Pair density waves in superconducting vortex halos

Abstract

The authors analyze the interplay between a $d$-wave uniform superconducting and a pair-density-wave order (PDW) parameter in the neighborhood of a vortex, and compute the resulting local density of states in the vortex halo. The intertwining of the two superconducting orders leads to a charge density modulation with the same periodicity as the PDW, which is twice the period of the charge density wave that arises as a second harmonic of the PDW itself. They discuss key features of the charge density modulation that can be directly compared with recent results from scanning tunneling microscopy and speculate on the role PDW order may play in the global phase diagram of the hole-doped cuprates.