Power-law liquid in cuprate superconductors from fermionic unparticles

Abstract

Recent photoemission spectroscopy measurements [arXiv:1509.01611] on cuprate superconductors have inferred that over a wide range of doping, the imaginary part of the electron self-energy scales as ${\Sigma }^{\prime \prime }\sim ({\omega }^2+{\pi }^2{T}^2{)}^a$ with $a=1$ in the overdoped Fermi-liquid state and $a<0.5$ in the optimal to underdoped regime. We show that this non-Fermi-liquid scaling behavior can naturally be explained by the presence of a scale-invariant state of matter known as unparticles. We evaluate analytically the electron self-energy due to interactions with fermionic unparticles. We find that, in agreement with experiments, the imaginary part of the self-energy scales with respect to temperature and energy as ${\Sigma }^{\prime \prime }\sim T^{2+2\alpha }$ and ${\omega }^{2+2\alpha }$, where $\alpha$ is the anomalous dimension of the unparticle propagator. In addition, the calculated occupancy and susceptibility of fermionic unparticles, unlike those of normal fermions, have significant spectral weights even at high energies. This unconventional behavior is attributed to the branch cut in the unparticle propagator which broadens the unparticle spectral function over a wide energy range and non-trivially alters the scattering phase space by enhancing (suppressing) the intrinsic susceptibility at low energies for negative (positive) $\alpha$. Our work presents new evidence suggesting that unparticles might be important low-energy degrees of freedom in strongly coupled systems such as the cuprate superconductors.

arXiv comment10 pages, 7 figures

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• Necessary and Sufficient Conditions for the Validity of Luttinger's Theorem
• Absence of Luttinger's theorem for fermions with power-law Green functions
• Probing a Bose Metal via Electrons: Inescapable non-Fermi liquid scattering and pseudogap physics
• Scale-invariance as the cause of the superconducting dome in the cuprates
• Landau Quasiparticles in Weak Power-Law Liquids
• Momentum-dependent scaling exponents of nodal self-energies measured in strange metal cuprates and modelled using semi-holography
• Strange metal in the doped Hubbard model via percolation