Valley density wave in graphite in the quantum limit

Graphite in the quantum limit shows unconventional in-plane and out-of-plane transport behavior. To uncover its microscopic origin, we construct an interacting electron model with a pair of electron band and hole band with the valley degree of freedom. We use a fermionic renormalization group (RG) method and study a parquet RG equation of the model with screened Coulomb interaction. We found that, for strong screening region, the one-loop RG indicates a dominant instability of valley charge density wave (VCDW) with a finite pairing between the two valleys. We further construct an effective mean-field theory and clarify the in-plane transport behavior of the VCDW phase.