Antiferromagnetic and van Hove Scenarios for the cuprates: Taking the best of both worlds

Abstract

The purpose of this paper is to describe a microscopically-based theory of the cuprates that combines the strong features of the above described antiferromagnetic and van Hove scenarios. The first step in the construction of such a theory is the observation that the ARPES quasiparticle dispersion may be caused by holes moving in a local antiferromagnetic environment, rather than by band structure effects. This idea is motivated by the existence of universal flat bands [5][6][7] near k = (π, 0), (0, π) in the spectrum of hole-doped cuprates (2D square lattice language), which are difficult to understand unless caused by correlation effects in the CuO 2 planes. Recently, [8,9] it has been shown that models of correlated electrons can account for such flat bands, and here we further elaborate on this idea showing that the agreement with ARPES is quantitative.Using the well-known two dimensional (2D) t − J model defined by the Hamiltonian,2 in the standard notation, the dispersion of one hole in an antiferromagnet can be calculated accurately [8] with numerical or analytical techniques. At small J/t, it was found that the hole dispersion iswhich was calculated using a Green's Function Monte Carlo method.[8] J = 0.125eV is the actual scale of the problem, and Eq. (2) shows that holes move within the same sublattice to avoid distorting the AF background. To improve the quantitative agreement with experiments described below, here a small hopping amplitude along the plaquette diagonals t ′ = 0.05t has been included in the Hamiltonian to produce the dispersion Eq.(2), but the qualitative physics presented in this paper is the same as long as |t ′ /t| is small. Now, let us assume a rigid band picture for the quasiparticles.[8] The dispersion is plotted in Fig.1a against momentum with the Fermi level at the flat band which corresponds to a hole density of x = 0.15 (in Fig.1a and 1c below, ǫ k is inverted i.e. the electron language is used rather than the hole language to facilitate the comparison with experiments). ǫ k contains a saddle-point located close to k = (π, 0), (0, π), which induces a large DOS in the spectrum.In addition, ǫ k is nearly degenerate along the cosk (Fig.1b). The most important detail to consider at a small but finite hole density is that the quasiparticle weight is smaller for the bands centered at momentum (π, π) than those at (0, 0) (as represented pictorially in Fig.1a-b, with dashed lines). These are the "shadow bands" which were discussed before in the spin-bag approach.[11] Another argument in favor of using our hole dispersion at a finite 3 density also comes from experiments. In Fig.1c we compare ǫ k along the k = (0, 0) − (π, 0) direction against ARPES results by the Argonne group [5,12] for YBCO. The agreement is excellent. It is worth emphasizing that the theoretical curve of Fig.1c is derived from a microscopic Hamiltonian, and it is not a fit of ARPES data. This is a major difference between the present approach and previous vH scenario calculations.To further elaborate on whether our...

High- - a negative-Uinterpretation of cuprate superconductivity, incorporating questions of crossover, micro-inhomogeneity and a compound order parameter

“…Not infrequently YBa 2 Cu 3 O 7 has been presented as the archetypal HTSC material and indeed through its planes and chains it would make direct show of formally Cu 2+ planar sites (with their attendant d 9 Jahn-Teller distortion) and formally Cu 3+ chain sites (with characteristic d 8 square-planar coordination). However, this crystallographic separation of formal valence in YBa 2 Cu 3 O 7 masks the role of the chains in introducing holes and metallicity to the planes and chains alike.…”

“…HTSC phenomena do nonetheless clearly entail a considerable degree of coupling to the lattice, as witnessed by the wide variety of structural modifications registered around T c [36]. Such changes directly follow in the wake of specific electronic adjustments to site carrier counts (both static and dynamic), as, for example, the d 9 Jahn-Teller distortion. It is inevitable here, just as with CDWs, that in the prevailing highly-correlated circumstances charge and lattice are closely coupled.…”

“…The magnetic channel, as controlled by the extensive saddle-points featuring around (π, 0)(0, π), is associated with carriers of significantly enhanced mass [f] and appreciable residual local spin character [8,9]. In any normal single-channel system one would not anticipate incorporating such magnetic character into a superconducting scenario.…”

“…The energy f is very close to degeneracy with E F . E F is largely dictated by the electrons of the centres in the low-valent (electron rich) subsystem, loosely labelled through the symbol 9 Cu 0 II (remembering of course some charge is transferred permanently to the higher valent subsystem).…”

Replace `van Hove singularity' by `negative-Usingularity' and proceed: a comment on the analysis of HTSC Seebeck data by McIntosh and Kaiser - and related matters concerning the mechanism

“…The experimental and theoretical work of Gofron et al [23], Dagotto et al [24], and Beenen and Edwards [25] has demonstrated how within the framework of a generalized Hubbard model (but still excluding any double occupancy) spin-fluctuation phenomena may become expressly associated with a very considerable sharpening up of the LDA van Hove singularities. Such sharpening is what, it has been claimed, is manifest in the 'giant anomalous extension' of the vHs features detected in angle-resolved photoemission data above T c [26].…”