Superconductivity in BiS2 layers

When I was in Delhi, Satyabrata Patnaik, introduced me to a fascinating new family of superconductors. He had just published a JACS
Bulk superconductivity in Bismuth Oxysulfide Bi₄O₄S₃
Shiva Kumar Singh, Anuj Kumar, Bhasker Gahtori, Gyaneshwar Sharma, Satyabrata Patnaik, and Veer P. S. Awana

Immediate questions are:

• is the superconductivity unconventional?
• are strong correlations important [crucial]?
• what is the simplest possible effective Hamiltonian?

On the latter, the following two PRBs are helpful

Minimal electronic models for superconducting BiS2 layers
Hidetomo Usui, Katsuhiro Suzuki, and Kazuhiko Kuroki

BiS2-based layered superconductor Bi4O4S3

Yoshikazu Mizuguchi, Hiroshi Fujihisa, Yoshito Gotoh, Katsuhiro Suzuki, Hidetomo Usui, Kazuhiko Kuroki, Satoshi Demura, Yoshihiko Takano, Hiroki Izawa, and Osuke Miura

Here is the layered crystal structure

Electronic structure calculations support the idea that the BiS2 is where the electronic action is. The SO4 sites are not all occupied, which leads to doping into the BiS2 layer. One can write Bi4O4 (SO4)1-x Bi2S4 where x is the occupancy of the SO4 site.
Hence, the superconductor Bi4O4S3 has x=0.5.

What is the simplest model for the electronic structure within the BiS2 layers?

Usui, Suzuki, and Kuroki consider a two-band and a four-band model. The latter has this band structure

The two-band model is obtained from the four-band model by "integrating" out the orbitals on the S atoms, leaving two p-type orbitals on the Bi atoms, with the hopping integrals shown below (and given values in Table II of the paper)

It is interesting that the hopping t and t', between nearest and next-nearest neighbours is comparable, possibly meaning frustration may play a significant role.
x=0 is a band insulator. The horizontal dashed lines correspond to x=0.25 and x=0.5 (the superconductor).

Within the two-band model, it looks like the system is a long way from a half- or quarter- filling band where strong correlations may matter. Also, the relevant p-orbitals are much more extended than the localised d-orbitals in Fe pnictide and Cu oxide based superconductors.

However, the four band model is in some sense close to "half filling". Then the system can be viewed as two coupled charge-transfer insulators. The hybridisation leading to the energy gap and "band insulator" for x=0 may actually be overwhelmed by large Hubbard interactions and/or Hund's rule couplings. 

It will be interesting to see how this subject develops....