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arXiv:1306.3941 · Physical Review Letters

Phenomenological Characterization of Semiholographic Non-Fermi Liquids

Ayan Mukhopadhyay, Giuseppe Policastro

Published Nov 27, 2013• 17 citations
arXivHTMLPDF

Abstract

We analyze some phenomenological implications of the most general semiholographic models for non-Fermi liquids that have emerged with inputs from the holographic correspondence. We find generalizations of Landau-Silin equations with few parameters governing thermodynamics, low-energy response, and collective excitations. We show that even when there is a Fermi surface with well-defined quasiparticle excitations, the collective excitations can behave very differently from Landau's theory.

DOI
10.1103/physrevlett.111.221602

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We analyze some phenomenological implications of the most general semiholographic models for non-Fermi liquids that have emerged with inputs from the holographic correspondence. We find generalizations of Landau-Silin equations with few parameters governing thermodynamics, low-energy response, and collective excitations. We show that even when there is a Fermi surface with well-defined quasiparticle excitations, the collective excitations can behave very differently from Landau's theory.
Semiholographic models of non-Fermi liquids have been shown to have generically stable generalized quasiparticles on the Fermi surface. Although these excitations are broad and exhibit particle-hole asymmetry, they were argued to be stable from interactions at the Fermi surface. In this work, we use this observation to compute the density response and collective behaviour in these systems. Compared to the Fermi liquid case, we find that the boundaries of the particle-hole continuum are blurred by incoherent contributions. However, there is a region inside this continuum, that we call inner core, within which salient features of the Fermi liquid case are preserved. A particularly striking prediction of our work is that these systems support a plasmonic collective excitation which is well-defined at large momenta, has an approximately linear dispersion relation and is located in the low-energy tail of the particle-hole continuum. Furthermore, the dynamic screening potential shows deep attractive regions as a function of the distance at higher frequencies which might lead to long-lived pair formation depending on the behavior of the pair susceptibility. We also find that Friedel oscillations are present in these systems but are highly suppressed.
Landau (1958) gave a rigorous microscopic derivation of his phenomenological Fermi -liquid theory starting from the first principles Hamiltonian of strongly interacting Fermions. The derivation is based on an asymptotic expansion in small parameters such as q/kF, bc.>/EF, kT/EF, where q and c.> represent the wave numbers and frequencies of real excitations of the system. Landau showed that the dynamics of these low-lying excitations (quasiparticles and collective modes) is governed by classical transport equations with all quantum many-body effects absorbed into effective interaction parameters. Landau's approach has been generalized to superfluid Fermi liquids and superconductors by Leggett (1965) and, going beyond linear response, by Eliashberg (1971). Their ideas merged into a recent review on the quasiclassical approach to superfluid 3 He by Serene and Rainer (1983). I will use the notation of this review throughout this paper. Landau's transport theory together with its offsprings will be called 'quasiclassical theory in the following. In this context it is important to mention that Eilenberger (1968) and Larkin and Ovchinnikov (1968) have shown that the complete theory of superconductors can be formulated as a quasiclassical transport theory. Surprisingly, this theory permits calculating microscopic properties, e.g. the quasiparticle excitation spectrum, which are predominantly governed by quantum effects.
A phenomenological theory is presented for two-dimensional quantum liquids in terms of the Fermi surface geometry. It is shown that there is a one-to-one correspondence between the properties of an interacting electron system and its corresponding Fermi surface. By doing this, the concept of Fermi surface is generalized to include different topologies. It is shown that for a Fermi liquid the corresponding Fermi surface is rough. In the presence of a condensate, the Fermi surface is faceted, while for a ferromagnetc instability, the Fermi surface becomes a frozen solid. I also determine the surface tension, the step free energy, low lying excitations and other surface and transport properties of the Fermi surface. The different transitions between these phases are also determined. A non-Fermi liquid phase is shown to be a pre-roughening state of the Fermi surface, the properties of which are briefly analyzed.
A phenomenological theory is presented for two-dimensional quantum liquids in terms of the Fermi surface geometry. It is shown that there is a one-to-one correspondence between the properties of an interacting electron system and its corresponding Fermi surface. By doing this, the concept of Fermi surface is generalized to include different topologies. It is shown that for a Fermi liquid the corresponding Fermi surface is rough. In the presence of a condensate, the Fermi surface is faceted while, for a ferromagnetic instability, the Fermi surface becomes a frozen solid. I also determine the surface tension, the step free energy, low-lying excitations and other surface and transport properties of the Fermi surface. The different transitions between these phases are also determined. A non-Fermi-liquid phase is shown to be a pre-rough state of the Fermi surface, the properties of which are briefly analysed.
Non-Fermi liquids are unconventional metals whose physical properties deviate qualitatively from those of noninteracting fermions due to strong quantum fluctuations near Fermi surfaces. They arise when metals are subject to singular interactions mediated by soft collective modes. In the absence of well-defined quasiparticles, universal physics of non-Fermi liquids is captured by interacting field theories which replace Landau Fermi liquid theory. However, it has been difficult to understand their universal low-energy physics due to a lack of theoretical methods that take into account strong quantum fluctuations in the presence of abundant low-energy degrees of freedom. In this review, we discuss two approaches that have been recently developed for non-Fermi liquid theory with emphasis on two space dimensions. The first is a perturbative scheme based on a dimensional regularization, which achieves a controlled access to the low-energy physics by tuning the codimension of Fermi surface. The second is a nonperturbative approach which treats the interaction ahead of the kinetic term through a non-Gaussian scaling called interaction-driven scaling. Examples of strongly coupled non-Fermi liquids amenable to exact treatments through the interaction-driven scaling are discussed.
Modern quantum materials host a wide range of electronic phases in which transport properties are governed by strong interactions and collective effects. This thesis investigates charge, heat, and momentum transport in interacting electronic systems across different theoretical frameworks, ranging from Fermi liquid theory to strongly coupled strange metals.The first part of the thesis focuses on two-dimensional Fermi liquids at finite temperature, where rapid electron-electron scattering can give rise to hydrodynamic behavior. A kinetic-theory framework allowing an exact treatment of quasiparticle distribution functions beyond the asymptotic low-temperature regime is used to compute the full spectrum of collective modes, providing a detailed characterization of long-lived odd-parity excitations and the intermediate transport regime between ballistic and hydrodynamic flow. The same framework is employed to determine the shear viscosity of interacting electron liquids beyond conventional perturbative limits.The second part of the thesis concerns strongly interacting quantum systems where the quasiparticle picture breaks down.Holographic duality is used to study transport and thermoelectric response in quantum critical systems subject to periodic potentials, providing a controlled framework for momentum relaxation and magnetotransport in non-Fermi liquids. The thesis further develops holographic models of collective charge dynamics in systems with dynamical electromagnetism, including bulk plasmons and surface plasmon polaritons, and explores connections between Fermi surface physics and holographic gauge-field dynamics.