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تسجيل مستخدم جديدAtomic-scale Electronic Structure of the Cuprate Pair Density Wave State Coexisting with Superconductivity
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The defining characteristic of hole-doped cuprates is $d$-wave high temperature superconductivity. However, intense theoretical interest is now focused on whether a pair density wave state (PDW) could coexist with cuprate superconductivity (D. F. Agterberg et al., Annual Review of Condensed Matter Physics 11, 231 (2020)). Here, we use a strong-coupling mean-field theory of cuprates, to model the atomic-scale electronic structure of an eight-unit-cell periodic, $d$-symmetry form factor, pair density wave (PDW) state coexisting with $d$-wave superconductivity (DSC). From this PDW+DSC model, the atomically-resolved density of Bogoliubov quasiparticle states N(r,E) is predicted at the terminal BiO surface of Bi$_2$Sr$_2$CaCu$_2$O$_8$ and compared with high-precision electronic visualization experiments using spectroscopic imaging STM. The PDW+DSC model predictions include the intra-unit-cell structure and periodic modulations of N(r,E), the modulations of the coherence peak energy $Delta_p$ (r), and the characteristics of Bogoliubov quasiparticle interference in scattering-wavevector space (q-space). Consistency between all these predictions and the corresponding experiments indicates that lightly hole-doped Bi$_2$Sr$_2$CaCu$_2$O$_8$ does contain a PDW+DSC state. Moreover, in the model the PDW+DSC state becomes unstable to a pure DSC state at a critical hole density p*, with empirically equivalent phenomena occurring in the experiments. All these results are consistent with a picture in which the cuprate translational symmetry breaking state is a PDW, the observed charge modulations are its consequence, the antinodal pseudogap is that of the PDW state, and the cuprate critical point at p* ~ 19% occurs due to disappearance of this PDW.
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Extensive research into high temperature superconducting cuprates is now focused upon identifying the relationship between the classic pseudogap phenomenon$^{1,2}$ and the more recently investigated density wave state$^{3-13}$. This state always exhi
bits wave vector $Q$ parallel to the planar Cu-O-Cu bonds$^{4-13}$ along with a predominantly $d$-symmetry form factor$^{14-17}$ (dFF-DW). Finding its microscopic mechanism has now become a key objective$^{18-30}$ of this field. To accomplish this, one must identify the momentum-space ($k$-space) states contributing to the dFF-DW spectral weight, determine their particle-hole phase relationship about the Fermi energy, establish whether they exhibit a characteristic energy gap, and understand the evolution of all these phenomena throughout the phase diagram. Here we use energy-resolved sublattice visualization$^{14}$ of electronic structure and show that the characteristic energy of the dFF-DW modulations is actually the pseudogap energy $Delta_{1}$. Moreover, we demonstrate that the dFF-DW modulations at $E=-Delta_{1}$ (filled states) occur with relative phase $pi$ compared to those at $E=Delta_{1}$ (empty states). Finally, we show that the dFF-DW $Q$ corresponds directly to scattering between the hot frontier regions of $k$-space beyond which Bogoliubov quasiparticles cease to exist$^{31,32,33}$. These data demonstrate that the dFF-DW state is consistent with particle-hole interactions focused at the pseudogap energy scale and between the four pairs of hot frontier regions in $k$-space where the pseudogap opens.
When very high magnetic fields suppress the superconductivity in underdoped cuprates, an exceptional new electronic phase appears. It supports remarkable and unexplained quantum oscillations and exhibits an unidentified density wave (DW) state. Altho
ugh generally referred to as a charge density wave (CDW) because of the observed charge density modulations, theory indicates that this could actually be the far more elusive electron-pair density wave state (PDW). To search for evidence of a field-induced PDW in cuprates, we visualize the modulations in the density of electronic states $N(bf{r})$ within the halo surrounding Bi$_2$Sr$_2$CaCu$_2$O$_8$ vortex cores. This reveals multiple signatures of a field-induced PDW, including two sets of $N(bf{r})$ modulations occurring at wavevectors $bf{Q}_P$ and $2bf{Q}_P$, both having predominantly $s$-symmetry form factors, the amplitude of the latter decaying twice as rapidly as the former, along with induced energy-gap modulations at $bf{Q}_P$ . Such a microscopic phenomenology is in detailed agreement with theory for a field-induced primary PDW that generates secondary CDWs within the vortex halo. These data indicate that the fundamental state generated by increasing magnetic fields from the underdoped cuprate superconducting phase is actually a PDW with approximately eight CuO$_2$ unit-cell periodicity ($lambda = 8a_0$) and predominantly $d$-symmetry form factor.
An unidentified quantum fluid designated the pseudogap (PG) phase is produced by electron-density depletion in the CuO$_2$ antiferromagnetic insulator. Current theories suggest that the PG phase may be a pair density wave (PDW) state characterized by
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