Strong impurities freezing nematicity in underdoped d-wave high–temperature superconductors*

The physical properties of high-$T_c$ superconductors are affected by spatial inhomogeneities introduced by impurities. In addition, superconductivity, smectic and electronic nematicity seem intertwined in these materials. Due to a connection between dislocation positions and the position of dopants which represent external disorder, we examine effects of multiple non-magnetic impurities on the stripe phase induced by antiferromagnetic ordering in underdoped region. The calculation is based on self-consistent Bogoliubov-de Gennes’ (BdG) equations derived from a mean-field $t-t'-U-V$ Hamiltonian. Our results indicate that the quasi one-dimensional stripe is pinned by non-magnetic impurities in the system. In addition, as the impurity concentration increases, the system undergoes phase transitions from the stripe phase to a smectic phase and then from the smectic phase to a nematic phase. We further examine the spatial distribution of order parameters and compute disorder effects on the density of states and the superfluid density for the pure d-wave superconducting phase and the stripe phase.