Nodal liquid ands-wave superconductivity in transition metal dichalcogenides

We explore the physical properties of a unified microscopic theory for the coexistence of superconductivity and charge-density waves (CDWs) in two-dimensional transition-metal dichalcogenides. In the case of particle-hole symmetry, the elementary particles are Dirac fermions at the nodes of the charge density wave gap. When particle-hole symmetry is broken, electron (hole) pockets are formed around the Fermi surface. The superconducting ground state emerges from the pairing of nodal quasiparticles mediated by acoustic phonons via a piezoelectric coupling. We calculate several properties in the s-wave superconducting phase, including specific heat, ultrasound absorption, nuclear magnetic relaxation (NMR), and thermal and optical conductivities. In the case with particle-hole symmetry, the specific-heat jump at the transition deviates strongly from ordinary superconductors. The NMR response shows an anomalous anisotropy due to the broken time-reversal symmetry of the superconducting gap, induced by the triple CDW state. The loss of the lattice inversion center in the CDW phase leads to anomalous coherence factors in the optical conductivity and to the appearance of an absorption edge at the optical gap energy. In addition, optical and thermal conductivities display anomalous peaks in the infrared when particle-hole symmetry is broken.