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arXiv:1311.0374

Low-Frequency Quantum Oscillations due to Strong Electron Correlations

A. Sherman

Published Nov 2, 2013• 0 citations
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Abstract

The normal-state energy spectrum of the two-dimensional $t$-$J$ model in a homogeneous perpendicular magnetic field is investigated. The density of states at the Fermi level as a function of the inverse magnetic field $\frac{1}{B}$ reveals oscillations in the range of hole concentrations $0.08

DOI
10.48550/arxiv.1311.0374

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The normal-state energy spectrum of the two-dimensional ttt-JJJ model in a homogeneous perpendicular magnetic field is investigated. The density of states at the Fermi level as a function of the inverse magnetic field 1B\frac{1}{B}B1​ reveals oscillations in the range of hole concentrations $0.08
The spectrum of a Hamiltonian for NNN harmonically interacting two-dimensional particles in a constant perpendicular magnetic field is determined exactly by the transformation to normal coordinates. The energy of the ground state consistent with Fermi-Dirac statistics is calculated in the limit of a strong magnetic field. The Fermi energy is found to exhibit de Haas---van Alphen---like oscillations.
Hole and magnon spectral functions of the 2D ¢-J model are self-consistently calculated from a set of Dyson's equations for the hole concentrations z < 0.3.For J < ¢, itis shown that near z = 0.05 the hole spectrum changes drastically, acquiring features of a weakly correlated spectrum.This change is accompanied by the entering of the chemical potential u into a sharp maximum of the density of states.With z increasing the maximum moves together with u upto z =~0.15 and then lags behind.This concentration is also distinctive in that the Fermi surface becomes a simply connected surface and the overdamped magnons which appear near z = 0.02 occupy the widest region in k space.Besides, a limiting frequency of usual magnons passes through a minimum here.Significant deviations from the normal Fermi liquid, which partly resemble the marginal Fermi liquid, are observed for x > 0.05.
The normal-state energy spectrum of the two-dimensional t-J model in a homogeneous perpendicular magnetic eld B is investigated using the Mori projection operator technique.The density of states at the Fermi level as a function of 1/B reveals both high-and low-frequency oscillations.The high-frequency oscillations correspond to large Fermi surfaces, while the low-frequency components are related to van Hove singularities in the Landau subbands, which stem from their bending due to strong electron correlations.Frequencies of the low-frequency components are of the same order of magnitude as those observed in underdoped cuprates.These components become dominant if smoothing processes are involved.It is shown that despite increased distances between subbands the pseudogap aects only slightly the frequency of density of states oscillations.
Novel controlled nonperturbative techniques are a must in the study of strongly correlated systems, especially near quantum criticality. One of these techniques, bosonization, has been extensively used to understand one-dimensional, as well as higher-dimensional electronic systems at finite density. In this paper, we generalize the theory of two-dimensional bosonization of Fermi liquids, in the presence of a homogeneous weak magnetic field perpendicular to the plane. Here, we extend the formalism of bosonization to treat free spinless fermions at finite density in a uniform magnetic field. We show that particle-hole fluctuations of a Fermi surface satisfy a covariant Schwinger algebra, allowing to express a fermionic theory with forward scattering interactions as a quadratic bosonic theory representing the quantum fluctuations of the Fermi surface. By means of a coherent-state path integral formalism, we compute the fermion propagator as well as particle-hole bosonic correlations functions. We analyze the presence of de Haas-van Alphen oscillations and show how the quantum oscillations of the orbital magnetization, the Lifshitz-Kosevich theory, are obtained by means of the bosonized theory. We also study the effects of forward scattering interactions. In particular, we obtain oscillatory corrections to the Landau zero sound collective mode.