Interaction-driven intervalley coherence with emergent Kekulé orbitons

The authors report here an intervalley coherent phase with the liberated orbital degree of freedom in a $p$-band honeycomb lattice. This phase is analyzed based on an orbital exchange model in the strong-coupling regime. The ensuing classical ground-state manifold enjoys a continuous symmetry dictated by the coherent phase between \ifmmode\pm\else\textpm\fi{}$K$ valleys. The quantum fluctuation ultimately selects a unique ground state with emergent Kekul\'e orbitons through the order-by-disorder mechanism. These findings reveal a fundamentally new mechanism for the intervalley coherent phase.