Magnetically Induced Chessboard Pattern in the Conductance of a Kondo Quantum Dot

We quantitatively describe the main features of the magnetically induced conductance modulation of a Kondo quantum dot—or chessboard pattern—in terms of a constant-interaction double quantum dot model. We show that the analogy with a double dot holds down to remarkably low magnetic fields. The analysis is extended by full 3D spin density functional calculations. Introducing an effective Kondo coupling parameter, the chessboard pattern is self-consistently computed as a function of magnetic field and electron number, which enables us to explain our experimental data quantitatively .

Figure 1

(a) Scanning electron micrograph of the device. Metal gates are yellow; dot is indicated by a red circle. Ungated 2DEG mobility is $2.3\times {10}^6{\mathrm{c}\mathrm{m}}^2/(\mathrm{V}\mathrm{s})$ and electron density is $1.9\times {10}^{15}{\mathrm{m}}^{-2}$ at 4.2 K. Nominal dot size is $320\times 320{\mathrm{n}\mathrm{m}}^2$. (b) Color scale plot of the experimental linear conductance $G$ through dot as function of $B$ and $V_{gl}$ at 10 mK. The dotted hexagons highlight the shape of a few chessboard fields; ellipses indicate some regions where Coulomb peak suppression occurs. (c) Calculated self-consistent potential landscape of device; white lines denote contours of the metal gates.

Figure 2

(a) Schematic of the dot in terms of two Landau levels (LLs). (b) Results of numerical minimization of Eq. (1). Color stripes are regions of constant $N=N_0+N_1$. Numbers in parentheses show $N_0,N_1$. Solid lines bound regions of constant $N_0$. Dotted lines show “$N_1$ boundaries”. The $N_1$ boundary lengths alternate [compare to Fig. 1b]. Capacitances and dot parabolicity estimated for $N_0^0=25$, $N_1^0=10$, $B_0=0.6T$: $C_{00}=3.3$, $C_{11}=2.2$, $C_{01}=-2.1$, $C_{g0}=-0.10$, and $C_{g1}=-0.056$ (all in attofarad), ${\omega }_0=0.4\mathrm{m}\mathrm{e}\mathrm{V}$. The dashed line is the approximate third LL filling boundary. (c) Schematic honeycomb structure in the $B,V_{gl}$ plane resulting from the double dot model. Typical occupancy configurations (energy versus position) of LL1 (white-on-black arrows) and LL0 (black arrows) at the dot boundary are shown for different honeycomb cells.

Figure 3

Color scale plot of Kondo parameter $K$ in the $B,V_{gl}$ plane. Red (blue) corresponds to large (small) $K$. Third LL filling begins below $\sim 0.5\mathrm{T}$. $K$ is calculated in the Coulomb valley center at each $B$ (see text). Upper panel shows Fermi energy vs $B$ for $N=37$ and fixed $V_{gl}=-407\mathrm{m}\mathrm{V}$. $E_F$ drops at each reconstruction (i.e., at each end of each Kondo zone). Inset: $K$ fully calculated from Eq. (2) on fine mesh for small $B,V_{gl}$ region (i.e., no approximation for the $V_{gl}$ dependence is used here).