Scale-invariance as the cause of the superconducting dome in the cuprates

Abstract

Recent photoemission spectroscopy measurements (T. J. Reber et al., arXiv:1509.01611) of cuprate superconductors have inferred that the self-energy exhibits critical scaling over an extended doping regime, thereby calling into question the conventional wisdom that critical scaling exists only at isolated points. In particular, this new state of matter, dubbed a power-law liquid, has a self-energy whose imaginary part scales as ${\Sigma }^{\prime \prime }\sim ({\omega }^2+{\pi }^2{T}^2{)}^{\alpha }$, with $\alpha =1$ in the overdoped Fermi-liquid state and $\alpha \le 0.5$ in the optimal to underdoped regime. Previously, we showed that this self-energy can arise from interactions between electrons and unparticles, a scale-invariant sector that naturally emerges from strong correlations. Here, taking the self-energy as a given, we first reconstruct the real part of the self-energy. We find that the resultant quasiparticle weight vanishes for any doping level less than optimal, implying an absence of particle-like excitations in the underdoped regime. Consequently, the Fermi velocity vanishes and the effective mass diverges for $\alpha \le \frac{1}{2}$, in agreement with earlier experimental observations. We then use the self-energy to reconstruct the spectral function and compute the superconducting $T_c$ within the BCS formalism. We find that the $T_c$ has a dome-like structure, implying that broad scale invariance manifested in the form of a power-law liquid is the likely cause of the superconducting dome in the cuprates.

arXiv comment9 pages, 6 figures. to be published in Phys. Rev. B

References in corpus (26)

• Unparticle Physics
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Charge density wave and superconducting dome in TiSe2 from electron-phonon interaction
• Critical fermi surfaces and non-fermi liquid metals
• Soft Fermi Surfaces and Breakdown of Fermi Liquid Behavior
• Quantum critical origin of the superconducting dome in SrTiO${}_3$
• Metal-insulator quantum critical point beneath the high Tc superconducting dome
• Doping-dependent nodal Fermi velocity in Bi-2212 revealed by high-resolution ARPES
• Breakdown of Fermi liquid description for strongly interacting fermions
• Phonon mechanism in the most dilute superconductor: n-type SrTiO3
• Photoemission "experiments" on holographic superconductors
• Non-Fermi liquid behavior of large N_B quantum critical metals
• Magnetic quantum oscillations in YBa${}_2$Cu${}_3$O${}_{6.61}$ and YBa${}_2$Cu${}_3$O${}_{6.69}$ in fields of up to 85 T; patching the hole in the roof of the superconducting dome
• Absence of Luttinger's Theorem due to Zeros in the Single-Particle Green Function
• Criterion for stability of Goldstone Modes and Fermi Liquid behavior in a metal with broken symmetry
• Superconducting dome in MoS2 and TiSe2 generated by quasiparticle-phonon coupling
• Hidden Fermi Liquid: Self-Consistent Theory for the Normal State of High-Tc Superconductors
• Un-Fermi Liquids: Unparticles in Strongly Correlated Electron Matter
• Unparticles and Anomalous Dimensions in the Cuprates
• Two types of superconducting domes in unconventional superconductors
• Power-law liquid in cuprate superconductors from fermionic unparticles
• Realizing infrared power-law liquids in the cuprates from unparticle interactions
• Power-law Optical Conductivity from Unparticles: Application to the Cuprates
• Geodesically Complete Metrics Induce Boundary Non-locality in Holography: Consequences for the Entanglement Entropy
• Unparticle mediated superconductivity
• Self-energy effects in cuprates and the dome-shaped behavior of the superconducting critical temperature

Cited by in corpus (2)

• Pairing in quantum-critical systems: $T_c$, $\Delta$, and their ratio
• Gapped dilatons in scale invariant superfluids