Discovery and Exploration of the Cuprate Pair Density Wave State
J.C. Séamus Davis
Cooper-pairs, if they have finite center-of-mass momentum QP, can form a remarkable state in which the density of pairs modulates periodically in spaceat wavevector QP. Intense theoretical interest has recently emergedin whether such a ‘pair density wave’ (PDW) state could, due to strong electron-electron interactions, be another principal state in the phase diagram of underdoped cuprates. The most common model invoked is an eight unit-cell (8a0) periodic modulation of the electron-pair condensate.
To search for a cuprate PDW at zero field, we developed a nanometer-resolution scanned Josephson tunneling microscopy (SJTM) to image Cooper-pair tunneling from a d-wave superconducting STM tip at millikelvin temperatures to the Cooper-pair condensate of underdoped Bi2Sr2CaCu2O8. The resulting images of the Cooper-pair condensate show clear pair-density modulations oriented along the Cu-O bond directions wavevectors QP≈(0.25,0);(0,0.25)2π/a0 .
Application of high magnetic fields in cuprates generates an exceptional electronic phase supporting exceptional quantum oscillations and an extraordinary density wave state (J.Chang et al Nature Physics 8, 871 (2012)), which could also be a PDW. To search for evidence of such a PDW state at high fields, we visualize the modulations in the density of electronic states N(r) within the halo surrounding vortex cores. This revealed multiple signatures of a field-induced PDW, including two sets of N(r) modulations occurring at wavevectors QP and 2QP both having predominantly s-symmetry form factors, the amplitude of the latter decaying twice as rapidly as the former. This is in detailed agreement with theory for a field-induced primary PDW that generates secondary CDWs within the vortex halo .
These data indicate that a PDW state exists in the superconducting and high-field pseudogap regimes of cuprates. Its order-parameter exhibits approximately eight CuO2 unit-cell periodicity and predominantly d-symmetry form factor. We review the implications from these discoveries for the microscopic theory of the cuprate pseudogap phase.
 Nature 532, 343(2016)
 arXiv:1802.04673 & to appear Science (2019)
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