Unconventional Transport in the “Hole” Regime of a Si Double Quantum Dot

Studies of electronic charge transport through semiconductor double quantum dots rely on a conventional “hole” model of transport in the three-electron regime. We show that experimental measurements of charge transport through a Si double quantum dot in this regime cannot be fully explained using the conventional picture. Using a Hartree-Fock (HF) formalism and relevant HF energy parameters extracted from transport data in the multiple-electron regime, we identify a novel spin-flip cotunneling process that lifts a singlet blockade.

Figure 1

(a) Transport current $I_{\mathrm{SD}}$ in a $\mathrm{Si}/\mathrm{SiGe}$ double quantum dot (color scale) as a function of controlling gate voltages, $V_G$ (V) and $V_{\mathrm{CS}}$ (V), reported in Ref. 8. Inset shows an SEM image of the gates with a numerically simulated double dot overlayed. White letters ($T$, $B_L$, $G$, $B_R$ and CS) label gates and red letters ($S$, $D$) label the source and drain. For this data, electrons flow from left to right. (b) A cartoon of the bias triangles and lines of high current. Inset shows the energy axes of the dots. The lower (upper) features are the electron (hole) triangles. Red dashed lines represent current through the singlet (singletlike) channel of the electron (hole) bias triangle and blue dot-dashed lines the triplet (tripletlike) triangle. $A$ and $B$ are resonant peaks of the singlet and triplet electron triangles. $C$ is the resonant peak of the singletlike hole triangle. $A$ and $C$ are the triple points at the boundary of the (1,0), (1,1), (2,0) and (1,1), (2,0), (2,1) charge occupations. $F$ lies along the line extending from the tail; it is a representative point where cotunneling is dominant. $E_{\mathrm{ST}}$ is the (2,0) singlet-triplet energy splitting. Data are obtained at a reverse-bias source-drain voltage, $V_{\mathrm{SD}}=-0.274\mathrm{mV}$, first published in Ref. 8 as $-0.3\mathrm{mV}$. Ref. 13 details the quantitative fits to identify the triangles. (c) The prediction using the conventional hole picture in the three-electron regime is shown as two parallel lines (black), which is inconsistent with the tail observed in the data.

Figure 2

Diagrams for transport through excited states and the process of spin-flip cotunneling. (a) Triplet channel transport in the two-electron regime. At $B$, the resonant peak of the triplet channel, transport is allowed through the triplet levels, ${\mu }_{T(2,0)}$ and ${\mu }_{T(1,1)}$. (b) When the singlet level ${\mu }_{S(2,0)}$ is loaded, transport is energetically uphill and blockaded. Cotunneling of a left dot electron out to the right lead lifts the blockade to resume triplet channel transport. (c) In the three-electron regime, transport occurs in the following cycle: step 1, $(1,1)\to (2,1)$; step 2, $(2,1)\to (2,0)$; step 3, $(2,0)\to (1,1)$. At $D$, these occur through the tripletlike channel (blue). (d) Because of the loading of the singletlike ${\mu }_{c,S^{*}}$ level (red) at $D$, the system ends up in the $S(2,0)$ state, whereby transport is blockaded. (e) When an electron cotunnels from the left lead into the right dot to form a tripletlike state, it puts the left dot into an admixture of singlet and triplet. (f) The right dot discharges from ${\mu }_{d,T^{*}}$, leaving a triplet state in the left dot, thus causing a spin-flip and resuming transport.