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 $\Sigma^{\prime\prime}\sim(\omega^2+\pi^2T^2)^a$ 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.Comment: 10 pages, 7 figure

Probing a Bose Metal via Electrons: Inescapable non-Fermi liquid scattering and pseudogap physics

“…Our large scattering rate is unimaginable to-date since many theories [35,[39][40][41][42][43][44][45][46][47][48][49]61] have willingly explored extreme exotic fermions but strictly maintain dissipationless behavior when the system is clean. On the other hand, having accepted this new possibility, any smooth analytic scattering rate can show NFL behavior ImΣ(ω, T ) ≈ c + aω + bT + • • • .…”

Absence of Luttinger's theorem for fermions with power-law Green functions

“…A concrete example would be the Green function of fermionic unparticles used in Ref. [18]. The Green function is of the form, G ∼ 1 (ω−εp) α , where α is an anomalous exponent with α = 1 corresponding to a Fermi liquid.…”

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

“…Specific to Eq. 1, since the scaling form is robust up to 0.1 eV and 250 K [1], we showed previously that such a behavior can originate from interactions between electrons and unparticles, a scale-invariant sector that naturally emerges due to strong correlations in the cuprates [12,13]. Originally proposed as a scale-invariant sector within the standard model [14], unparticles can arise in the cuprates because any nontrivial infrared dynamics in a strongly correlated electron system is controlled by a critical fixed point.…”

“…In particular, a power-law liquid can be obtained from interactions between electrons and unparticles [12,13]. The propagator of fermionic unparticles can be written as G u (k, iω n ) = [iω n − u k ] −1+du , where d u is the anomalous dimension and u k is the energy spectrum of unparticles.…”

“…Due to the branch cut in the unparticle propagator, the scattering phase space for electron-unparticle interactions is nontrivially altered. Consequently, the electron self-energy due to such interactions scales with energy and temperature, with the scaling exponent α dependent on the anomalous dimension d u of the unparticle propagator as d u = α − 1 [13].…”