Quantized adiabatic quantum pumping due to interference

Recent theoretical calculations, demonstrating that quantized charge transfer due to adia- batically modulated potentials in mesoscopic devices can result purely from the interference of the electron wave functions (without invoking electron-electron interactions) are reviewed: (1) Anew formula is derived for the pumped charge Q (per period); It reproduces the Brouwer formula without a bias, and also yields the effect of the modulating potential on the Landauer formula in the presence of a bias. (2) For a turnstile geometry, with time-dependent gate voltages V_L(t) and the magnitude and sign of Q are determined by the relative position and orientation of the closed contour traversed by the system in the {V_L - V_R} plane, relative to the transmission resonances in that plane. Integer values of Q (in units of e) are achieved when a transmission peak falls inside the contour, and are given by the winding number of the contour. (3) When the modulating potential is due to surface acoustic waves, Q exhibits a staircase structure, with integer values, reminiscent of experimental observations.