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Charge order in kagome metals is of extensive current interest. Recently, acharge density wave was discovered in the magnetic binary kagome metal FeGe. Inanalogy 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 systemmanifestly shows effects of substantial correlations. Here we identify thetopological bands crossing the Fermi energy (E$_F$) in FeGe and characterizethe correlation-induced renormalization of these bands. We then derive a chargeorder from an effective model comprising topological kagome `flat' bands in thepresence of a magnetic order. We demonstrate edge states as well as excessout-of-plane magnetic moment associated with the charge order; both arefingerprints of non-trivial band topology and consistent with recentexperimental observations. Our results point to FeGe as an ideal platform torealize and elucidate correlated topological physics.

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