Entropy and de Haas-van Alphen oscillations of a three-dimensional marginal Fermi liquid

Abstract

We study de Haas-van Alphen oscillations in a marginal Fermi liquid resulting from a three-dimensional metal tuned to a quantum-critical point (QCP). We show that the conventional approach based on extensions of the Lifshitz-Kosevich formula for the oscillation amplitudes becomes inapplicable when the correlation length exceeds the cyclotron radius. This breakdown is due to (i) non-analytic finite-temperature contributions to the fermion self-energy (ii) an enhancement of the oscillatory part of the self-energy by quantum fluctuations, and (iii) non-trivial dynamical scaling laws associated with the quantum critical point. We properly incorporate these effects within the Luttinger-Ward-Eliashberg framework for the thermodynamic potential by treating the fermionic and bosonic contributions on equal footing. As a result, we obtain the modified expressions for the oscillations of entropy and magnetization that remain valid in the non-Fermi liquid regime.

arXiv comment20+6 pages, 6 figures

References in corpus (24)

• Quasiparticle mass enhancement approaching optimal doping in a high-Tc superconductor
• Evolution of the Fermi surface of BaFe_2(As_{1-x}P_x)_2 on entering the superconducting dome
• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• Universal quantum oscillations in the underdoped cuprate superconductors
• Metal-insulator quantum critical point beneath the high Tc superconducting dome
• Quasiparticle mass enhancement close to the quantum critical point in BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$
• Two - Dimensional Electron Liquid in a Weak Magnetic Field
• Large $N$ theory of critical Fermi surfaces
• Non-Fermi liquid behavior of large N_B quantum critical metals
• Eliashberg theory of phonon-mediated superconductivity -- when it is valid and how it breaks down
• Self-consistent approximations in relativistic plasmas: Quasiparticle analysis of the thermodynamic properties
• First-Matsubara-frequency rule in a Fermi liquid. Part I: Fermionic self-energy
• Large $N$ theory of critical Fermi surfaces II: conductivity
• Interaction effects on magnetooscillations in a two-dimensional electron gas
• Quantum magneto-oscillations in a two-dimensional Fermi liquid
• Two dimensional non-Fermi liquid metals: a solvable large N limit
• Quantum critical metals in $d=3+1$
• Normal state properties of quantum critical metals at finite temperature
• How non-Fermi liquids cure their infrared divergences
• Free energy and specific heat near a quantum critical point of a metal
• Quantum Oscillations of Electrons and of Composite Fermions in Two Dimensions: Beyond the Luttinger Expansion
• Non-Fermi liquids at finite temperature: normal state and infrared singularities
• Thermodynamic constraints on the amplitude of quantum oscillations
• Spectral Function Analysis of Fermi Liquids and of Composite Fermions in a Finite Magnetic Field: Renormalised Gaps

Cited by in corpus (5)

• Anomalous quantum oscillations from boson-mediated interband scattering
• Shot noise in a phenomenological model of a marginal Fermi liquid
• Dynamical magnetic breakdown and quantum oscillations from hot spot scattering
• Marginal Fermi liquids from Fermi surfaces coupled via matrix boson gas
• A theorem of Kohn applied to quantum oscillations in Cuprates