4Hb-TaS2 is a transition-metal dichalcogenide (TMD) comprising an alternate stack of two two-dimensional polymorphs, T and H, which are intriguing materials in their own right. The T-structure is the only TMD with one valence electron per unit cell that does not have a metallic ground state. The precise nature of its ground state is not known, but it is well established that it is some kind of non-magnetic Mott insulator on a triangular super lattice. On the other hand, the H-structure is a metal that becomes superconducting below 0.7K.
When these two elements are put together in the 4Hb structure, they form a superconductor that differs significantly from the superconducting state in the H-polymorph. First, it has an elevated Tc ~ 2.6K. Second, it exhibits a number of unusual phenomena, including linear-in-T specific heat, enhancement of the muon-relaxation rate below Tc, anisotropic in plane critical field, π-shift in the Little-Parks oscillations and a mysterious magnetic memory that exists in some temperature range above Tc.
I will describe these various experimental results and how we can understand some of them in theory. I will also spend some time discussing 1T-TaS2, which seems to be crucial to the unconventional superconductivity in this system.