Hyperfine-induced valley mixing and the spin-valley blockade in carbon-based quantum dots

Hyperfine interaction (HFI) in carbon nanotube and graphene quantum dots is due to the presence of ${}^{13}\text{C}$ atoms. We theoretically show that in these structures the short-range nature of the HFI gives rise to a coupling between the valley degree of freedom of the electron and the nuclear spin, in addition to the usual electron spin-nuclear spin coupling. We predict that this property of the HFI affects the Pauli blockade transport in carbon-based double quantum dots. In particular, we show that transport is blocked only if both the spin and the valley degeneracies of the quantum dot levels are lifted, e.g., by an appropriately oriented magnetic field. The blockade is caused by four “supertriplet” states in the (1,1) charge configuration.

Figure 1

(Color online) Averaged leakage current $⟨I⟩$ due to hyperfine interaction in a graphene DQD, as a function of spin and valley splittings. $I_{\text{max}}\approx 0.34e{\Gamma }_{\text{in}}$. Inset: transport through a DQD. Dot $R$ is always occupied by at least one electron.

Figure 2

(Color online) Averaged leakage current $⟨I⟩$ as a function of (upper solid line, black) spin splitting ${\Delta }_s$ for zero valley splitting ${\Delta }_v=0$, (lower solid line, green) valley splitting ${\Delta }_v$ for ${\Delta }_s=9$, and (dashed) ${\Delta }_s$ in a GaAs DQD [dashed line based on Eq. (11) of Ref. 21].

Figure 3

(Color online) Schematic energy diagrams of the (1,1) charge configuration corresponding to the three highlighted points of Fig. 1. The effect of hyperfine interaction is excluded. Dashed lines: transport-blocking supertriplet states.