Landau Quasiparticles in Weak Power-Law Liquids
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Landau Quasiparticles in Weak Power‑Law Liquids Joshuah T. Heath1 Received: 19 February 2020 / Accepted: 8 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The failure of Landau-Fermi liquid theory is often considered a telltale sign of universal, scale-invariant behavior in the emergent field theory of interacting fermions. Nevertheless, there exist borderline cases where weak scale invariance coupled with particle-hole asymmetry can coexist with the Landau quasiparticle paradigm. In this letter, I show explicitly that a Landau-Fermi liquid can exist for weak power-law scaling of the retarded Green’s function. Such an exotic variant of the traditional Fermi liquid is shown to always be incompatible with Luttinger’s theorem for any non-trivial scaling. This result yields evidence for a Fermi liquid-like ground state in the high-field, underdoped pseudogap phase of the high-temperature cuprate superconductors. Keywords Landau-Fermi liquids · Non-Fermi liquids · Quasiparticle methods · Luttinger’s theorem
1 Introduction In recent years, the study of non-Fermi liquids has been dominated by quantum critical phenomena [1–5]. In particular, the transport quantities of the optimally doped cuprate superconductors are now known to exhibit quantum critical scaling, with the electrical resistivity [6–8], the Hall angle [9, 10], and the Lorentz ratio [11] all exhibiting temperature dependencies inconsistent with super-Planckian lifetimes of the charge carriers [12, 13]. Nevertheless, the underlying microscopic origin of such behavior is still a matter of debate, with proposals ranging from coupled SYK islands [14–16] to an exotic phase of matter which lacks charge quantization [17, 18]. Mirroring the microscopic underpinnings of conventional Landau-Fermi liquids [19–22], Anderson first proposed that the unusual normal phase of the optimally * Joshuah T. Heath [email protected] 1
Physics Department, Boston College, 140 Commonwealth Avenue, Chestnut Hill, MA 02467, USA
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Journal of Low Temperature Physics
doped high-Tc cuprates can be explained via a “hidden Fermi liquid theory” [23, 24]. The Fourier-transformed Green’s function of such a system can be written as a Landau-like propagator raised to a power proportional to the sum of phase shifts over all scattering channels, reducing the quasiparticle pole to a branch cut. Such “power-law liquids”1 have recently been shown to violate the Luttinger sum rule [26] and interact with conventional electrons in such a way that may lead to a powerlaw scaling of the imaginary self-energy similar to what is seen in ARPES experiments on Bi2Sr2CaCu2O8+𝛿 in the underdoped pseudogap phase [25, 27, 28]. Indeed, such power-law behavior is often taken as the hallmark of an “unparticle”-like phase, where scale invariance naturally leads to a power-law Green’s function and the Standard Model notion of an independent particle breaks down [29, 30]. Nevertheless, there have been several cases in the past few years that have shown
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