color scale is different for positive and negative current. (b) $I\text{−}{V}_{\mathrm{SD}}$ curves at some constant $\epsilon$, extracted from (a). The arrows indicate the peak position $V_{\text{peak}}$ (unit: $\mu \mathrm{V}$). (c) The anticrossing energy diagram for the two-electron DQD with coherent interdot coupling. The inset shows the cotunneling transitions between the energy levels. (d) Schematic energy diagram of the DQD with incoherent interdot coupling. The inset shows some possible transitions between the two-electron charge states.

Figure 4

Zero-bias conductance $G_0$ (a) and (b), spin blockade current $I_{\mathrm{SB}}$ (c) and (d) at $V_{\mathrm{SD}}=50\mu \mathrm{V}$ and current peak position $V_{\text{peak}}$ (e) and (f) as a function of $\epsilon$ and $\delta$. Note that (a), (c), and (e) are obtained at $\delta =0$ and that (b), (d), and (f) are for $\epsilon =0$. The solid and dashed curves were calculated considering coherent and incoherent interdot coupling, respectively. The dash-dotted Lorentzian curves in (b) are guides for the sequential tunneling regions and the electrostatic coupling energy $U=255\mu \mathrm{eV}$ is determined from the energy spacing between peaks $A$ and $B$. The dotted line in (e) is a reference for $e{V}_{\text{peak}}=\epsilon$. The cotunneling region is confined to the $\delta$ range of $-90\text{to}90\mu \mathrm{eV}$ (between the two solid straight lines).