Complementary pair-density-wave andd-wave-checkerboard orderings in high-temperature superconductors

Abstract

The competing orders in the particle-particle ͑P-P͒ channel and the particle-hole ͑P-H͒ 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 ͑DWCB͒ order in the P-H channel and the pair-density-wave ͑PDW͒ 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 ϫ 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.

Visualization of the periodic modulation of Cooper pairing in a cuprate superconductor

“…Thirdly, our technique has the advantage of mapping the CDW and PDW orders simultaneously, which allow us to reveal that at least at this particular doping, the pair density and charge density modulations are positively correlated and in-phase with each other. This observation is consistent with the theoretical models where intertwined PDW, d-form factor charge order and d-wave superconductivity coexist 2,18,22,[25][26][27][28][29][30] , but is in contrast to the case of conventional BCS superconductors such as NbSe2, in which the SC coherence is shown to anti-correlate with local charge density wave order due to the competition of the two orders 50 .An important issue that deserves further investigation is whether the PDW is an induced secondary order by the charge order, or the other way around. Our previous STM experiment on lightly doped Bi2Sr2CuO6+δ reveals that the charge order emerges from the parent Mott insulator even before the global superconductivity sets in 10 .…”

“…For cuprates, several types of PDW orders have been proposed to be the origin of the charge order 16-30 , including unidirectional 16-22 , bidirectional 23 , and Ampere pairings 24 . More recently, theories involving the intertwinned PDW with d-form factor charge order and superconductivity have been extensively studied [25][26][27][28][29][30] , and it is proposed that both orders share a common wavevector.Although PDW in the cuprates has been predicted for more than 10 years, direct experimental proof of its existence has been lacking. The main challenge is how to probe the spatial distribution of Cooper pairing in the atomic scale.…”

“…It was found that the superfluid density ρS(r) shows a checkerboard pattern indicative of the PDW state, and it shares a common wavevector with the checkerboard charge order. The most probable scenario was proposed to be the coexisting of d-wave symmetry superconductivity and d-symmetry form factor CDW.If the PDW state is such a pronounced feature as revealed in the SJTM, one would expect that it should also manifest itself in single particle tunneling spectroscopy probed by plain STM.An obvious strategy is to investigate the spatial distribution of SC gap size, but recent theories show that the SC gap size may not show spatial periodicity even if there is PDW order [24][25][26][30][31][32] . Here we propose that there are two other key characteristics associated with superconductivity in a single particle tunneling spectrum.…”

“…To explain the origin of the charge order and its implication to the superconducting phase, many theoretical models have been proposed, such as charge stripes 13 , electronic nematicity 13,14 , and Fermi surface instability 6,15 The basic idea of PDW can date back to the original proposal of Fulde-Ferrell 33 and Larkin-Ovchinnikov 34,35 , in which the singlet pairing between the Zeeman-split Fermi surfaces will have a finite momentum Q, corresponding to periodic spatial modulations. For cuprates, several types of PDW orders have been proposed to be the origin of the charge order [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] , including unidirectional [16][17][18][19][20][21][22] , bidirectional 23 , and Ampere pairings 24 . More recently, theories involving the intertwinned PDW with d-form factor charge order and superconductivity have been extensively studied [25][26][27][28][29][30] , and it is proposed that both orders share a common wavevector.…”

Translational-invariant bipolarons and superconductivity

“…При этом возникают интересные особенности [195]. В настоящее время активно обсуждается также возможность образования неоднородного БЭК в форме так называемых волн плотности сконденсированных пар (PDW), разрушающих трансляционную инвариантность [154], [196][197][198][199][200]. Ситуация здесь, однако, отличается от обсуждаемой проблемы поляронов и биполяронов с нарушенной или присутствующей ТИ-симметрией ( § 1, 2).…”