Developing Effective Theories: A Case Study in Monolayer Iron Selenide

Abstract

In this work, we outline the development of a series of models which have allowed us to investigate the low-temperature phases of monolayer FeSe. These models are built using group theoretic arguments to ensure the constraints provided by the crystal symmetry are satisfied. We investigate the interplay between stripe antiferromagnetism and spin-vortex crystal order in the framework of the Landau theory of phase transitions. By considering inversion symmetry breaking terms in the Landau free-energy, we show that the spin-vortex crystal is preferred when the non-symmorphic parent symmetry group $P4/nmm$ is reduced to a symmorphic subgroup. We also consider symmetry constraints to develop a ten-orbital tight-binding model for monolayer FeSe. We observe that, following a renormalization of the $d_{XY}$ bands, an inversion of the states near the $M$-point gives rise to a well-separated pair of electron pockets---in accordance with experiment---and allows a simplified two-band model to capture the dynamics of the bands which cross the Fermi energy. Such a model is constructed by considering the irreducible representations for the states identified in the tight binding model. Finally, we classify the superconducting orders according to their symmetry character. We find that gaps belonging to the $A_{1g}$ and $B_{2g}$ representations each support nodeless superconductivity, despite the latter being a $d$-wave order. Using a model for antiferromagnetic spin interactions, we also show that the leading order (without spin-orbit coupling) is the $B_{2g}$ order. Additionally, our model for the $B_{2g}$ order produces a nodeless, anisotropic gap, with multiple coherence peaks in the density of states, in accordance to what is observed in experiment.