Charge order in the cuprates

Andrey V. Chubukov,
University of Minnesota


I analyze charge order in hole-doped cuprates. I argue that magnetically-mediated interaction, which is known to give rise to d-wave superconductivity, also gives rise to charge-density-wave instabilities with momenta Q_x =(Q,0) and Q_y =(0,Q), as seen in the experiments. I show that the emerging charge order with Q_x/Q_y is of stripe type and that a stripe CDW order parameter by itself has two components: one is incommensurate density variation, another is incommensurate current. Both components are non-zero in the CDW-ordered state, with the relative phase ±π/2. Such an order breaks time reversal and mirror symmetries and give rise to a non-zero Kerr effect. I further show that, before a true incommensurate CDW order sets in, the system develops a pre-emptive composite order which breaks lattice rotational symmetry and time-reversal symmetry but preserves a translational U(1) symmetry. I discuss the interplay between our CDW order and pair density-wave order (superconducting order with a finite total momentum of a pair) and present the phase diagram of underdoped cuprates.