Spectral signatures of modulated d -wave superconducting phases

We calculate, within a mean-field theory, the spectral signatures of various striped d -wave superconducting phases. We consider both in-phase and antiphase modulations of the superconducting order across a stripe boundary and the effects of coexisting inhomogeneous orders, including spin stripes, charge stripes, and modulated d -density wave. We find that the antiphase modulated d -wave superconductor exhibits zero-energy spectral weight, primarily along extended arcs in momentum space. Concomitantly, a Fermi surface appears and typically includes both open segments and closed pockets. When weak homogeneous superconductivity is also present, the Fermi surface collapses onto nodal points. Among them are the nodal points of the homogeneous d -wave superconductor, but others typically exist at positions that depend on the details of the modulation and the band structure. Upon increasing the amplitude of the constant component, these additional points move toward the edges of the reduced Brillouin zone where they eventually disappear. The above signatures are also manifested in the density of states of the clean, and the disordered system. While the presence of coexisting orders changes some details of the spectral function, we find that the evolution of the Fermi surface and the distribution of the low-energy spectral weight are largely unaffected by them.