Fano effect and Kondo effect in quantum dots formed in strongly coupled quantum wells

We present lateral transport measurements on strongly, vertically coupled quantum dots formed in separate quantum wells in a $\mathrm{GaAs}∕{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructure. Coulomb oscillations are observed forming a honeycomb lattice consistent with two strongly coupled dots. When the tunnel barriers in the upper well are reduced we observe the Fano effect due to the interfering paths through a resonant state in the lower well and a continuum state in the upper well. In both regimes an in-plane magnetic field reduces the coupling between the wells when the magnetic length is comparable to the center to center separation of the wells. We also observe the Kondo effect, which allows the spin states of the double dot system to be probed.

Figure 1

(Color online) (a) Schematic diagram of the device. The lithographic width of the dot is $500\mathrm{nm}$. (b) An example of a dip in the conductance (black) with a fit of Eq. (1) [red (dark gray)]. (c) The conductance measured as a function of $V_{PL}$ for $V_{TOP}=-0.05\mathrm{V}$ [line labeled I in Fig. 3a]. Here, $V_{L1}$, $V_{L2}$, $V_{PL}$, and $V_{SIDE}$ are swept together with $V_{L1}$ and $V_{L2}$ offset by $-0.1\mathrm{V}$ and $V_{SIDE}$ offset by $+4\mathrm{V}$.

Figure 2

(Color online) Differential conductance, $dI∕d{V}_{sd}$ measured as a function of $V_{PL}$ and $V_{sd}$ in the region of (a) Coulomb oscillations and (b) Fano dips. $V_{TOP}=-0.05\mathrm{V}$. The gray scale corresponds to $\mathrm{white}=0\mathrm{\mu }\mathrm{S}$ $\left(50\mathrm{\mu }\mathrm{S}\right)$ to $\mathrm{black}=65\mathrm{\mu }\mathrm{S}$ $\left(70\mathrm{\mu }\mathrm{S}\right)$ for (a) and (b), respectively. Note that the range of $V_{PL}$ does not match Figs. 1c or 3a due to switching events that occur between the measurements. Dashed white lines in (a) are a guide to the eye. (c) A schematic diagram showing the Fermi energy in each well in relation to the barriers created by $V_{L1}$ and $V_{L2}$. Arrows indicate possible electron paths that could give rise to the Fano dips. (d) The situation when a dot is formed in each well.

Figure 3

$dG∕d{V}_{PL}$ plotted as a function of $V_{PL}$ and $V_{TOP}$ for (a) $B=0\mathrm{T}$ and (b) $B=5\mathrm{T}$ in the plane of the 2DEGs. Lines I–V are explained in the text. The scale bar corresponds to (a) and (b).

Figure 4

(a) The magnetic field dependence of the splittings measured at points A–E in Fig. 3b corresponding to circles, squares, triangles, diamonds, and crosses, respectively. (b), (c) The dependence of the fitting parameters in Eq. (1) for the dips labeled 1 (circles), 2 (triangles), and 3 (crosses) in Fig. 1c.

Figure 5

(Color online) (a)–(c) The temperature dependence of the conductance for values of $V_{TOP}$ indicated by lines I, II, and III, respectively, in Fig. 3a. The arrows show the trend for increasing temperature. (d) An example of the logarithmic temperature dependence of the conductance between peaks $\alpha$ and $\beta$ in (a). The parameters are explained in the text.