Pair Density Wave in the Pseudogap State of High Temperature Superconductors

Recent scanning tunneling microscopy experiments of Bi₂Sr₂CaCu₂O_8+δ have shown evidence of real-space organization of electronic states at low energies in the pseudogap state [M. Vershinin et al., Science, 303, 1995 (2004).]. We argue based on symmetry considerations as well as model calculations that the experimentally observed modulations are due to a density wave of d-wave Cooper pairs without global phase coherence. We show that scanning tunneling microscopy measurements can distinguish a pair density wave from more typical electronic modulations such as those due to charge density wave ordering or scattering from an on site periodic potential.