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arXiv:2111.04891 · Annals of Physics

Dielectric response of electrons with strong local correlations and long-ranged Coulomb interactions

B. Sriram Shastry, Michael Arciniaga

Published May 18, 2022• 3 citations
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Abstract

Motivated by recent experiments, we append long ranged Coulomb interactions to dominant strong local correlations and study the resulting t-J-VC model for the 2-dimensional cuprate materials. This model includes the effect of short ranged Hubbard–Gutzwiller–Kanamori type correlations and long ranged Coulomb interactions on tight binding electrons. We calculate the {q→,ω} dependent charge density fluctuations in this model using the extremely correlated Fermi liquid theory characterized by quasiparticles with very small weight Z. We develop a novel set of formulae to represent the dynamical charge susceptibility and the dielectric function, using a version of the charge-current continuity equation for a band system, valid for arbitrary q→. Combining these ingredients, we present results for the irreducible dynamical charge susceptibility χ˜ρρ(q→,ω), (longitudinal) dielectric function ɛ(q→,ω), current susceptibility χ˜JJ(q→,ω), conductivity σ(q→,ω), and the plasma frequency for any q→. We also present calculations for the first moment of the structure function and discuss a characteristic energy scale Ωp(q→) which locates a peak in Imχ˜ρρ(q→,ω).

DOI
10.1016/j.aop.2022.168924

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Motivated by recent experiments, we append long ranged Coulomb interactions to dominant strong local correlations and study the resulting t-J-VC model for the 2-dimensional cuprate materials. This model includes the effect of short ranged Hubbard–Gutzwiller–Kanamori type correlations and long ranged Coulomb interactions on tight binding electrons. We calculate the {q→,ω} dependent charge density fluctuations in this model using the extremely correlated Fermi liquid theory characterized by quasiparticles with very small weight Z. We develop a novel set of formulae to represent the dynamical charge susceptibility and the dielectric function, using a version of the charge-current continuity equation for a band system, valid for arbitrary q→. Combining these ingredients, we present results for the irreducible dynamical charge susceptibility χ˜ρρ(q→,ω), (longitudinal) dielectric function ɛ(q→,ω), current susceptibility χ˜JJ(q→,ω), conductivity σ(q→,ω), and the plasma frequency for any q→. We also present calculations for the first moment of the structure function and discuss a characteristic energy scale Ωp(q→) which locates a peak in Imχ˜ρρ(q→,ω).
The dynamic density response and susceptibility of interacting electrons in 1D conductors is investigated taking into account the electron correlations reflecting the short-range order in a Luttinger liquid. We have shown that a narrow band of strong absorption appears in the dissipative susceptibility spectrum near to the wave vector 2kp due to the short-range correlations in addition to the commonly known delta-peak coming from the long-wave fluctuations. The adsorption band shape depends on the electron-electron interaction potential. This band is found to contribute dominantly to the dissipative conductance determined via the power absorbed in 1D conductor under local excitation.
We consider the dynamic charge susceptibility and the charge density waves in strongly-correlated electronic systems within the two-dimensional t-J-V model. Using the equation of motion method for the relaxation functions in terms of the Hubbard operators, we calculate the static susceptibility and the spectrum of charge fluctuations as functions of doped hole concentrations and temperature. Charge density waves emerge for a sufficiently strong intersite Coulomb interaction. Calculation of the dynamic charge susceptibility reveals a strong damping of charge density waves for a small hole doping and propagating high-energy charge excitations at large doping.
We present detailed results from a recent microscopic theory of extremely correlated Fermi liquids, applied to the ttt-JJJ model in two dimensions, developed recently by Shastry [Phys. Rev. Lett. 107, 056403 (2011); Phys. Rev. B 87, 125124 (2013)]. The second-order theory in the parameter $\ensuremath{\lambda}$, related to the density, is argued to be quantitatively valid in the overdoped regime for $0\ensuremath{\le}n\ensuremath{\lesssim}0.75$, with nnn denoting the particle density. The calculation involves the self-consistent solution of equations for an auxiliary Fermi liquid Green's function and an adaptive spectral weight. We present numerical results at low as well as high TTT, at various low to intermediate densities in the normal phase, using a minimal set of band parameters relevant to the cuprate superconductors. We display the momentum space occupation function mk{m}_{k}mk​, energy dispersion curves locating the peaks of spectral functions, the optical conductivity, relaxation rates for quasiparticles, and the electronic spectral functions on an absolute scale. The line shapes have an asymmetric shape and a broad background that is also seen in experiments, and our calculations validate approximate recent versions of the theory. The results also display the experimentally noted high-energy kink and provide an in-depth understanding of its origin and dependence on band parameters.
This dissertation examines the impact of long-range interactions in lattice models of low-dimensional strongly correlated systems with a focus on their relevance to anomalous electronic transport. Traditionally, the Hubbard model forms the basis of theoretical and numerical investigations of strongly correlated quantum matter. This effective model constitutes the simplest model of electronic correlation and relies on an approximation that truncates electron-electron interactions to a local, on-site potential. While this approximation has proved valid in several instances, certain unexplained phenomena in correlated materials challenge us to develop new perspectives and approaches.In the first part of this thesis, we discuss the historical motivation for our current work from both a theoretical and an experimental viewpoint. In particular, we cover the discovery of bad metallic transport and the associated breakdown of Boltzmann theory of electron transport. We further review examples of strongly correlated systems that exhibit bad metallic transport and other exotic phenomena that suggest the possibility of poorly screened electronic interactions acting as a common microscopic mechanism. This general feature justifies the development of a theoretical framework that is capable of examining long-range interactions in a controlled, systematic manner.Motivated by this, we analyze a long-range interacting lattice model for spinless electrons in two dimensions via exact diagonalization on a finite cluster in real space. As this method is susceptible to finite-size errors, we discuss at length its implementation and technical details designed specifically to reduce these errors, namely the use of twisted boundary conditions and the Ewald summation. We determine the phase diagram at zero temperature and demonstrate that the long-range interactions act as a source of self-generated disorder that drives the development of a strongly correlated pseudogap phase, in a manner reminiscent of the classical Efros-Shklovskii Coulomb gap. Furthermore, we establish that this phenomenon is independent of lattice geometry, a fact that represents the broad potential of long-range interactions in giving rise to a novel form of strongly correlated behavior.Following our zero-temperature study, we address the question of whether this self-generated disorder can survive in the presence of thermal fluctuations and local Coulomb repulsion (Hubbard terms) relevant in Mott systems, a situation closer to those in experimental systems. By means of classical Monte Carlo calculations, we show that not only does the self-generated disorder survive, but that it also acts as a microscopic mechanism that generates bad metallic transport. Upon further investigation, we determine that the long-range interactions, in combination with quantum fluctuations, cause a transient localization of the charge carriers, thereby suppressing the conductivity values below those predicted in conventional Boltzmann theory, as observed experimentally.In conclusion, we have established that long-range interactions in electronic models act as a microscopic mechanism that is capable of causing exotic phenomena in numerous materials. We conclude that a proper treatment of both quantum fluctuations and long-range interactions should next be studied with the finite temperature Lanczos method, which will act as a bridge between our exact diagonalization and Monte Carlo studies. Overall, this dissertation emphasizes the capability of long-range interactions to produce novel phenomena and elicits further thought-provoking questions concerning the interplay with Mott-Hubbard physics and external disorder, crucial in metallic systems.
The charge susceptibility of the two-dimensional repulsive Hubbard model is investigated by using the diagram technique developed for the case of strong correlations. In this technique, a power series in the hopping constant is used. It is shown that once the Fermi level crosses one of the Hubbard subbands, a sharp peak appears in the momentum dependence of the static susceptibility. With further departure from half-filling, the peak transforms to a ridge around the $\ensuremath{\Gamma}$ point. Within the considered range $0\ensuremath{\le}|1\ensuremath{-}\overline{n}|\ensuremath{\lesssim}0.2$ of the electron filling n‾\overline{n}n, the static susceptibility is finite, which points to the absence of long-range charge ordering. However, for $|1\ensuremath{-}\overline{n}|\ensuremath{\approx}0.12$, the susceptibility maxima are located halfway between the center and the boundaries of the Brillouin zone. In this case, an interaction of the carriers with the tetragonal distortions can stabilize the charge-density wave with the wavelength of four lattice spacings, as experimentally observed in the low-temperature tetragonal phase of lanthanum cuprates. Within the range of parameters inherent in cuprate perovskites, the character of the susceptibility evolution with n‾\overline{n}n depends only weakly on the ratio of the nearest-neighbor hopping constant to the Hubbard repulsion and on details of the initial band structure. The location of the susceptibility maxima in the Brillouin zone is mainly determined by the value of n‾\overline{n}n.
Understanding the impact of electronic correlations onto the properties of cuprate superconductors is one of the most prominent tasks of solid state physics. In particular, the intermingling of short range strong correlations, driving the Mott or charge-transfer insulator in the parent compound, and the long range antiferromagnetic scattering processes in the highly doped regime poses severe difficulties to the theoretical description. This thesis studies the impact of short and intermediate ranged strong correlations on the electronic properties of the 2D Hubbard model in the half-filled and doped cases by means of cellular dynamical mean-field theory (CDMFT), i.e. real-space clusters embedded in a dynamical mean-field. Specifically, the effect of incorporating gradually longer ranged correlations onto the metal-insulator transition is analysed and dynamic next-neighbour spin correlations are identified as the cause of the insulating state. Furthermore, by introducing the Bethe-Salpeter scheme for embedded clusters, spin, charge and pairing susceptibilities are computed, incorporating the short ranged strong correlations exactly via the effective interaction of CDMFT and at the same time treating long-ranged fluctuations in a perturbative manner. Firstly, this allows to study the charge response at the Mott transition, identifying the non-local extended s-wave character of the transition. Secondly, in the hole-doped case, the pseudogap, the Knight-shift, a d-wave superconducting instability and unilateral charge instabilities with a periodicity of 4 lattice sites in the s-wave and d-wave channel are observed, all of which strongly depend on next-neighbour spin singlet-like correlations contained in the effective interaction of CDMFT. This work paves the way for computing the conductivity at the boundary between the pseudogap regime and the Fermi liquid. This doctoral thesis was conducted at the Max Planck Institute for Solid State Research and the University of Stuttgart.