Pauli Blockade of Tunable Two-Electron Spin and Valley States in Graphene Quantum Dots

Pauli blockade mechanisms—whereby carrier transport through quantum dots (QD) is blocked due to selection rules even when energetically allowed—are a direct manifestation of the Pauli exclusion principle, as well as a key mechanism for manipulating and reading out spin qubits. The Pauli spin blockade is well established for systems such as GaAs QDs, but is to be further explored for systems with additional degrees of freedom, such as the valley quantum numbers in carbon-based materials or silicon. Here we report experiments on coupled bilayer graphene double quantum dots, in which the spin and valley states are precisely controlled, enabling the observation of the two-electron combined blockade physics. We demonstrate that the doubly occupied single dot switches between two different ground states with gate and magnetic-field tuning, allowing for the switching of selection rules: with a spin-triplet–valley-singlet ground state, valley blockade is observed; and with the spin-singlet–valley-triplet ground state, robust spin blockade is shown.

Figure 1

(a) Device illustration. Double electron dots are defined with plunger gates $L$ and $R$, and barrier gates LB, MB, and RB. A magnetic field $B$ is applied perpendicular to the BLG. (b) Charge-stability diagram at $V_{B_M}=-5.76\mathrm{V}$. (c) Finite-bias triangles at $V_{\mathrm{MB}}=-5.76\mathrm{V}$, $B=800\mathrm{mT}$ with (i) negative and (ii) positive source-drain bias $V_{\mathrm{SD}}$. $\epsilon$ is the total energy, and detuning $\delta ={\epsilon }_L-{\epsilon }_R$ the interdot energy difference. (iii) Line cuts along the dashed arrows, with $V_{L,R}$ converted into $\delta$. $\delta =0$ at the baseline of bias triangles. Current peaks are labeled by dots. Valley blockade (VB) and spin blockade (SB) suppress current in the positive-bias direction. Energies of relevant states are sketched for $\delta =0$ in (iv) and (v). For negative bias [electron transport $(2,0)\to (1,1)$], the spin-blockaded GS–GS transition [gray in (iv)] is readily circumvented by a transition close in energy (black). For positive bias [electron transport $(1,1)\to (2,0)$], the next available transition is higher in energy [red in (v)] and requires a valley flip. (d) Evolution of single-dot two-particle energies in magnetic field, sketched with $E_{\mathrm{ex}}=0.9\mathrm{eV}$, $g_v=28$, and $g_s=2$. The two different GSs (red) define regime $A$ and $B$.

Figure 2

Finite-bias triangles at $V_{\mathrm{MB}}=-5.81\mathrm{V}$ in $\mathbf{A}$: regime $A$ with $(2,0{)}_{\mathrm{GS}}:|T_s^{-}⟩|S_v⟩$ at $B=(a)0\mathrm{T}$ and (b) 200 mT, and in $\mathbf{B}$: regime $B$ with $(2,0{)}_{\mathrm{GS}}:|S_s⟩|T_v^{-}⟩$ at $B=800\mathrm{mT}$ for (i) negative [electron transport $(2,0)\to (1,1)$], and (ii) positive [electron transport $(1,1)\to (2,0)$] source-drain bias $V_{\mathrm{SD}}$. (iv), (v) Schematics of electrochemical potentials $\mu$ of relevant transitions for (i), (ii), sketched at $\delta =0$, when ${\mu }_{\mathrm{GS}}$s align. Nonzero $\delta$ allows for higher energy transitions. (iii) Line cuts along the dashed arrow, with $V_{L,R}$ converted into $\delta$. Current resonances are labeled by numbered colored circles. Valley-blockade (VB) and spin-blockade (SB) regions are marked. Current is suppressed for positive bias $(1,1)\to (2,0)$ by the valley and spin blockade, and is enhanced for clarity in the line cuts (iii) by a factor of 5, 10, and 15 for A(a), A(b), and B. In A(a,ii), the valley blockade is lifted at the edges of the triangles, where the electron in the dot can exchange with electrons in the source or drain leads [yellow arrows in A(a,ii) and schematic outlined in yellow in A(a,iii)]. In B, the line cut is taken at the dotted instead of the dashed line, due to a shift of the bias triangle along the $\epsilon$ direction, a result of the change of $(2,0{)}_{\mathrm{GS}}$.

Figure 3

Evolution in magnetic field of GS transitions for (a) negative and (b) positive source-drain bias $V_{\mathrm{SD}}$. Evolution in magnetic field for (i) line cut along the $\delta$ axis (dashed arrows in Fig. 2) and (ii) calculated transitions with $E_{\mathrm{ex}}=0.9\mathrm{meV}$, ${\mathrm{\Delta }}_{\mathrm{SO}}=80\mu \mathrm{eV}$, $g_v=28$, and $g_s=2$, from $(2,0{)}_{\mathrm{GS}}$ in (a,ii), and from $(1,1{)}_{\mathrm{GS}}$ in (b,ii). Except for the GS-GS transition (2) and $(2^{\prime })$, transitions requiring spin flips [sketched in light gray in (ii)] are not labeled. The thicker lines in (ii) represent the GS-GS transitions, and hence define the baselines of the bias triangles. Yellow, blue, and purple represent nonblockaded (NB), VB, and SB regions, respectively. At high field, oscillations periodic in $1/B$ are observed for both bias directions [29].