Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates

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We analyze incommensurate charge-density-wave (CDW) and pair-density-wave (PDW) orders with transferred momenta (± Q,0)/(0,± Q) in underdoped cuprates within the spin-fermion model. Both orders appear due to exchange of spin fluctuations before magnetic order develops.We argue that the ordered state with the lowest energy has non-zero CDW and PDW components with the same momentum. Such a state breaks C₄ lattice rotational symmetry, time-reversal symmetry, and mirror symmetries. We argue that the feedback from CDW/PDW order on fermionic dispersion is consistent with ARPES data. We discuss the interplay between the CDW/PDW order and dₓ₂₋y₂ superconductivity and make specific predictions for experiments.