Superconductivity of bad fermions and the origin of two gaps in cuprates

Abstract The spectral properties of the doped t – t ’ Hubbard model, using parameters typical for high-temperature cuprate superconductors, and the mechanism of d-wave pairing remain among the longstanding problems of many-body fermionic materials. We used a strong-coupling Green’s function expansion around a correlated reference system, namely a particle-hole-symmetric undoped Hubbard lattice with $${t}^{{\prime} }=0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>′</mml:mo> </mml:mrow> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:math> , which can be treated numerically exactly using sign-problem-free lattice Quantum Monte Carlo calculations. This reference system exhibits a large antiferromagnetic Mott-Hubbard-Slater gap in the electronic spectrum. We investigate how the Mott-like spectrum is reconstructed under finite doping and nonzero $${t}^{{\prime} }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>′</mml:mo> </mml:mrow> </mml:msup> </mml:math> using a dual-fermion-inspired perturbation expansion. For a large next-nearest-neighbor hopping $${t}^{{\prime} }=-0.3t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>′</mml:mo> </mml:mrow> </mml:msup> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mn>0.3</mml:mn> <mml:mi>t</mml:mi> </mml:math> , characteristic of cuprate families with T c around 100 K, the electronic spectral function reveals a strongly renormalized flat-band feature with a pseudogap near the antinodal point. The superconducting response of this system to a small $${d}_{{x}^{2}-{y}^{2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>x</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>−</mml:mo> <mml:msup> <mml:mrow> <mml:mi>y</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:msub> </mml:math> -like external field shows a pseudogap at the antinodal point in the normal part of the Nambu Green’s function, associated with “bad-fermion” behavior in the normal phase. At the same time, the anomalous Green’s function exhibits a d-wave-like structure with zero response at the nodal point of the Brillouin zone.