Atomic-scale electronic structure of the cuprate d-symmetry form factor density wave state

Abstract

Research on high-temperature superconducting cuprates is at present focused on identifying the relationship between the classic 'pseudogap' phenomenon 1,2 and the more recently investigated density wave state 3-13 . This state is generally characterized by a wavevector Q parallel to the planar Cu-O-Cu bonds 4-13 along with a predominantly d-symmetry form factor 14-16 (dFF-DW). To identify the microscopic mechanism giving rise to this state 17-29 , one must identify the momentum-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 reveal that the characteristic energy of the dFF-DW modulations is actually the 'pseudogap' energy ∆ 1 . Moreover, we demonstrate that the dFF-DW modulations at E = −∆ 1 (filled states) occur with relative phase π compared to those at E = ∆ 1 (empty states). Finally, we show that the conventionally defined dFF-DW Q corresponds to scattering between the 'hot frontier' regions of momentum-space beyond which Bogoliubov quasiparticles cease to exist [30][31][32] . These data indicate that the cuprate dFF-DW state involves particle-hole interactions focused at the pseudogap energy scale and between the four pairs of 'hot frontier' regions in momentum space where the pseudogap opens.A conventional 'Peierls' charge density wave (CDW) in a metal results from particle-hole interactions which open an energy gap at specific regions of k-space that are connected by a common wavevector Q. This generates a modulation in the density of free charge at Q along with an associated modulation of the crystal lattice parameters. Such CDW states are now very well known 33 . In principle, a density wave modulating at Q can also exhibit a 'form factor' (FF) with different possible symmetries 34,35 (see Supplementary Section 1). This is relevant to the high-temperature superconducting cuprates because numerous researchers have recently proposed that the 'pseudogap' regime 1,2 (PG in Fig. 1a) contains an unconventional density wave with a d-symmetry form factor [17][18][19][20][21][22][23][24][25][26][27][28][29] . The basic phenomenology of such a state is that intraunit-cell (IUC) symmetry breaking renders the O x and O y sites within each CuO 2 unit-cell electronically inequivalent, and that this inequivalence is then modulated periodically at wavevector Q parallel to (1,0);(0,1). The real-space (r-space) schematic of such a d-symmetry FF density wave (dFF-DW) at Q x , as shown in Fig. 1b, exemplifies periodic modulations at the O x sites that are π out of phase with those at the O y sites. Such a state is then described by A(r) = D(r) cos(φ(r) + φ 0 (r)), where A(r) represents whatever is the modulating electronic degree of freedom, φ(r) = Q x · r is the DW spatial phase at location r, φ 0 (r) represents disorde...

Spin-fermion model with overlapping hot spots and charge modulation in cuprates

“…For example, moderate magnetic fields suppress the superconductivity and then CDW appears 49 in agreement with the experiment 32 . The core of the vortex should display the charge modulation 50 and the latter is well seen in, e.g., STM experiments 51,52 . It is clear that many features of the charge modulation and its competition with the superconductivity are well captured in the framework of the SF model.…”

Plaquette valence bond theory of high-temperature superconductivity

“…After the 30-year history of extremely intensive experimental [1][2][3][4] and theoretical [5][6][7][8][9][10] studies of the high-temperature superconductivity (HTSC) in copper oxides we are still far from understanding the basic mechanism of this fascinating phenomenon. Taking into account the enormous number of researchers involved in this field, one can assume that almost all possible ideas were expressed and that the main problem is just to select the basic simple concepts from the pile of available theoretical results.…”

Spatial distribution of superconducting and charge-density-wave order parameters in cuprates and its influence on the quasiparticle tunnel current (Review Article)

“…The existence of intrinsic disorder in high-c T oxides is another factor, which makes the identification of CDW gaps more complicated than that of their superconducting counterparts [33][34][35][36][37][38] as comes about from the scanningtunnel-microscopy (STM) measurements. The spread of the latter over the sample surface is also quite wide, although the distribution histogram for the superconducting gaps is narrower than that for the CDW ones in the cases when the both kinds can be distinguished [39].…”