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arXiv:2308.01956 · Physical review. B./Physical review. B

Cyclotron resonance and quantum oscillations of critical Fermi surfaces

Haoyu Guo, Davide Valentinis, Jörg Schmalian, Subir Sachdev A, Aavishkar A. Patel

Published Feb 27, 2024• 17 citations
arXivHTMLPDF

Abstract

Kohn's theorem places strong constraints on the cyclotron response of Fermi liquids. Recent observations of a doping dependence in the cyclotron mass of ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ [Legros et al., Phys. Rev. B 106, 195110 (2022)] are therefore surprising because the cyclotron mass can only be renormalized by large momentum umklapp interactions, which are not expected to vary significantly with doping. We show that a version of Kohn's theorem continues to apply to disorder-free non-Fermi-liquids with a critical boson near zero momentum. However, marginal Fermi liquids arising from a spatially random Yukawa coupling between the electrons and bosons do give rise to significant corrections to the cyclotron mass that we compute. This is the same theory that yields linear-in-temperature resistivity and other properties of strange metals at zero fields [Patel et al., Science 381, 790 (2023)].

DOI
10.1103/physrevb.109.075162

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Kohn's theorem places strong constraints on the cyclotron response of Fermi liquids. Recent observations of a doping dependence in the cyclotron mass of La2\ensuremath−xSrxCuO4{\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}La2\ensuremath−x​Srx​CuO4​ [Legros et al., Phys. Rev. B 106, 195110 (2022)] are therefore surprising because the cyclotron mass can only be renormalized by large momentum umklapp interactions, which are not expected to vary significantly with doping. We show that a version of Kohn's theorem continues to apply to disorder-free non-Fermi-liquids with a critical boson near zero momentum. However, marginal Fermi liquids arising from a spatially random Yukawa coupling between the electrons and bosons do give rise to significant corrections to the cyclotron mass that we compute. This is the same theory that yields linear-in-temperature resistivity and other properties of strange metals at zero fields [Patel et al., Science 381, 790 (2023)].
We use the Kubo response functions to calculate the electrical and thermal conductivity and Seebeck coefficient at low temperatures and frequencies in the quantum-critical region for fermions on a lattice. The theory uses scattering of the fermions with the previously derived collective fluctuations due to topological defects of the quantum XY model coupled to fermions. The microscopic model is applicable to the fluctuations of the loop-current order in cuprates as well as to a class of quasi-two-dimensional heavy-fermion and other metallic antiferromagnets, and proposed recently also for the possible loop-current order in Moiré twisted bi-layer graphene and bilayer WSe2_22​. All these metals have a linear-in-temperature electrical resistivity in the quantum-critical region of their phase diagrams, often termed ``Planckian" resistivity. The solution of the Kubo equation for transport shows that vertex renormalizations to the external fields, beside those caused by Aslamazov-Larkin (A-L) processes, are absent. A-L appears as an Umklapp scattering matrix, which gives a temperature-independent multiplicative factor for the electrical resistivity but does not affect the thermal conductivity. We also show that the mass renormalization which gives a logarithmic enhancement of the marginal Fermi-liquid specific heat does not appear in the electrical resistivity and, more remarkably, in the thermal conductivity. On the other hand the mass renormalization ∝ln⁡ωc/T\propto \ln ω_c/T∝lnωc​/T appears in the Seebeck coefficient. We also discuss in detail the conservation laws which play a crucial role in all transport properties. We calculate exactly, the numerical coefficients of the transport properties for a circular Fermi surface. The leading temperature dependences is shown to remain the same for a general Fermi surface, but it is too messy to calculate the numerical coefficient.
Resilient strange metal at an unconventional quantum critical point in d=2d=2d=2
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Kinetic properties of a two-dimensional model of fermions interacting with antiferromagnetic spin excitations near the quantum critical point are considered. The temperature or doping are assumed to be sufficiently high, such that the pseudogap does not appear. In contrast to standard spin-fermion models, it is assumed that there are intrinsic inhomogeneities in the system suppressing space correlations of the antiferromagnetic excitations. It is argued that the inhomogeneities in the spin excitations in the ``strange metal'' phase can be a consequence of the existence of ``$\ensuremath{\pi}$-shifted'' domain walls in the doped antiferromagnetic phase. Averaging over the inhomogeneities and calculating physical quantities such as resistivity and some others one can explain unusual properties of cuprates unified under the name ``marginal Fermi liquid.'' The dependence of the slope of the linear temperature dependence of the resistivity on doping is compared with experimental data.
In this Letter I apply Kohn's theorem to quantum oscillations in cuprates. I show that when combined with Gell-Mann and Low theorem, there is rigorous justification of quantum oscillations as in a Fermi liquid for cuprates. For simplicity, understanding the lack of interaction effects in quantum oscillations can be addressed in the language of a fully translationally invariant system. The Gell-Mann and Low theorem is not perturbative, and applies more generally as long as the adiabatic evolution from an isolated nondegenerate state is the case. Oscillation frequencies are identical to the noninteracting problem. It is the cyclotron gap that justifies Fermi-liquid-based theory of quantum oscillations. This is not to imply that other properties of the cuprates that do not have a gap in the spectrum could not exhibit non-Fermi-liquid behavior, for example, angle-resolved photoemission spectroscopy.
The problem of continuous quantum phase transitions in metals involves critical bosons coupled to a Fermi surface. We solve the theory in the limit of a large number, NB{N}_{B}NB​, of bosonic flavors, where the bosons transform in the adjoint representation (a matrix representation), while the fermions are in the fundamental representation (a vector representation) of a global SU(NB)SU({N}_{B})SU(NB​) flavor symmetry group. The leading large NB{N}_{B}NB​ solution corresponds to a non-Fermi liquid coupled to Wilson-Fisher bosons. In a certain energy range, the fermion velocity vanishes---resulting in the destruction of the Fermi surface. Subleading 1/NB1/{N}_{B}1/NB​ corrections correspond to a qualitatively different form of Landau damping of the bosonic critical fluctuations. We discuss the model in $d=3\ensuremath{-}\ensuremath{\epsilon}$ but because of the additional control afforded by large NB{N}_{B}NB​, our results are valid down to d=2d=2d=2. In the limit $\ensuremath{\epsilon}\ensuremath{\ll}1$, the large NB{N}_{B}NB​ solution is consistent with the renormalization group analysis of Fitzpatrick et al. [Phys. Rev. B 88, 125116 (2013)].
We study the problem of disorder-free metals near a continuous quantum critical point. We depart from the standard paradigm [Hertz, Phys. Rev. B 14, 1165 (1976) and Millis, Phys. Rev. B 48, 7183 (1993)] and treat both fermions and bosons (i.e., order parameter fields) on equal footing. We construct a Wilsonian effective field theory that integrates out only high-energy boson and fermion modes. Below the upper critical dimension of the theory (d=3d=3d=3 spatial dimensions), we find new fixed points in which the bosons are described by the Wilson-Fisher fixed point and are coupled to a non-Fermi-liquid metal. We describe subtleties with the renormalization group flow of four-Fermi interactions, which can be surmounted in a controlled large-NNN limit. In this limit, we find that the theory has no superconducting instability.