Flat band assisted topological charge pump in the dice lattice

Abstract

We comparatively study the possible topological charge pump (TCP) in the Dice lattice by considering two types of time-dependent mass terms of the Dirac electrons, the ${S}_{z}$ and $U$ term, which are taken as the pumping potentials. It is shown that the former ${S}_{z}$ pumping potential preserving the electron-hole symmetry of the system leads to a vanishing charge pump, whereas the later $U$ mass term breaking the electron-hole symmetry can pump out an integer number of charges in a pumping cycle, even the Berry phases of Dirac electrons in both cases are the same vanishing, $\ensuremath{\gamma}=0$. The topological interface state (TIS), due to the flat bands bridging the two pumping regions not from the Dirac-cone bands, can account for the TCP found in the $U$-mass pumping case and oppositely, there is no TIS due to the flat bands in the ${S}_{z}$ pumping case. Our findings imply that the flat band in the Dice lattice may contribute to the electron transport under appropriate settings.