Figure 1

(a) Structure of double quantum dot device. Top and bottom contacts serve as drain and source electrodes. Side gates (SG1, SG2) tune electron number in each dot; two center gates (CG) tune tunnel coupling between dots. Center insets: Schematic figure of electric transport and scanning electron micrograph of device. (b) Schematic honeycomb stability diagram in the $V_{s1}\mathrm{\text{−}}{V}_{s2}$ plane, stable electron numbers in dots 1 and 2 noted. Inset: Close-up of single anticrossing, showing evolution of states along central diagonal. Delocalization region connects two “triple points” (black dots). Energies and descriptions of states 1, 2, and 3 in text.Reuse & Permissions

Figure 2

(a) Coulomb peak positions in $V_{s1}\mathrm{\text{−}}{V}_{s2}$ plane for center gate voltage $V_c=-2.4\mathrm{V}$ and (b) $V_c=-2.0\mathrm{V}$. Anticrossings in squares and circles in (a) are used for statistical analysis (see Fig. 3). Those in squares show different dependence on angular momenta of states (see Fig. 4).Reuse & Permissions

Figure 3

Center gate voltage $V_c$ dependencies of mean value $\overline{\Delta V}$ (solid line) and standard deviation $\mathrm{\sigma }$ (dashed line) of tunnel-coupling energy $\Delta V$, calculated using anticrossings enclosed by circles and squares in Fig. 2a.Reuse & Permissions

Figure 4

(a) Magnetic field dependencies of Coulomb peak position shifts, $\Delta V_{s1}$, measured along the dashed line i–ii of Fig. 2a. Inset: Correlation function [19] of the anticrossing widths for states in dot 1. (b) Same for Coulomb peaks position shifts $\Delta V_{s2}$ along dashed line iii–iv of Fig. 2a. The labeled Coulomb oscillations correspond to those of Fig. 2a. Inset: Same as inset in (a) for dot 2. In 2a, 2b main panels, $\Delta V_{s1}$ ($\Delta V_{s2}$) indicates the shift value from $V_{s1}$ ($V_{s2}$) at $B=0\mathrm{T}$. Here $\Delta V_{s1}$ and $\Delta V_{s2}$ are smoothed across five magnetic field points and the plots are shifted by multiples of 0.02 V. (c) Tunnel coefficient calculated from Fock-Darwin spectra for two adjacent parabolic wells versus product of state angular momenta $|M_I||m_j|$. $N_I$, $n_j$ are principle quantum numbers. (d) Anticrossing gap sizes, relative to mean $\overline{\Delta V}$, versus product of angular momenta of Fermi surface states derived from slopes at $B=0$ in (a) and (b). Solid squares indicate gaps inside squares and solid circles for gaps inside circles in Fig. 2a.Reuse & Permissions