# Power-law liquid in cuprate superconductors from fermionic unparticles

## TL;DR

This paper explains the non-Fermi-liquid behavior observed in cuprate superconductors using the concept of fermionic unparticles, showing how their scale-invariant properties influence electron self-energy and spectral functions.

## Contribution

It analytically demonstrates that fermionic unparticles can account for the anomalous scaling of electron self-energy in cuprates, linking unparticle physics to high-temperature superconductivity phenomena.

## Key findings

- Self-energy scales as T^{2+2α} and ω^{2+2α}, matching experiments.
- Unparticles exhibit broad spectral functions due to branch cuts in their propagator.
- Spectral weights remain significant at high energies, unlike normal fermions.

## 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 $\Sigma^{\prime\prime}\sim(\omega^2+\pi^2T^2)^a$ 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.