We performed scanning tunneling microscopy/spectroscopy measurements in the superconducting state of underdoped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+x}$, and demonstrated that the checkerboard (CB) and Bogoliubov quasiparticle interference (QPI) modulations, which are considered to be characteristic features for the low-energy states around the antinodal and nodal regions of the Fermi surface, respectively, coexist in identical regions of the Cu-O plane. In the present work, these electronic superstructures are successfully separated from each other, and the local amplitude and phase are evaluated for the CB modulation and the ${\mathit{q}}_1$ component of QPI, which are characterized by similar wave vectors. The ${\mathit{q}}_1$-QPI component tends to be in-phase and antiphase with the CB modulation for positive and negative bias voltages, respectively. The significant spatial phase relationship is confirmed in regions where the local amplitude of CB modulation is comparatively large. This finding implies an interplay between the QPI and CB modulations.

• Received 11 September 2020
• Revised 22 October 2020
• Accepted 22 October 2020
• Corrected 24 December 2020

DOI:https://doi.org/10.1103/PhysRevB.102.184513