Complementary pair-density-wave and d-wave-checkerboard orderings in high-temperature superconductors

The competing orders in the particle-particle P-P channel and the particle-hole P-H channel have been proposed separately to explain the pseudogap physics in cuprates. By solving the Bogoliubov-de Gennes equation self-consistently, we show that there is a general complementary connection between the d-wave-checkerboard DWCB order in the P-H channel and the pair-density-wave PDW order in the P-P channel. A small pair density localization generates DWCB and PDW orders simultaneously. The result suggests that suppressing superconductivity locally or globally through phase fluctuation should induce both orders in underdoped cuprates. The presence of both DWCB and PDW orders with 4a 4a periodicity can explain the checkerboard modulation observed in Fourier transform scanning tunneling spectroscopies from scanning tunneling microscopy and the puzzling dichotomy between the nodal and antinodal regions as well as the characteristic features such as nondispersive Fermi arc in the pseudogap state.