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

Journal Article · 31 October 2018 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.98.184501 · OSTI ID:1566682

Leong, Zhidong ^[1]; Limtragool, Kridsanaphong ^[1]; Setty, Chandan ^[1]; Phillips, Philip W. ^[1]

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1. Univ. of Illinois, Urbana, IL (United States)

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 ofmatter, dubbed a power-law liquid, has a self-energy whose imaginary part scales as $$Σ" \sim (ω^2 + π^2T^2)^α$$, with $α = 1$ in the overdoped Fermi-liquid state and $α = 0.5$ 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 particlelike excitations in the underdoped regime. Consequently, the Fermi velocity vanishes and the effective mass diverges for $$α ≤ \frac{1}{2}$$, 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. Finally, we find that the $$T_c$$ has a domelike 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.

• Research Organization: Brookhaven National Lab. (BNL), Upton, NY (United States); Energy Frontier Research Centers (EFRC) (United States). Center for Emergent Superconductivity (CES)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
• Grant/Contract Number: AC02-98CH10886
• OSTI ID: 1566682
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 18 Vol. 98; ISSN 2469-9950; ISSN PRBMDO
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English