Adiabatic Pumping through Interacting Quantum Dots

We present a general formalism to study adiabatic pumping through interacting quantum dots. We derive a formula that relates the pumped charge to the local, instantaneous Green’s function of the dot. This formula is then applied to the infinite-$U$ Anderson model for both weak and strong tunnel-coupling strengths.

Figure 1

Pumped charge in units of $e\eta /{\overline{\Gamma }}^2$ as a function of the level position in units of $\overline{\Gamma }$ for $U\to \infty$ (solid line) and $U=0$ (dashed line). The temperature is $k_{\mathrm{B}}T=5\overline{\Gamma }$, and $E_{\mathrm{c}}=20\overline{\Gamma }$.

Figure 2

Pumped charge in units of $e\eta /{\overline{\Gamma }}^2$ as a function of temperature (in units of the level position), for $U\to \infty$ (solid line) and for $U=0$ (dashed line). The level position is fixed at $ϵ=-2.5\overline{\Gamma }$. In both cases, a maximum appears at almost the same temperature. The cutoff energy is $E_{\mathrm{c}}=20\overline{\Gamma }$. Inset: Pumped charge as a function of temperature (in units of $T_{\mathrm{K}}$) for $U\to \infty$. For $0<T<0.5T_{\mathrm{K}}$, $Q$ is obtained by means of the mean-field slave-boson method, performing a Sommerfeld expansion. For $T>1.5T_{\mathrm{K}}$, it is computed numerically using the equation-of-motion Green’s function.

Figure 3

Pumped charge in units of $e\eta /{\overline{\Gamma }}^2$ as a function of the level position in units of $\overline{\Gamma }$, for $U\to \infty$, $T=0$, and $E_{\mathrm{c}}=20\overline{\Gamma }$, computed by means of the mean-field slave-boson method.