Coexistence of a double-Qspin-density wave and a multi-Qpair-density wave in cuprate oxide superconductors

Abstract

Spatial 4a × 4a modulations, with a the lattice constant of CuO2 planes, or the so called checkerboards can arise from double-Q spin density wave (SDW) with Q1 = (±π/a, ±3π/4a) and Q2 = (±3π/4a, ±π/a). When multi-Q pair density wave, that is, the condensation of dγ-wave Cooper pairs with zero total momenta, ±2Q1, ±2Q2, ±4Q1, ±4Q2, and so on is induced by the SDW, gaps can have fine structures similar to those of the so called zero-temperature pseudogaps.PACS numbers: 74.20.-z, 75.10.-b, 74.90.+n, 71.10.-w High critical-temperature (high-T c ) superconductivity in cuprate oxides is an important and long standing issue since its discovery [1]. Many unconventional properties are observed in addition to high T c : the so called spin gap [2] or pseudogap above T c [3,4,5,6,7,8,9, 10], 4a × 4a spatial modulations called checkerboards, with a the lattice constant of CuO 2 planes, of local density of states (LDOS) around vortex cores [11], above T c [12], and below T c [13,14,15], the so called zero-temperature pseudogaps (ZTPG) [16], and so on. The issue cannot be settled unless not only high T c but also unconventional properties are explained within a theoretical framework.Since cuprates are highly anisotropic, thermal critical superconducting (SC) fluctuations, which would be divergent at nonzero T c in two dimensions [17], must play a role in the opening of pseudogaps. This issue is examined in another paper [18].The period of checkerboard modulations is independent of energies. Their amplitude depends on energies; it is only large in the gap region. When the modulating part is divided into symmetric and asymmetric ones with respect to the chemical potential, the symmetric one is larger than the asymmetric one [14]. Fine structures are observed in ZTPG [16]. It is difficult to explain these observations in terms of charge density wave (CDW). Several possible mechanisms have been proposed: Fermi surface nesting [19], valence-bond solids [20,21], pair density waves [22,23], hole-pair [19,24,25] or single-hole [19,20] Wigner solids, and Wigner supersolids [26,27]. The purpose of this Letter is to propose another mechanism: The spatial modulation of LDOS is due to spin density wave (SDW) and ZTPG is due to the coexistence of SDW and superconductivity or pair density waves induced by SDW.Cuprates with no dopings are Mott-Hubbard insulators, which exhibit antiferromagnetism. As dopings are increased, they exhibit the Mott-Hubbard transition or crossover and they becomes metals. High-T c superconductivity occurs in such a metallic phase. According to a previous theory [28], which is consistent with a combined one of Hubbard's [29] and Gutzwiller's [30] ones, a three-peak structure appears in the density of states; the so called Gutzwiller's quasiparticle band between the lower and upper Hubbard bands (LHB and UHB). This is confirmed by the single-site approximation (SSA) [31,32] that includes all the single-site terms or by the dynamical mean-filed theory (DMFT) [33]. The three-peak structure corresponds to the so cal...

Opening of a pseudogap in a quasi-two-dimensional superconductor due to critical thermal fluctuations

“…A mechanism of ZTPG is proposed in a previous paper. 49 As is discussed in the Appendix, magnetic exchange interactions are responsible for superconductivity as well as magnetism in cuprate oxide superconductors. Then, the competition or an interplay between superconductivity and antiferromagnetism or SDW can play a crucial role.…”

“…A 4a-period stripe structure can arise from an 8a-period single-Q SDW; a 4a ϫ 4a checkerboard structure can arise from a double-Q SDW; a fine structure similar to that of ZTPG can arise from the coexistence of the single-Q or double-Q SDW and a multi-Q pair density wave of d␥-wave Cooper pairs. 49 On the other hand, the normal phase above T c has no phase boundary between under-doped and over-doped regions. Then, the examination of this paper implies that a pseudogap due to thermal SC and SDW critical fluctuations can open in the normal phase of under-doped cuprates where ZTPG and the checkerboard structure are present below T c .…”

Scanning tunneling microscopy and spectroscopy study of4a×4aelectronic charge order and the inhomogeneous pairing gap in superconductingBi2Hashimoto1, Momono2, Oda3 et al. 2006Phys. Rev. B371320View full textAdd to dashboardCite

“…9,10,[33][34][35] The appearance of the charge order within the pairing gap is not inconsistent with the models of pair density waves, electronic supersolids, paired-hole Wigner crystallization, or the coexistence of multitype SC and spin density wave. [36][37][38][39][40][41][42][43][44][45][46] On the other hand, Vershinin et al have claimed that the nondispersive ϳ4a ϫ 4a charge order at T Ͼ T c is a hidden order of the electron system in the pseudogap state ͑T Ͼ T c ͒. 3 In that case, the observation that the nondispersive charge order survives even in the SC state means that the hidden order of the pseudogap state will remain essentially unchanged down to below T c .…”

Origin and roles of a strong electron-phonon interaction in cuprate oxide superconductors

“…On the other hand, the symmetric component is large when the 2Q modulation is due to a simple second-harmonic effect of an ordered SDW with Q. 51 The second-harmonic effect of the SDW can explain the observed almost symmetric 2Q ͑͒. When stripes and checkerboards are really static orders, stripes must be due to single-Q SDW and checkerboards must be due to double-Q SDW.…”