Recent experiments have reported valley gauge symmetry broken phases, identified as intervalley coherent (IVC) states. Exploration of anomalous responses, particularly those analogous to superconductivity, has become an urgent theoretical issue. In this study, we show that the IVC order gives rise to anomalous valley current generation driven by surface acoustic waves (SAWs). The anomalous valley current exhibits a characteristic power-law dependence for low-frequency SAWs. Furthermore, we demonstrate by numerical analysis that the IVC order leads to huge valley current generations in rhombohedral graphene. These results open a pathway toward exploring exotic phenomena emerging from valley gauge symmetry breaking, in close analogy with gauge symmetry breaking in superconductors.

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• Electronic structure
• Transport phenomena
• Valley degrees of freedom
• Graphene
• Bogoliubov-de Gennes equations
• Mean field theory
• Surface acoustic wave