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AIP conference proceedings

Renormalized modes in cuprate superconductors

Anushri Gupta, Anita Kumari, Sanjeev K. Verma, B. D. Indu

Published Jan 1, 2018• 0 citations
Publisher

Abstract

The renormalized mode frequencies are obtained with the help of quantum dynamical approach of many body phonon Green’s function technique via a general Hamiltonian (excluding BCS Hamiltonian) including the effects of phonons and electrons, anharmonicities and electron-phonon interactions. The numerical estimates have been carried out to study the renormalized mode frequency of high temperature cuprate superconductor (HTS) YBa2Cu3O7-δ using modified Born-Mayer-Huggins interaction potential (MBMHP) best applicable to study the dynamical properties of all HTS.

DOI
10.1063/1.5029104

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The renormalized mode frequencies are obtained with the help of quantum dynamical approach of many body phonon Green’s function technique via a general Hamiltonian (excluding BCS Hamiltonian) including the effects of phonons and electrons, anharmonicities and electron-phonon interactions. The numerical estimates have been carried out to study the renormalized mode frequency of high temperature cuprate superconductor (HTS) YBa2Cu3O7-δ using modified Born-Mayer-Huggins interaction potential (MBMHP) best applicable to study the dynamical properties of all HTS.
Using the versatile double time thermodynamic Green's function approach based on many body theory the renormalized frequencies, phonon energy line widths, shifts and phonon density of states (PDOS) are investigated via a newly formulated Hamiltonian (does not include BCS type Hamiltonian) that includes the effects of electron-phonon, anharmonicities and that of isotopic impurities. The automatic appearance of pairons, temperature, impurity and electron-phonon coupling of renormalized frequencies, widths, shifts and PDOS emerges as a characteristic feature of present theory. The numerical investigations on PDOS for the YBa2Cu3O7 − δ crystal predicts several new feature of high temperature superconductors (HTS) and agreements with experimental observations.
The pairon spectral function for the high-[Formula: see text] cuprate superconductor [Formula: see text] has been evaluated through renormalized pairon frequency, analogous to the frequency (energy) of excited pairons. The exercise has been carried out with the help of many-body quantum dynamical Green’s function theory via a model Hamiltonian that includes the effects of the electrons, phonons, impurities and anharmonic fields. The analysis of the obtained results reveals that renormalized pairon frequency progressively increases up to the critical temperature [Formula: see text] and afterwards, instead of dropping to zero, it decreases smoothly with increasing temperature, capturing the essence of the pseudogap in high-[Formula: see text] cuprates. A further analysis of temperature-dependent spectral function also establishes the presence of the pseudogap above [Formula: see text]. The spectral function displays a conscious behavior with the variation of electron–phonon coupling constant ([Formula: see text]).
The evaluation of one electron thermodynamic Green’s functions using the equation of motion technique of quantum dynamics via newly formulated Hamiltonian and using Dyson’s equation approach. This involves approximation free approach and different cooper pairs are emerged automatically in the system and stands as an ab-initio approach. The detailed description of enhancement in the electron density of states (EDOS) for high temperature superconductors has been investigated. The investigated expressions of EDOS in the new framework are found responsible to describe a large number of dynamical properties of high temperature superconductors. The temperature dependence of EDOS has been found as a unique feature of the theory, which certainly becomes the outcome of the anharmonic interactions. The presence of electron-phonon interaction parameter in each term is an additional and new feature of the theory.
A wide variety of phenomena in condensed matter systems is driven primarily by interactions between electrons in the system. This work is concerned with the application of functional renormalization group (fRG) as a generalized solver for the multi-band Hamiltonians that describe these systems. We consider a decoupled formulation of the fRG equations that is optimized in the frequency and momentum domains and retains the flow of relevant modes in the system. Approximate truncations that extend the scheme to arbitrary multiband systems are addressed. This optimized decoupling is then used to derive the flow equations that describe fluctuations in model Hamiltonians for Cuprate and Pnictide superconductors. We construct a full phase diagram of the systems studied as a function of doping, temperature and coupling. Access to the frequency modes in the system allows us to explore the impact of coupling phonons to these model Hamiltonians. Alterations to the diagram due to electron-phonon coupling is derived. The results of the decoupled formulation is in agreement with results in the literature for many of the models considered. Further the fRG captures the sensitivity of susceptibilities of Cuprate Hamiltonians to band structure, the enhanced role of Hunds coupling in Pnictide systems and the impact of phonons in multiband Hamiltonians.
The properties of the electron-phonon interaction in the presence of a sizable electronic repulsion at finite doping are studied by investigating the metallic phase of the Hubbard-Holstein model with dynamical mean-field theory. Analyzing the quasiparticle weight at finite doping, we find that a large Coulomb repulsion reduces the effect of electron-phonon coupling at low energy, while this reduction is not present at high energy. The renormalization of the electron-phonon coupling induced by the Hubbard repulsion depends in a surprisingly strong and nontrivial way on the phonon frequency. Our results suggest that phonon might affect differently high-energy and low-energy properties and this, together with the effect of phonon dynamics, should be carefully taken into account when the effects of the electron-phonon interaction in a strongly correlated system, like the superconducting cuprates, are discussed.
We investigate the dynamical effects of pairing interaction on superconductivity in BCS-BEC crossover by studying the Holstein model at half filling where the electron-phonon coupling ggg controls the crossover. The dynamical mean-field theory was employed in combination with the numerical renormalization group technique to study the frequency dependence of phonon mediated interaction between electrons in a superconductive state. The frequency dependence induces distinct features such as the absence of the dispersion back bending of Bogoliubov quasiparticles, nonmonotonous coupling dependence of the pairing gap, and the critical temperature Tc{T}_{c}Tc​ being maximum at gc1{g}_{c1}gc1​, the lower critical coupling of the normal state insulator to metal transition. Some of these features have intriguing similarities with the recent observations in the ${\mathrm{FeSe}}_{1\ensuremath{-}x}{\mathrm{S}}_{x}$ and ${\mathrm{Fe}}_{1+y}{\mathrm{Se}}_{x}{\mathrm{Te}}_{1\ensuremath{-}x}$ iron chalcogenides in the BCS-BEC crossover.