Auto-correlation ARPES study of Pb-Bi2201

It is important to understand the electronic structure in momentum (k-) and real (r-) spaces in a unified picture. In high-temperature (Tc) cuprates, the different shape of superconducting gap anisotropies have been found by scanning tunneling microscopy (STM) and angle-resolved photoemission spectroscopy (ARPES). While the ARPES studies show simple d-wave superconducting gap around the node below Tc, the STM studies which approach superconducting gap anisotropy in k-space by employing the ``octet model'' show the deviation from simple d-wave superconducting gap especially in the underdoped region. To explore this issue, we study auto-correlation (AC-) ARPES spectra of optimally doped Pb-Bi2201 measured at T $<<$ Tc, Tc $<$ T $<<$ T*, and T $>$ T*. The obtained AC-ARPES spectra show very similar behavior to the reported Fourier transformed STM spectra. In the presentation, we will compare these ARPES and STM results and discuss the relationship between r- and k-space focusing on the superconducting gap anisotropy.