Periodic density-of-states modulations in superconducting ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$

In this paper we show, using scanning tunneling spectroscopy, the existence of static striped density of electronic states in nearly optimally doped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ in zero field. The observed modulation is strongest at roughly half the superconducting gap energy and is aligned with the Cu-O bonds, with a periodicity of four lattice constants, exhibiting features characteristic of a two-dimensional system of line objects. These features also exhibit asymmetries between the two orthogonal directions locally, pointing to a possible broken symmetry state (i.e., a stripe phase). We further show that the density of states modulation manifests itself as a shift of states from above to below the superconducting gap. The fact that a single energy scale (i.e., the gap) appears for both superconductivity and stripes suggests that these two effects have the same microscopic origin.