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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 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.
Hua Chen (Wed,) studied this question.