Topological Non-Fermi Liquid

Abstract

In this paper we investigate the $(2+1)$-dimensional topological non-Fermi liquid in strongly correlated electron system, which has a holographic dual description by Einstein gravity in $(3+1)$-dimensional anti-de Sitter (AdS) space-time. In a dyonic Reissner-Nordstrom black hole background, we consider a Dirac fermion coupled to the background $U(1)$ gauge theory and an intrinsic chiral gauge field $b_M$ induced by chiral anomaly. UV retarded Green's function of the charged fermion in the UV boundary from AdS${}_4$ gravity is calculated, by imposing in-falling wave condition at the horizon. We also obtain IR correlation function of the charged fermion at the IR boundary arising from the near horizon geometry of the topological black hole with index $k=0,\pm 1$. By using the UV retarded Green's function and IR correlation function, we analyze the low frequency behavior of the topological non-Fermi liquid at zero and finite temperatures, especially the relevant non-Fermi liquid behavior near the quantum critical region. In addition, we find that when $k=\pm 1$, the effective mass of bulk Dirac fermion at IR fixed point is topologically quantized, consequently the Fermi momentum presents a discrete sparse distributed pattern, in contrary to the Ricci flat case with $k=0$. As demonstrated examples, we calculate the spectral functions of topological non-Fermi liquid due to anomalous Hall effect (AHE) ($|\vec{b}|\ne 0,b_0=0$) and chiral magnetic effect (CME) ($|\vec{b}|=0,b_0\ne 0$), which can be tested in topological materials such as topological insulator and topological metal with strong couplings.

69 pages, 10 figures

References in corpus (24)

• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Topological Field Theory of Time-Reversal Invariant Insulators
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• The Chiral Magnetic Effect
• Experimental discovery of Weyl semimetal TaAs
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Experimental observation of Weyl points
• Topological response in Weyl semimetals and the chiral anomaly
• Heavy Fermions and Quantum Phase Transitions
• Viscosity, Black Holes, and Quantum Field Theory
• Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
• Non-relativistic holography
• A Non-Fermi Liquid from a Charged Black Hole; A Critical Fermi Ball
• Are non-Fermi-liquids stable to Cooper pairing?
• Consequences of a condensed matter realization of Lorentz violating QED in Weyl semi-metals
• Real-time response in AdS/CFT with application to spinors
• Critical fermi surfaces and non-fermi liquid metals
• Lifshitz Gravity for Lifshitz Holography
• Dynamically Generated Gap from Holography: Mottness from a Black Hole
• The holographic Weyl semi-metal
• Dynamical Gap and Cuprate-like Physics from Holography
• Continuous transitions between composite Fermi liquid and Landau Fermi liquid: a route to fractionalized Mott insulators
• Incompressible Navier-Stokes Equations from Einstein Gravity with Chern-Simons Term
• Holographic CFTs on maximally symmetric spaces: correlators, integral transforms and applications

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