Scattering from incipient stripe order in the high-temperature superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$

We use spectroscopic mapping with the scanning tunneling microscope to probe modulations of the electronic density of states in single crystals of the high temperature superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ as a function of temperature. We show that the Cu-O bond-oriented modulations, with periodicity near four lattice constants (4a), that form below the pseudogap temperature have a temperature-dependent energy dispersion displaying different behaviors in the superconducting and pseudogap states. We demonstrate that quasiparticle scattering off impurities does not capture the experimentally observed energy- and temperature-dependence of these modulations. Instead, a model of scattering of quasiparticles from short-range stripe order is necessary to reproduce the experimentally observed energy dispersion of the bond-oriented modulations and its temperature dependence across the superconducting critical temperature, T$_{c}$.