Superconductivity of Bad Fermions: Origin of Two Gaps in HTSC Cuprates

TL;DR

This paper models the spectral properties of doped Hubbard systems relevant to cuprate superconductors, revealing a two-gap structure and unusual superconducting response linked to a pseudogap and bad-fermion behavior.

Contribution

It introduces a novel strong-coupling Green's function expansion that explains the origin of two gaps and pseudogap phenomena in high-temperature cuprates.

Findings

Spectral function shows a flat band with a pseudogap around the antinodal point.

Superconducting response exhibits a pseudogap and a d-wave-like structure with shifted extrema.

Anomalous Green's function response deviates from the simple ( ext{cos}k_x - ext{cos}k_y) form due to pseudogap effects.

Abstract

We investigate the spectral properties of the doped ${t-t'}$ Hubbard model with parameters typical for high-temperature cuprate superconductors. Our approach is based on a novel strong-coupling Green's function expansion around a reference system -- the exactly solvable undoped particle-hole symmetric Hubbard lattice -- that possesses a large antiferromagnetic Mott-Hubbard-Slater gap in the electron spectrum. The electron spectral function in the case of a large next-nearest-neighbor hopping ${t'=-0.3t}$, which is characteristic of the ${T_c \approx 100\,\text{K}}$ family of cuprates, reveals a strongly renormalized flat band feature with a pseudogap around the antinodal point. The superconducting response of this system to a small ${d_{x^2-y^2}}$-like external field exhibits a very unusual form. It features a pseudogap at the antinodal point in the normal part of the Nambu Green's function, related to a ``bad-fermion'' behavior in a normal phase, as well as a ${d}$-wave-like structure in the anomalous (Gorkov's) Green's function, with zero response at the nodal point of the Brillouin zone. Remarkably, we find that the anomalous part of the response deviates essentially from the simplest ${(\cos{k_x}-\cos{k_y})}$ form in momentum space. Specifically, its extrema are shifted away from the ${(\pi,0)}$ and ${(0,\pi)}$ points due to suppression of the response by the pseudogap. The observed two-gap structure of the electron spectra in a generic strong-coupling model of cuprates can serve as a basis for phenomenological treatment of different physical properties of high-temperature superconductors within two-fluid model.