Pristine and intercalated transition metal dichalcogenide superconductors

Transition metal dichalcogenides (TMDs) are quasi-two-dimensional layered compounds exhibiting strongly competing charge-density wave (CDW) and superconducting (SC) order parameters (OPs). The weak van der Waals interlayer bonding between hexagonal layers of octahedral or trigonal prismatic TMD building blocks allows for many polytypes. The non-superconducting $1T$ polytypes can have one or more CDWs. The $2H$ polytypes have two or more Fermi surfaces and saddle bands, allowing for dual orderings, which can be coexisting CDW and SC orderings, two SC gaps as in MgB$_2$, or two CDW gaps. The CDW transitions $T_{\rm CDW}$s usually greatly exceed the low superconducting $T_{\rm c}$s, their orbital OPs are generally highly anisotropic and can even contain nodes, are remarkably similar to the the high-$T_{\rm c}$ cuprate pseudogaps, and the SC OPs can be greatly affected by their presence. In 2$H$-NbSe$_2$, the CDW renders its general $s$-wave SC OP orbital symmetry to be highly anisotropic and strongly reduces its Josephson coupling strength ($I_{\rm c}R_{\rm n}$) with Pb. Pressure and intercalation generally suppress the CDWs, enhancing $T_{\rm c}$. The misfit intercalation compound (LaSe)$_{1.14}$(NbSe$_2$) and many intercalated $2H$-TMDs, such as TaS$_2$(pyridine)$_{1/2}$, have completely incoherent $c$-axis transport, dimensional-crossover effects, and behave as stacks of intrinsic Josephson junctions. Except for the anomalously large violation of the Pauli limit of the upper critical field of (LaSe)$_{1.14}$(NbSe$_2$), these properties are very similar to those of the cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ and of the organic layered superconductor, $\kappa$-(ET)$_2$Cu[N(CN)$_2$]Br. Intercalates of TMDs with water and metallic ions are very similar to Na$_x$CoO$_2\cdot y$H$_2$O.