Modern Physics Letters B

Three-Spin-Polarons and Their Elastic Interaction in Cuprates

Boris I. Kochelaev, Aisylu Safina, А. Shengelaya, Hugo Keller, K. A. Müller, K. Conder

Published May 20, 2003• 16 citations

Abstract

Properties of quasiparticles in doped cuprates formed by an oxygen hole and two adjacent copper holes are investigated on the basis of the extended Hubbard model. The ground state energy, wave functions and the polaron-phonon coupling are calculated. We also analyzed the polaron-polaron interaction via the phonon field. It was found that this interaction is highly anisotropic and can explain the experimentally observed phase separation in the strongly underdoped LaSrCuO:Mn system.

DOI: 10.1142/s0217984903005433

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Modern Physics Letters B

Three-Spin-Polarons and Their Elastic Interaction in Cuprates

Boris I. Kochelaev, Aisylu Safina, А. Shengelaya, Hugo Keller, K. A. Müller, K. Conder

Published May 20, 2003• 16 citations

Publisher

Abstract

DOI: 10.1142/s0217984903005433

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We show that a strongly renormalized band of polaronic quasiparticle excitations is induced at the Fermi level of an interacting many-electron system on increasing the coupling of the electrons to local phonons. We give results for the local density of states at zero temperature both for the electrons and phonons. The polaronic quasiparticles satisfy Luttinger's theorem for all regimes considered, and their dispersion shows a kink similar to that observed experimentally in copper oxides. Our calculations are based on the dynamical mean field theory and the numerical renormalization group for the hole-doped Holstein-Hubbard model and large on-site repulsion.We show that a strongly renormalized band of polaronic quasiparticle excitations is induced at the Fermi level of an interacting many-electron system on increasing the coupling of the electrons to local phonons. We give results for the local density of states at zero temperature both for the electrons and phonons. The polaronic quasiparticles satisfy Luttinger's theorem for all regimes considered, and their dispersion shows a kink similar to that observed experimentally in copper oxides. Our calculations are based on the dynamical mean field theory and the numerical renormalization group for the hole-doped Holstein-Hubbard model and large on-site repulsion.

arXiv:cond-mat/0508463Physical Review LettersDec 13, 200530 citations

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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.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, 20060 citations

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.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 matterOct 1, 199825 citations

Variational studies of dressed quasiparticles' properties and their interactions with external potentials

Ebrahimnejad Rahbari

In this thesis, we investigated the spectral properties of polaronic quasiparticles resulting from the coupling of a charge carrier to the bosonic excitations of ordered environments. Holstein polarons, describing an electron locally coupled to dispersionless phonons, and spin polarons in hole-doped antiferromagnets are considered. The Green's function of the Holstein polaron in a lattice with various kinds of impurities is calculated using the momentum average approximation. The main finding is that the scenario where the mere effect of the coupling to phonons is to enhance the electron's effective mass is incomplete as the phonons are found to also renormalize the impurity potential the polaron interacts with. This formalism is applied first to the case of a single impurity and the range of parameters where the polaron's ground state is localized is identified. The lifetime of the polaron due to scattering from weak but extended disorder is then studied and it is shown that the renormalization of the disorder potential leads to deviation of the strong coupling results from Fermi's golden rule's predictions. Motivated by the hole-doped cuprate superconductors, the motion of a hole in a two-dimensional Ising antiferromagnet and its binding to an attractive impurity is studied next, based on a variational scheme that allows for configurations with a certain maximum number of spin flips. The role of the magnetic sublattices in determining the symmetry of the resulting bound states is discussed. Next, a more realistic model describing a hole in a CuO₂ layer which retains the O explicitly, is considered. By neglecting the fluctuations of the Cu spins and using a variational principle similar to that of the previous chapter, a semi-analytic solution for the Green's function of the hole in an infinite 2D lattice is constructed. The resulting quasiparticle dispersion shows the proper ground state and other features observed in experiments. The lack of importance of the background spin fluctuations is justified based on the hole's ability to move on the O sublattice without disturbing the Cu spins. Finally, the model is generalized to gauge the importance of other relevant O orbitals.In this thesis, we investigated the spectral properties of polaronic quasiparticles resulting from the coupling of a charge carrier to the bosonic excitations of ordered environments. Holstein polarons, describing an electron locally coupled to dispersionless phonons, and spin polarons in hole-doped antiferromagnets are considered. The Green's function of the Holstein polaron in a lattice with various kinds of impurities is calculated using the momentum average approximation. The main finding is that the scenario where the mere effect of the coupling to phonons is to enhance the electron's effective mass is incomplete as the phonons are found to also renormalize the impurity potential the polaron interacts with. This formalism is applied first to the case of a single impurity and the range of parameters where the polaron's ground state is localized is identified. The lifetime of the polaron due to scattering from weak but extended disorder is then studied and it is shown that the renormalization of the disorder potential leads to deviation of the strong coupling results from Fermi's golden rule's predictions. Motivated by the hole-doped cuprate superconductors, the motion of a hole in a two-dimensional Ising antiferromagnet and its binding to an attractive impurity is studied next, based on a variational scheme that allows for configurations with a certain maximum number of spin flips. The role of the magnetic sublattices in determining the symmetry of the resulting bound states is discussed. Next, a more realistic model describing a hole in a CuO₂ layer which retains the O explicitly, is considered. By neglecting the fluctuations of the Cu spins and using a variational principle similar to that of the previous chapter, a semi-analytic solution for the Green's function of the hole in an infinite 2D lattice is constructed. The resulting quasiparticle dispersion shows the proper ground state and other features observed in experiments. The lack of importance of the background spin fluctuations is justified based on the hole's ability to move on the O sublattice without disturbing the Cu spins. Finally, the model is generalized to gauge the importance of other relevant O orbitals.

Jan 1, 20140 citations

Spin and charge dynamics in a one-dimensional two-band Hubbard model

Hong Q. Ding, William A. Goddard

A CuO chain with one or two holes doped is studied via the two-band Hubbard model in the large-U limit on a finite cluster. The quasiparticle band is ${\mathit{E}}_{\mathit{k}}$ \ensuremath{\sim}0.87J cos(2ka) with the bottom at ka=\ensuremath{\pi}/2. The quasiparticles are kinks which have the character of three-spin polarons. The copper spin excitations are incommensurate spin waves. The two doped holes repel each other very slightly, in contrast to the slight attraction in the t-J model. Spin-charge separation also occurs.A CuO chain with one or two holes doped is studied via the two-band Hubbard model in the large-U limit on a finite cluster. The quasiparticle band is ${\mathit{E}}_{\mathit{k}}$\ensuremath{\sim}0.87J cos(2ka) with the bottom at ka=\ensuremath{\pi}/2. The quasiparticles are kinks which have the character of three-spin polarons. The copper spin excitations are incommensurate spin waves. The two doped holes repel each other very slightly, in contrast to the slight attraction in the t-J model. Spin-charge separation also occurs.

Physical review. B, Condensed matterJan 1, 19934 citations

We extend the methods recently introduced [Phys. Rev. Lett. 106, 036401 (2011)] to investigate correlations between two spin-polarons in a quasi-two-dimensional CuO

{}_{2}

layer. The low-energy wave functions for two doped holes introduced in a half filled CuO

{}_{2}

plane with 32 copper and 64 oxygen sites are calculated explicitly using an efficient yet accurate truncation scheme to model the antiferromagnet background. The energetics and wave functions show that the charges form three spin-polarons and the spin is carried by a disturbance around the three spin-polaron core. The low-energy band results from the competition between the kinetic energy and a local attractive potential, which favors ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ states. Last, we point out features that are expected to be robust for larger systems.

\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.

A CuO chain with one or two holes doped is studied via the two-band Hubbard model in the large-U limit on a finite cluster. The quasiparticle band is

{\mathit{E}}_{\mathit{k}}

\ensuremath{\sim}0.87J cos(2ka) with the bottom at ka=\ensuremath{\pi}/2. The quasiparticles are kinks which have the character of three-spin polarons. The copper spin excitations are incommensurate spin waves. The two doped holes repel each other very slightly, in contrast to the slight attraction in the t-J model. Spin-charge separation also occurs.