Adiabatic charge pumping through a dot at the junction of $N$ quantum wires

We study adiabatic charge pumping through a quantum dot placed at the junction of $N$ quantum wires. We explicitly map out the pattern of pumped charge as a function of the time-varying tunneling parameters coupling the wires to the dot and the phase between any two time-varying parameters controlling the shape of the dot. We find that with $N-2$ time-independent well-coupled leads, the maximum pumped charge in the remaining two leads is strongly suppressed with increasing $N$, leading to the possibility of tuning of the pumped charge by modulating the coupling of the $N-2$ leads.

Figure 1

(Color online) Contour plot of the pumped charge for $N=2$ and $3$ wires going from left to right. The $x$ and $y$ axes are $P\cos \varphi$ and $P\sin \varphi$. The color scale is on the right of each plot. Note that the pattern remains the same in both; for $N=2$, the pumped charge reaches a maximum of $\sim \pm 2$, whereas for $N=3$, it reaches a maximum of $\pm 1.11$.

Figure 2

(Color online) Typical pumping contours as a function of the pumping parameters $X_1=J_1^2$ and $X_2=J_2^2$. For $N=2$, the full pumping contours are shown for three classes corresponding to the regions A, B, and C in Fig. 1a. For $N=3$, only a small part of contours of classes $A$ and $C$ corresponding to regions A and C in Fig. 1b is shown, along with the resonance points $R=0$ (black dots). Note that contour A does not enclose the resonance points and contour C encloses both once.

Figure 3

(Color online) Different contributions to the pumped charge $Q$ for $N=2$ (a) and 3 (b). The full red line is $Q_{\mathrm{int}}$, the blue dash-dotted line is the total pumped charge $Q$, and the green (and magenta for $N=3$) dotted lines are $Q_{\mathrm{tran}}$. Note that the large pumped charge is correlated with $Q_{\mathrm{int}}\ne 0$. (b) shows only a small region of $P$, because the width of $P$ for which pumped charge is large is smaller. The numerical values chosen to obtain $Q$ are $J=1.0,J_{10}=J_{20}=2.0,\varphi =0.05\pi$, $ka=0.001\pi ,\omega =1.0$.

Figure 4

(Color online) (a) Contour plot of transmission maxima $(T_{12}+T_{13})$ for three values of $J_3$. Lines A, B and C denote resonance lines for $J_3=0.1$, 0.9, and $1.1$, respectively. The crosses denote the $R=0$ points. Note that in the lower left quadrant, lines A and B are indistinguishable and the resonance point on A, B, and C is indistinguishable and denoted by a single cross. (b) Pumped charge $Q$ as a function of the pumping amplitude $P$ for three values of $J_3=0.1$, 1.1, and $J_3=10.0$. The other parameters are the same as in Fig. 2.

Figure 5

(Color online) Maximum pumped charge versus the number of wires.