Topological charge-pumping effects induced by bulk magnetic fluxes

The Hall conductance of quantum Hall systems can be related to topological (Thouless) pumping according to Laughlin’s celebrated argument. In the conventional setting, topological charge pumping is induced by threading a Aharonov-Bohm flux through the hole of the system in cylinder or Corbino disk geometry. Here, we explore the analog of topological pumping induced, instead, by the insertion of flux quanta through the bulk of the system. Focusing on the low-energy edge physics in the general framework of Chern-Simons theory, we discuss physical effects induced by this alternative type of pumping in the context of integer and fractional quantum Hall systems. Our construction provides an intuitive setting to understand known effects and explore new ones. In particular, we show that adding superconductivity to the picture allows us to recover the 4π Josephson effect of Majorana fermions and its generalizations to parafermions.