Anomalies in the pseudogap phase of the cuprates: competing ground states and the role of umklapp scattering

Abstract

Over the past two decades, advances in computational algorithms have revealed a curious property of the two-dimensional Hubbard model (and related theories) with hole doping: the presence of close-in-energy competing ground states that display very different physical properties. On the one hand, there is a complicated state exhibiting intertwined spin, charge, and pair density wave orders. We call this 'type A'. On the other hand, there is a uniform d-wave superconducting state that we denote as 'type B'. We advocate, with the support of both microscopic theoretical calculations and experimental data, dividing the high-temperature cuprate superconductors into two corresponding families, whose properties reflect either the type A or type B ground states at low temperatures. We review the anomalous properties of the pseudogap phase that led us to this picture, and present a modern perspective on the role that umklapp scattering plays in these phenomena in the type B materials. This reflects a consistent framework that has emerged over the last decade, in which Mott correlations at weak coupling drive the formation of the pseudogap. We discuss this development, recent theory and experiments, and open issues. * If one did not refermionise the spin sector, the non-linear interaction term within the bosonic theory reads −4g a =b cos Θ a cos Θ b , which is suggestive of a high symmetry. * This is easy to see in the purely bosonic language, as the interaction term −4g cos Θ sf cos Θ f at strong coupling pins the bosons to (Θ sf , Θ f ) = (2mπ, 2nπ or (Θ sf , Θ f ) = [2m + 1]π, [2n + 1]π with n, m ∈ Z. * Interestingly, recent gauge theory calculations that are proposed to apply to the pseudogap phase of the cuprates find such a deformation of the Fermi surface. See figure 7(a) of (Sachdev et al. 2018).

Ground state phase diagram of the doped Hubbard model on the four-leg cylinder

“…In this paper, we will consider a square lattice geometry compactified on a cylinder, specializing the hopping integral to t i j = t for nearest-neighbor (NN) and t i j = t for nextnearest-neighbor (NNN) sites, respectively. This is among the most studied models in the history of physics in the case of fermions [1][2][3][4][5][6]. Its simple appearance is an illusion; after tens of thousands of papers it has been brought under mathematical control in one and infinite dimensions [7,8].…”

Peculiarities of pseudogap in Y0.95Pr0.05Ba2Cu3O7−δ single crystals under pressure up to 1.7 GPa

“…The pseudogap (PG) state, which is realized in high-temperature superconductors (HTSCs) at the characteristic temperature T* » T c with the doping less than optimal, is one of the most mysterious properties of HTSC cuprates 1–9 . Understanding the physics of the PG would answer the question about the mechanism of superconducting pairing in HTSCs, which is also not fully clarified yet 3–7,10,11 .…”

Using Uniaxial Stress to Probe the Relationship between Competing Superconducting States in a Cuprate with Spin-stripe Order

“…Cuprate superconductors are believed to exhibit competing superconducting orders: uniform d wave vs pair density wave (PDW) order [1,2]. The latter was proposed [3] to explain the observation of 2D superconductivity with depressed 3D order in La 2−x Ba x CuO 4 (LBCO) near x ¼ 1=8 with spin-stripe order [4].…”