The recently discovered family of kagome metals has attracted significant interest as a result of reports of charge-bond order, orbital magnetism, and superconductivity. Some of these phases may exhibit time-reversal symmetry breaking. 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 loop-current bond order (NLCBO) that breaks both rotational and time-reversal symmetries. Examining an effective patch model that captures one $p$-type and one $m$-type van Hove singularity at each $M$ point, we find that frustration of the complex order-parameter phases leads to NLCBO. We further present conditions for overcoming other competing phases, including isotropic charge-bond and loop-current orders. Applying our findings to a previously studied model for ${A\mathrm{V}}_3{\mathrm{Sb}}_5$ $(A=\mathrm{K},\mathrm{Rb},\mathrm{Cs})$, we find that NLCBO emerges within a small region of phase space within mean-field theory. Our theory provides a microscopic description that goes beyond symmetry-allowed free-energy analyses and is broadly applicable to other kagome metals featuring van Hove singularities near the Fermi level.

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• Charge density waves
• Nematic order
• Phase diagrams
• Van Hove singularity
• Kagome metal
• Mean field theory