Possible surface nematic order in iron pnictides

Nematic fluctuations play important role in the physics of the iron-based superconductors. Indications for weak precursor nematic transition has been found in the compound BaAs$_{2-x}$P$_x$Fe$_2$$[$1$]$. However, high-resolution specific-heat measurements did not reveal any bulk transition$[$2$]$. To resolve this controversy, we consider the possibility of the surface nematic transition preceding the bulk transition. We consider the simplest model of two interacting quasi-two-dimensional electronic bands and explore the free-surface effects on the nematic order. We found that three-dimensional effects suppress the bulk nematic order and therefore this order is enhanced near the surface.\\ $[$1$]$Kasahara, S., et al. "Electronic nematicity above the structural and superconducting transition in Ba(As$_{1-x}$P$_x$Fe$)_2$." Nature 486.7403 (2012): 382-385.\\ $[$2$]$Luo, X., et al. "Antiferromagnetic and nematic phase transitions in Ba(As$_{1-x}$P$_x$Fe$)_2$ studied by ac microcalorimetry and SQUID magnetometry." Physical Review B 91.9 (2015): 094512.