Emergence of nematic loop-current bond order in vanadium Kagome metals

The family of layered Kagome metals $\mathrm{A}\mathrm{V}_3\mathrm{Sb}_5$ $(\mathrm{A}=\mathrm{K,Rb,Cs})$ has recently attracted significant interest due to reports of charge-bond order, orbital magnetism, and superconductivity. Some of these phases may exhibit time-reversal symmetry breaking, as suggested by their response to magnetic fields. More recently, experiments have reported the emergence of nematic order that lowers the rotational symmetry of the system from sixfold to twofold. Here we investigate the mechanism behind a nematic phase that breaks both rotational and time-reversal symmetries. Starting from a nine-band tight-binding model and nearest-neighbour Coulomb interactions, we find nematic order to emerge in a narrow region of phase space within mean-field theory. The nematic state is a superposition of charge-bond order along one Kagome bond and loop-current order on the other two, preserving one of the three mirror planes. To understand this behaviour, we examine an effective patch model that captures one $p$-type and one $m$-type van Hove singularity at each $M$ point on the Brillouin zone boundary. Within the effective model, nematic order is stabilized by the coupling between the complex phases of the three bond order parameters. As a consequence, the nematic phase develops an elongated Fermi surface distinct from those of competing phases.