Magnetoconductance switching in an array of oval quantum dots

Employing oval-shaped quantum billiards connected by quantum wires as the building blocks of a linear quantum-dot array, we calculate the ballistic magnetoconductance in the linear-response regime. Optimizing the geometry of the billiards, we aim at a maximal finite over zero-field ratio of the magnetoconductance. This switching effect arises from a relative phase change in scattering states in the oval quantum dot through the applied magnetic field, which lifts a suppression of the transmission characteristic for a certain range of geometry parameters. It is shown that a sustainable switching ratio is reached for a very low-field strength, which is multiplied by connecting only a second dot to the single one. The impact of disorder is addressed in the form of remote impurity scattering, which poses a temperature-dependent lower bound for the switching ratio, showing that this effect should be readily observable in experiments.

Figure 1

Geometry of the billiard for $N=2$, $\delta =0.5$, and $L=W=0.3R$, consisting of the repeated module and the outer leads which represent the connection to reservoirs (see text).

Figure 2

(Color online) Transmission spectra in the first transversal channel for varying number of dots $N$ with deformation parameter $\delta =0.5$ and connecting lead length $L=W=0.3R$, at $B=0$ (solid black line) and $B=B_c\approx 20\text{mT}$ (dotted red line).

Figure 3

(Color online) (A) $T\left(\kappa \right)$ for $B=0$ (solid black line) and $B=B_c$ (dotted red line) for $L=W$ and varying $N$, in the vicinity of ${\kappa }_p\approx 1.384$, with labels a, b, c, d, and e for the resonances referred to in the text, (B) $T\left(\kappa \right)$ (solid black line) and $g\left(\Theta =0.2\text{K};{\kappa }_F\right)$ (dashed magenta line) for a single dot (bottom) and for two dots with varying bridge length $L$, within a small window of the channel number $\kappa$ covering the energy range of a smooth hump in the single-dot transmission.

Figure 4

(Color online) Zero-field local DoS for $N=1,2,3,4$ dots with $\delta =0.5$ and $L=W$ for energies in the vicinity of the $\left(N-1\right)$-fold split resonance peak at $\kappa ={\kappa }_p\approx 1.384$, with incoming electron on the left. Rows (a), (b), (c), (d), and (e) correspond to the energies of the resonances labeled with the same letters in Fig. 3A. The color map for the DoS in each subplot is normalized to its maximal value, further the color maps the square root of the DoS to enhance contrast.

Figure 5

Minimal zero-field conductance $g_{\text{off}}^{\text{min}}$ (see text) as a function of the deformation parameter $\delta$ for a single dot at temperatures (bottom to top) $\Theta =1.0,1.1,\dots ,2.0\text{K}$; the inset shows the change in the optimized channel number ${\kappa }^{\text{min}}$ with $\delta$ at $\Theta =2\text{K}$ (the dependence is the same for the other temperature values).

Figure 6

Single-dot switching ratio $S^{\left(1\right)}$ at $\kappa ={\kappa }_c\approx 1.46$ as a function of the magnetic field for temperatures (top to bottom) $\Theta =0.7,1.0,1.4\text{K}$; the inset shows the irregular oscillations for low field strengths.

Figure 7

Switching ratio $S_c^{\left(N\right)}=S^{\left(N\right)}\left(B=B_c\approx 20\text{mT}\right)$ for varying number of dots $N$ with connecting bridge length $L=W$ for different temperatures $\Theta$.

Figure 8

Configuration mean and standard deviation of the switching ratio $S_{\text{imp}}^{\left(2\right)}\left(B=B_c\right)$ of two connected dots as a function of the impurity layer distance $d$ for different temperatures. The dashed lines give the values $S_c^{\left(2\right)}$ of the disorder-free case.