Isotropic Cooper pairs with emergent sign changes in a single-layer iron superconductor

We model a single layer of heavily electron-doped FeSe by spin-$\frac{1}{2}$ moments over a square lattice of iron atoms that include the $3d_{xz}$ and $3d_{yz}$ orbitals, at strong on-site Coulomb repulsion. Above half filling, we find emergent hole bands below the Fermi level at the center of the one-iron Brillouin zone in a half-metal state characterized by hidden magnetic order and by electron-type Fermi surface pockets at wave numbers that double the unit cell along the principal axes. “Replicas” of the emergent hole bands exist at lower energy in the two-iron Brillouin zone. Exact calculations with two mobile electrons find evidence for isotropic Cooper pairs that alternate in sign between the electron bands and the emergent hole bands.

Figure 1

(a) The imaginary part of the transverse spin susceptibility, Eq. (3), in the true spin channel and (b) the imaginary part of the one-electron propagator near half filling, Eq. (5), at site-orbital concentration $x=0.01$. Not shown in (b) is intrinsic broadening due to the incoherent contributions in Eq. (4).

Figure 2

(a) Low-energy spectrum of two-orbital $t\text{−}J$ model, Eq. (1) plus constant $\frac{3}{4}(N_{\mathrm{Fe}}-1)J_0$, over a $4\times 4$ lattice, with one electron more than half filling. Model parameters coincide with those listed in Fig. 1, except $t_1^{\parallel }=2J_1^{\parallel }$ and $-J_0=1.733J_1^{\parallel }$. (b) Low-energy spectrum of Eq. (1) plus repulsive interactions (see text) plus constant $\frac{1}{4}(N_{\mathrm{Fe}}-2)J_0$, but with two electrons more than half filling, with $-J_0=2.25J_1^{\parallel }$, and with $U_0^{\prime }=\frac{1}{4}{J}_0+1000J_1^{\parallel }$. Some points in the spectra are artificially moved slightly off their quantized values along the momentum axis for the sake of clarity.

Figure 3

The complex order parameter for superconductivity, Eq. (6), symmetrized with respect to both reflections about the principal axes.