A Landau Theory for Pair Density Modulation in Fe(Te,Se) flakes

Motivated by recent scanning tunneling microscopy (STM) experiments reporting a pair-density modulation (PDM) in flakes of FeTe${_{0.55}}$Se${_{0.45}}$, we develop a Landau theory to elucidate its physical origin. We analyze the PDM in terms of screw and glide symmetries, interpreting it as a hybridized state of two order parameters with opposite glide and screw parity. To explain the absence of PDM in the bulk, we argue that the breaking of glide symmetry at the surface allows nematic order to selectively stabilize the PDM in thin flakes. From these symmetry constraints, we show that the opposing glide and screw parities of the condensate favor a site-based, rather than bond-based, pairing mechanism. Thus the discovery of PDM in superconducting flakes suggests that the pairing in iron-based superconductors is local to the iron atoms, possibly driven by Hunds coupling. We argue that the mismatch in Knight shift between the even and odd parity order parameters will lead to a magnetic-field enhancement of the PDM at low fields, and a reentrant triplet phase at high fields that can be tested in STM experiments.