Recent scanning tunneling microscopy experiments of ${\mathrm{B}\mathrm{i}}_2{\mathrm{S}\mathrm{r}}_2{\mathrm{C}\mathrm{a}\mathrm{C}\mathrm{u}}_2{\mathrm{O}}_{8+\delta }$ 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.

• Received 27 January 2004

DOI:https://doi.org/10.1103/PhysRevLett.93.187002