Electron correlations and charge density wave in the topological kagome metal FeGe

Charge order in kagome metals is of extensive current interest. Recently, a charge density wave was discovered in the magnetic binary kagome metal FeGe. In analogy to its predecessor, the non-magnetic $A$V$_3$Sb$_5$ ($A$=K, Cs, Rb), the in-plane ordering occurs at the $M$ point. In contrast, however, the system manifestly shows effects of substantial correlations. Here we identify the topological bands crossing the Fermi energy (E$_F$) in FeGe and characterize the correlation-induced renormalization of these bands. We then derive a charge order from an effective model comprising topological kagome `flat' bands in the presence of a magnetic order. We demonstrate edge states as well as excess out-of-plane magnetic moment associated with the charge order; both are fingerprints of non-trivial band topology and consistent with recent experimental observations. Our results point to FeGe as an ideal platform to realize and elucidate correlated topological physics.