Melting transition of the nematic state in an under-doped d-wave superconductor

We study the melting transition of smectic state in an under-doped d-wave superconductivity. We demonstrate that the transition is discontinuous to the nematic state by increasing the impurities. We calculate the entropy as a function of impurities which shows a sharp transition between the smectic and nematic states. We also show that the density-of-states at the Fermi energy emerges as the sub-gap induced by the SDW order is smeared out gradually. The transition between the smectic and nematic states is associated the reconstruction of the electronic Fermi surface. We calculate the superfluid density that exhibit a plateau and indicates that the nematic state development in d-wave superconductor is distinct from high-temperature pseudogap.