title: Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates.
abstract: 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 an exchange of spin fluctuations before magnetic order develops. We argue that the ordered state with the lowest energy has nonzero CDW and PDW components with the same momentum. Such a state breaks C_{4} 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 d_{x^{2}-y^{2}} superconductivity and make specific predictions for experiments.
authors.affiliation: Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA.
authors.forename: Yuxuan
authors.initials: Y
authors.lastname: Wang
authors.affiliation: Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53211, USA.
authors.forename: Daniel F
authors.initials: DF
authors.lastname: Agterberg
authors.affiliation: William I. Fine Theoretical Physics Institute and School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA.
authors.forename: Andrey
authors.initials: A
authors.lastname: Chubukov