[Paper Review] Gossamer Superconductivity

R. B. Laughlin|arXiv (Cornell University)|Sep 11, 2002

Advanced Chemical Physics Studies7 citations

TL;DR

This paper proposes a new Hamiltonian that stabilizes a gossamer superconductor—characterized by a full d-wave gap, suppressed quasiparticle spectral weight, low superfluid density, and incipient Mott-Hubbard gap—by introducing a strong attractive interaction that preserves the resonating valence bond (RVB) ground state. The model explains the coexistence of superconductivity and antiferromagnetism in underdoped cuprates and predicts experimentally testable signatures in tunneling and photoemission spectra.

ABSTRACT

An new superconducting hamiltonian is introduced for which the exact ground state is the Anderson resonating valence bond. It differs from the t-J and hubbard hamiltonians in possessing a powerful attractive force. Its superconducting state is characterized by a full and intact d-wave tunneling gap, quasiparticle photoemission intensities that are strongly suppressed, a suppressed superfluid density, and an incipient Mott-Hubbard gap.

Motivation & Objective

• To resolve the cuprate superconductivity dilemma by constructing a Hamiltonian that stabilizes a gossamer superconducting state with low superfluid density and intact d-wave gap.
• To explain the coexistence of superconductivity and antiferromagnetism in the underdoped regime, particularly in the insulating phase.
• To provide a model where the superconducting order persists into the Mott insulator, disrupted only by low superfluid density and phase fluctuations.
• To offer a falsifiable theoretical framework for the pseudogap and anomalous transport in cuprates via a modified Hamiltonian with strong electron attraction.

Proposed method

• Introduces a new Hamiltonian with a powerful attractive interaction to stabilize the Anderson RVB state as the exact ground state, distinct from t-J and Hubbard models.
• Uses a projected BCS wavefunction with a projection operator Πα that suppresses double occupancy and enhances superconducting pairing.
• Derives the quasiparticle excitation spectrum via the energy expectation value of c†kσ|Ψ⟩, showing a mid-gap band of gossamer quasiparticles.
• Models the system as a dilute gas of bosons, where phase fluctuations and crystallization explain the insulating behavior and stripe formation.
• Incorporates a modified dispersion relation with an additional gap Δ₀ due to spin density wave instability at half-filling, linked to magnetization via α₀ and Δ₀.
• Derives the electron spectral function and shows it exhibits Mott-Hubbard lobes at high energy and faint mid-gap states, with no chemical potential jump at half-filling.

Experimental results

Research questions

• RQ1 Can a superconducting state with a full d-wave gap and suppressed quasiparticle weight coexist with antiferromagnetism in a Mott insulator?
• RQ2 Does a strong attractive interaction stabilize a gossamer superconductor with low superfluid density and incipient Mott gap?
• RQ3 Can the observed linear Tc and superfluid density suppression in underdoped cuprates be explained by a phase instability analogous to Kosterlitz-Thouless?
• RQ4 Is the pseudogap in cuprates the energy scale for pre-formed Cooper pairs, and can it be detected in tunneling or photoemission experiments?
• RQ5 Why do stripes form at δ=1/8 and how can their commensurability and pressure sensitivity be explained?

Key findings

• The gossamer superconductor exhibits a full d-wave tunneling gap and strongly suppressed quasiparticle photoemission intensity, consistent with experimental observations in underdoped cuprates.
• The superfluid density is suppressed due to phase fluctuations, and the system shows a linear decrease in Tc and superfluid density with doping, matching the Uemura plot.
• At half-filling, the quasiparticle spectral function develops Mott-Hubbard lobes at high energy and a faint mid-gap band, with no discontinuity in the chemical potential.
• The model predicts a small, physically detectable quasiparticle gap Δ₀ at half-filling, related to the spin magnetization m via Δ₀ ≈ (2/N)ΣEₖ × m₀, with m₀ = Δ₀ / (2/N)ΣEₖ.
• The system becomes unstable to spin density wave formation at the d-wave node nesting wavevector when the on-site repulsion is slightly increased, leading to a modified gap Eₖ = √((εₖ−μ)² + Δₖ² + Δ₀²).
• Lattice-mediated crystallization of the gossamer superconductor provides a natural explanation for the commensurate stripe formation at δ=1/8 and their suppression under pressure or magnetic fields.