Topological strongly correlated phases in orthorhombic diamond lattice compounds

We explore the Mott transition in orthorhombic diamond lattices relevant to $(\mathrm{ET}){\mathrm{Ag}}_{4}{(\mathrm{CN})}_{5}$ molecular compounds. The noninteracting phases include nodal line, Dirac and/or Weyl semimetals depending on the strength of spin-orbit coupling, and the degree of dimerization of the lattice. Based on an extension of slave-rotor mean-field theory which accounts for magnetic order, we find a transition from a semimetal to a paramagnetic Mott insulator at a critical onsite Coulomb repulsion ${U}_{c}$, which becomes N\'eel ordered at a larger ${U}_{\mathrm{cm}}>{U}_{c}$. The resulting intermediate Mott phase is a $\text{U}(1)$ quantum spin liquid (QSL) consisting on spinons preserving the nodal structure of the nearby semimetallic phases. While the QSL can be regarded a nodal-line Mott insulator (NLMI) in the absence of spin-orbit interaction (SOI), it behaves as a Dirac Mott insulator for nonzero SOI. An analysis of the Green's function in the NLMI shows how the zeros follow the spinon nodal-line bands carrying the topology while the poles describe the Hubbard bands. Our results are relevant to recent observations in $(\mathrm{ET}){\mathrm{Ag}}_{4}{(\mathrm{CN})}_{5}$ molecular compounds in which the ambient pressure N\'eel ordered Mott insulator is gradually suppressed until semimetallic behavior arises at larger pressures.