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Electron(hole)-phonon interaction in YBCO high temperature superconductor using quantum path integral molecular dynamics

Edward D. Amavisca, Edward D. Amavisca

Published Jan 1, 1991• 0 citations
OpenAlex

Abstract

In this research, we have implemented an original technique to study the electronic properties of a single electron placed in YBa2 at 300K. Using a discretized extension of Feynman's Quantum Path Integral, we have been able to characterize effective electron-phonon interactions, and electron location site probability. We find that the electron stabilizes at oxygen vacant sites in the copper-oxygen chains. In the copper-oxygen planes, the electron is unstable and moves into the chain. Upon complementing the quantum electron to a positive charge thereby simulating a hole, we then find that the hole moves into favorable sites in the copper-oxygen planes. These sites are surrounded by four oxygens and two copper ions. Next, by decoupling the electron and hole from the lattice, we obtain effective electron-phonon and hole-phonon coupling constants on the order of 30. These results indicate that the next area of research is to move toward a multi-electron system and allow for further study of the electrons near the Fermi level. Some of the difficulties associated with multi-electron systems such as "exchange", are briefly discussed.

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Exact-diagonalization study of electron-lattice coupling in the effective two-band t − J model

Yury Petrov, T. Egami

The effective two-band $t\ensuremath{-}J$ Hamiltonian for holes in Cu-O planes of cuprates is obtained from the three-band Hubbard Hamiltonian. In this model a doped oxygen hole together with two neighboring copper holes is treated as a composite spin-$\frac{1}{2}$ three-sites particle. The model is studied by exact diagonalization in a ${\mathrm{Cu}}_{16}{\mathrm{O}}_{32}$ square cluster. Both binding energy and hole-hole correlation function indicate that two holes bind together for $J/t>0.11$ and are predominantly located on the next-nearest oxygen sites in the same Cu-O chain. Electron-phonon interaction is studied in the adiabatic phonons approximation. Copper (\ensuremath{\pi},0) ``half-breathing'' mode is shown to couple strongly to doped holes and increase the hole-hole correlation as well as the binding energy. These results are compared with experimental data.

Physical review. B, Condensed matter•Oct 1, 1998•25 citations

Electron-phonon interactions in the presence of strong correlations

M. Grilli, Claudio Castellani

We investigate the effect of strong electron-electron repulsion on the electron-phonon interaction from a Fermi-liquid point of view. In particular, we show that the strong interaction is responsible for vertex corrections, which are strongly dependent on the ${\mathit{v}}_{\mathit{F}}$q/\ensuremath{\omega} ratio, where ${\mathit{v}}_{\mathit{F}}$ is the Fermi velocity and q and \ensuremath{\omega} are the transferred momentum and frequency, respectively. These corrections generically lead to a strong suppression of the effective coupling between quasiparticles mediated by a single phonon exchange in the ${\mathit{v}}_{\mathit{F}}$q/\ensuremath{\omega}\ensuremath{\gg}1 limit. However, such effect is not present when ${\mathit{v}}_{\mathit{F}}$q/\ensuremath{\omega}\ensuremath{\ll}1. Analyzing the stability criterion for the compressibility, which involves the effective interactions in the dynamical limit, we show that a sizable electron-phonon interaction can push the system towards a phase separation instability. A detailed analysis is then carried out using a slave-boson approach for the infinite-U three-band Hubbard model describing the basic structure of a ${\mathrm{CuO}}_{2}$ plane in copper oxides. In the presence of a coupling between the local hole density and a dispersionless optical phonon, we explicitly confirm the strong dependence of the hole-phonon coupling on the transferred momentum versus frequency ratio. We also find that the exchange of phonons leads to an unstable phase with negative compressibility already at small values of the bare hole-phonon coupling. Close to the unstable region, we detect Cooper instabilities both in s- and d-wave channels supporting a possible connection between phase separation and superconductivity in strongly correlated systems.

arXiv:cond-mat/9404019•Physical review. B, Condensed matter•Dec 15, 1994•128 citations

The infinite range Heisenberg model and high temperature superconductivity

Jamil Tahir‐Kheli

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The thesis deals with the theory of high temperature superconductivity from the standpoint of three-band Hubbard models. Chapter 1 of the thesis proposes a strongly coupled variational wavefunction that has the three-spin system of an oxygen hole and its two neighboring copper spins in a doublet and the background Cu spins in an eigenstate of the infinite range antiferromagnet. This wavefunction is expected to be a good "zeroth order" wavefunction in the superconducting regime of dopings. The three-spin polaron is stabilized by the hopping terms rather than the copper-oxygen antiferromagnetic coupling Jpd. Considering the effect of the copper-copper antiferromagnetic coupling Jdd, we show that the three-spin polaron cannot be pure Emery (Dg), but must have a non-negligible amount of doublet-u (Du) character for hopping stabilization. Finally, an estimate is made for the magnitude of the attractive coupling of oxygen holes. Chapter 2 presents an exact solution to a strongly coupled Hamiltonian for the motion of oxygen holes in a 1-D Cu-O lattice. The Hamiltonian separates into two pieces: one for the spin degrees of freedom of the copper and oxygen holes, and the other for the charge degrees of freedom of the oxygen holes. The spinon part becomes the Heisenberg antiferromagnet in 1-D that is soluble by the Bethe Ansatz. The holon piece is also soluble by a Bethe Ansatz with simple algebraic relations for the phase shifts. Finally, we show that the nearest neighbor Cu-Cu spin correlation increases linearly with doping and becomes positive at x [...] 0.70.

•May 12, 2006•0 citations

One hole in a three-band model of a high-temperature superconductor

Iain B. Styles, M W Long

We study a three-band effective model of a CuO 2 plane for the simple case of a single hole, with the aim of investigating the nature of the ground state stabilized by the motion of a single hole on the CuO 2 lattice. Our model is derived from, and retains the essential physics of the Anderson lattice model, but is more amenable to further investigation by virtue of the lifting of the spin degeneracy on the copper sites provided by perturbation theory. We use the Lanczos algorithm to numerically solve a series of finite systems which tend to the CuO 2 plane in the thermodynamic limit. Although we only study finite systems, the largest systems are sufficiently large to demonstrate behaviour that is independent of the boundary conditions, and is hence representative of the behaviour in the thermodynamic limit. In order to gain a good understanding of the competing energy scales, we consider only a single hole at T = 0. Our calculations predict that the ground state of the three-band model for a single hole is strongly quantum, dominated by short-range dimer correlations, reminiscent of a resonating valence bond state. There is no evidence for a discontinuity in the occupation number, indicating that the system is not a Fermi liquid. These predictions are in contrast to those of the t – J model, where the hole motion alone predicts Nagaoka ferromagnetism for the planar system, and one must include magnetic exchange terms in order to obtain the experimentally observed low-spin ground state.

Journal of Physics A Mathematical and General•Aug 20, 2003•3 citations

Correlated-Electron Systems and High-Temperature Superconductivity

Takashi Yanagisawa, Mitake Miyazaki, Yamaji K.

We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors has been extensively studied on the basis of various electronic models and also electron-phonon models. In this study, we investigate the properties of superconductivity in correlated-electron systems by using numerical methods such as the variational Monte Carlo method and the quantum Monte Carlomethod. The Hubbard model is one of basic models for strongly correlated electron systems, and is regarded as the model of cuprate high temperature superconductors. The d-p model is more realistic model for cuprates. The superconducting condensation energy obtained by adopting the Gutzwiller ansatz is in reasonable agreement with the condensation energy estimated for YBa2Cu3O7. We show the phase diagram of the ground state using this method. We have further investigated the stability of striped and checkerboard states in the under-doped region. Holes doped in a half-filled square lattice lead to an incommensurate spin and charge density wave. The relationship of the hole density x and incommensurability δ, δ~x, is satisfied in the lower doping region, as indicated by the variationalMonte Carlocalculations for the two-dimensional Hubbard model. A checkerboard-like charge-density modulation with a roughly period has also been observed by scanning tunneling microscopy experiments in Bi2212 and Na-CCOC compounds. We have performed a variational Monte Carlo simulation on a two-dimensional t-t′-t″- U Hubbard model with a Bi-2212 type band structure and found that the period checkerboard spin modulation, that is characterized by multi Q vectors, is indeed stabilized. We have further performed an investigation by using a quantumMonte Carlomethod, which is a numerical method that can be used to simulate the behavior of correlated electron systems. We present a new algorithm of the quantum Monte Carlo diagonalization that is a method for the evaluation of expectation value without the negative sign problem. We compute pair correlation functions and show that pair correlation is indeed enhanced with hole doping.

arXiv:1307.2456•Journal of Modern Physics•Jan 1, 2013•23 citations

Orbital structure of the effective pairing interaction in the high-temperature superconducting cuprates

Peizhi Mai, Giovanni Balduzzi, Steven Johnston +1 more

Abstract The nature of the effective interaction responsible for pairing in the high-temperature superconducting cuprates remains unsettled. This question has been studied extensively using the simplified single-band Hubbard model, which does not explicitly consider the orbital degrees of freedom of the relevant CuO2 planes. Here, we use a dynamical cluster quantum Monte Carlo approximation to study the orbital structure of the pairing interaction in the three-band Hubbard model, which treats the orbital degrees of freedom explicitly. We find that the interaction predominately acts between neighboring copper orbitals, but with significant additional weight appearing on the surrounding bonding molecular oxygen orbitals. By explicitly comparing these results to those from the simpler single-band Hubbard model, our study provides strong support for the single-band framework for describing superconductivity in the cuprates.

arXiv:2009.14235•npj Quantum Materials•Mar 17, 2021•29 citations
In this research, we have implemented an original technique to study the electronic properties of a single electron placed in YBa2 at 300K. Using a discretized extension of Feynman's Quantum Path Integral, we have been able to characterize effective electron-phonon interactions, and electron location site probability. We find that the electron stabilizes at oxygen vacant sites in the copper-oxygen chains. In the copper-oxygen planes, the electron is unstable and moves into the chain. Upon complementing the quantum electron to a positive charge thereby simulating a hole, we then find that the hole moves into favorable sites in the copper-oxygen planes. These sites are surrounded by four oxygens and two copper ions. Next, by decoupling the electron and hole from the lattice, we obtain effective electron-phonon and hole-phonon coupling constants on the order of 30. These results indicate that the next area of research is to move toward a multi-electron system and allow for further study of the electrons near the Fermi level. Some of the difficulties associated with multi-electron systems such as "exchange", are briefly discussed.
The effective two-band $t\ensuremath{-}J$ Hamiltonian for holes in Cu-O planes of cuprates is obtained from the three-band Hubbard Hamiltonian. In this model a doped oxygen hole together with two neighboring copper holes is treated as a composite spin-12\frac{1}{2}21​ three-sites particle. The model is studied by exact diagonalization in a Cu16O32{\mathrm{Cu}}_{16}{\mathrm{O}}_{32}Cu16​O32​ square cluster. Both binding energy and hole-hole correlation function indicate that two holes bind together for J/t>0.11J/t>0.11J/t>0.11 and are predominantly located on the next-nearest oxygen sites in the same Cu-O chain. Electron-phonon interaction is studied in the adiabatic phonons approximation. Copper (\ensuremath{\pi},0) ``half-breathing'' mode is shown to couple strongly to doped holes and increase the hole-hole correlation as well as the binding energy. These results are compared with experimental data.
We investigate the effect of strong electron-electron repulsion on the electron-phonon interaction from a Fermi-liquid point of view. In particular, we show that the strong interaction is responsible for vertex corrections, which are strongly dependent on the vF{\mathit{v}}_{\mathit{F}}vF​q/\ensuremath{\omega} ratio, where vF{\mathit{v}}_{\mathit{F}}vF​ is the Fermi velocity and q and \ensuremath{\omega} are the transferred momentum and frequency, respectively. These corrections generically lead to a strong suppression of the effective coupling between quasiparticles mediated by a single phonon exchange in the vF{\mathit{v}}_{\mathit{F}}vF​q/\ensuremath{\omega}\ensuremath{\gg}1 limit. However, such effect is not present when vF{\mathit{v}}_{\mathit{F}}vF​q/\ensuremath{\omega}\ensuremath{\ll}1. Analyzing the stability criterion for the compressibility, which involves the effective interactions in the dynamical limit, we show that a sizable electron-phonon interaction can push the system towards a phase separation instability. A detailed analysis is then carried out using a slave-boson approach for the infinite-U three-band Hubbard model describing the basic structure of a CuO2{\mathrm{CuO}}_{2}CuO2​ plane in copper oxides. In the presence of a coupling between the local hole density and a dispersionless optical phonon, we explicitly confirm the strong dependence of the hole-phonon coupling on the transferred momentum versus frequency ratio. We also find that the exchange of phonons leads to an unstable phase with negative compressibility already at small values of the bare hole-phonon coupling. Close to the unstable region, we detect Cooper instabilities both in s- and d-wave channels supporting a possible connection between phase separation and superconductivity in strongly correlated systems.
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The thesis deals with the theory of high temperature superconductivity from the standpoint of three-band Hubbard models. Chapter 1 of the thesis proposes a strongly coupled variational wavefunction that has the three-spin system of an oxygen hole and its two neighboring copper spins in a doublet and the background Cu spins in an eigenstate of the infinite range antiferromagnet. This wavefunction is expected to be a good "zeroth order" wavefunction in the superconducting regime of dopings. The three-spin polaron is stabilized by the hopping terms rather than the copper-oxygen antiferromagnetic coupling Jpd. Considering the effect of the copper-copper antiferromagnetic coupling Jdd, we show that the three-spin polaron cannot be pure Emery (Dg), but must have a non-negligible amount of doublet-u (Du) character for hopping stabilization. Finally, an estimate is made for the magnitude of the attractive coupling of oxygen holes. Chapter 2 presents an exact solution to a strongly coupled Hamiltonian for the motion of oxygen holes in a 1-D Cu-O lattice. The Hamiltonian separates into two pieces: one for the spin degrees of freedom of the copper and oxygen holes, and the other for the charge degrees of freedom of the oxygen holes. The spinon part becomes the Heisenberg antiferromagnet in 1-D that is soluble by the Bethe Ansatz. The holon piece is also soluble by a Bethe Ansatz with simple algebraic relations for the phase shifts. Finally, we show that the nearest neighbor Cu-Cu spin correlation increases linearly with doping and becomes positive at x [...] 0.70.
We study a three-band effective model of a CuO 2 plane for the simple case of a single hole, with the aim of investigating the nature of the ground state stabilized by the motion of a single hole on the CuO 2 lattice. Our model is derived from, and retains the essential physics of the Anderson lattice model, but is more amenable to further investigation by virtue of the lifting of the spin degeneracy on the copper sites provided by perturbation theory. We use the Lanczos algorithm to numerically solve a series of finite systems which tend to the CuO 2 plane in the thermodynamic limit. Although we only study finite systems, the largest systems are sufficiently large to demonstrate behaviour that is independent of the boundary conditions, and is hence representative of the behaviour in the thermodynamic limit. In order to gain a good understanding of the competing energy scales, we consider only a single hole at T = 0. Our calculations predict that the ground state of the three-band model for a single hole is strongly quantum, dominated by short-range dimer correlations, reminiscent of a resonating valence bond state. There is no evidence for a discontinuity in the occupation number, indicating that the system is not a Fermi liquid. These predictions are in contrast to those of the t – J model, where the hole motion alone predicts Nagaoka ferromagnetism for the planar system, and one must include magnetic exchange terms in order to obtain the experimentally observed low-spin ground state.
We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors has been extensively studied on the basis of various electronic models and also electron-phonon models. In this study, we investigate the properties of superconductivity in correlated-electron systems by using numerical methods such as the variational Monte Carlo method and the quantum Monte Carlomethod. The Hubbard model is one of basic models for strongly correlated electron systems, and is regarded as the model of cuprate high temperature superconductors. The d-p model is more realistic model for cuprates. The superconducting condensation energy obtained by adopting the Gutzwiller ansatz is in reasonable agreement with the condensation energy estimated for YBa2Cu3O7. We show the phase diagram of the ground state using this method. We have further investigated the stability of striped and checkerboard states in the under-doped region. Holes doped in a half-filled square lattice lead to an incommensurate spin and charge density wave. The relationship of the hole density x and incommensurability δ, δ~x, is satisfied in the lower doping region, as indicated by the variationalMonte Carlocalculations for the two-dimensional Hubbard model. A checkerboard-like charge-density modulation with a roughly period has also been observed by scanning tunneling microscopy experiments in Bi2212 and Na-CCOC compounds. We have performed a variational Monte Carlo simulation on a two-dimensional t-t′-t″- U Hubbard model with a Bi-2212 type band structure and found that the period checkerboard spin modulation, that is characterized by multi Q vectors, is indeed stabilized. We have further performed an investigation by using a quantumMonte Carlomethod, which is a numerical method that can be used to simulate the behavior of correlated electron systems. We present a new algorithm of the quantum Monte Carlo diagonalization that is a method for the evaluation of expectation value without the negative sign problem. We compute pair correlation functions and show that pair correlation is indeed enhanced with hole doping.
Abstract The nature of the effective interaction responsible for pairing in the high-temperature superconducting cuprates remains unsettled. This question has been studied extensively using the simplified single-band Hubbard model, which does not explicitly consider the orbital degrees of freedom of the relevant CuO2 planes. Here, we use a dynamical cluster quantum Monte Carlo approximation to study the orbital structure of the pairing interaction in the three-band Hubbard model, which treats the orbital degrees of freedom explicitly. We find that the interaction predominately acts between neighboring copper orbitals, but with significant additional weight appearing on the surrounding bonding molecular oxygen orbitals. By explicitly comparing these results to those from the simpler single-band Hubbard model, our study provides strong support for the single-band framework for describing superconductivity in the cuprates.