Realizing infrared power-law liquids in the cuprates from unparticle interactions

TL;DR

This paper models the strange metal behavior in cuprates using unparticle interactions, showing that incoherent backgrounds produce power-law scaling consistent with experiments, and explores sum rule violations.

Contribution

It introduces a perturbative unparticle-based framework to explain power-law scaling and sum rule violations in cuprate strange metals.

Findings

Imaginary part of self-energy is linear in temperature at high T.

Power-law behavior in self-energy depends on unparticle scaling dimension.

Incoherent background from unparticles can violate sum rules.

Abstract

Recent photoemission experiments \cite{dessau} reveal that the excitations along the nodal region in the strange metal of the cuprates, rather than corresponding to poles in the single-particle Green function, exhibit power-law scaling as a function of frequency and temperature. Because such power-law scaling is indicative of a scale-invariant sector, as a first step, we perturbatively evaluate the electron self-energy due to interactions with scale-invariant unparticles. We focus on a $G_0W$ type diagram with an interaction $W$ mediated by a bosonic scalar unparticle. We find that, in the high-temperature limit, the imaginary part of the self-energy $\mathrm{Im}\Sigma$ is linear in temperature. In the low-temperature limit, $\mathrm{Im}\Sigma$ exhibits the same power law in both temperature and frequency, with an exponent that depends on the scaling dimension of an unparticle operator. Such behavior is qualitatively consistent with the experimental observations. We then expand the unparticle propagator into coherent and incoherent contributions, and study how the incoherent part violates the density of states (DOS) and density-density correlation function sum rules (f-sum rule). Such violations can, in principle, be observed experimentally. Our work indicates that the physical mechanism for the origin of the power-law scaling is the incoherent background, which is generated from the Mott-scale physics.