Motivated by quantum oscillations observed in highly ordered ortho-II ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{6.5}$, we study the Fermi-surface topology of $d$ density wave (DDW) or antiferromagnetic ordering in the presence of the ortho-II potential. We find that the electron pocket is unaffected by the presence of the ortho-II potential. This further strengthens the proposal that quantum oscillations observed in ortho-II-free ${\text{YBa}}_2{\text{Cu}}_4{\text{O}}_8$ arise from an electron pocket. On the other hand, the hole pocket topology is sensitive to the ortho-II potential. We show that there exist generically three distinct quantum oscillations associated with one electronlike and two holelike Fermi pockets. We compare our results to the quantum oscillations observed in experiments. We discuss possible ways to distinguish between DDW and antiferromagnetic orders in a potential single-layer ortho-II material.

• Received 17 November 2008

DOI:https://doi.org/10.1103/PhysRevB.78.224516