Minimal electronic models for superconducting BiS${}_2$ layers

We construct minimal electronic models for a newly discovered superconductor LaO${}_{1-x}$F${}_x$BiS${}_2$ ($T_c=10.6$ K) possessing BiS${}_2$ layers based on a first-principles band calculation. First, we obtain a model consisting of two Bi $6p$ and two S $3p$ orbitals, which give nearly electron-hole symmetric bands. Further focusing on the bands that intersect the Fermi level, we obtain a model with two $p$ orbitals. The two bands (per BiS${}_2$ layer) have a quasi-one-dimensional character with a double minimum dispersion, which gives good nesting of the Fermi surface. At around $x\sim 0.5$ the topology of the Fermi surface changes, so that the density of states at the Fermi level becomes large. Possible pairing states are discussed.

Figure 1

The lattice structure of LaOBiS${}_2$.

Figure 2

The first-principles band structure is shown.

Figure 3

(a) The 24 orbital model and (b) the four orbital model. In (b), the dashed (dotted-dashed) lines denote the Fermi energy for the doping ratio $\delta =0.5$ ($\delta =0.25$).

Figure 4

(a) The tight-binding model on the Bi square lattice is shown along with the hoppings of $p_X$ and $p_Y$ orbitals. The stars denote the position of the S atom, whose $p$ orbitals are explicitly considered in the four orbital model, but are integrated out in the two orbital model. (b) The band structure of the two orbital model. The dashed (dotted-dashed) lines denote the Fermi energy for the doping ratio $\delta =0.5$ ($\delta =0.25$). (c) The Fermi surface of the two orbital model for the doping rate of $\delta =0.25$ and $\delta =0.5$. (d) A schematic figure of the $p_X$ band along $(-\pi ,-\pi )\to (0,0)\to (+\pi ,+\pi )$. Three types of nesting vectors are shown by the arrows.

Figure 5

The largest eigenvalue of the irreducible susceptibility matrix for $\delta =0.25$ and 0.5.

Figure 6

(a) Sign conserving $s$ wave for attractive pairing interactions such as mediated by phonons or charge fluctuations, (b) sign reversing $s$ wave, and (c) $d$-wave superconducting gaps obtained for repulsive pairing interactions mediated by spin fluctuations.