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Physical review. B./Physical review. B

Exact diagonalization study of the effects of Zn and Ni impurities on the pseudogap of underdoped cuprate high-Tc superconductors

Jiří Vašátko, D. Munzar

Published Mar 9, 2016• 3 citations
Publisher

Abstract

The influence of Zn and Ni impurities on the normal-state pseudogap of underdoped $\text{high-}{T}_{c}$ cuprate superconductors is studied using exact diagonalization of effective $t\ensuremath{-}J\text{-like}$ Hamiltonians describing low energy electronic excitations of the ${\mathrm{CuO}}_{2}$ plane with some of the copper ions replaced with Zn/Ni. The Ni case Hamiltonian has been obtained by a sequence of approximations from a more complete model involving Cu $3d$, Ni $3d$, and O $2p$ orbitals. Our main findings are: (i) The width ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{PG}}$ of the pseudogap occurring in the many body density of states, and manifesting itself also in the $c\text{-axis}$ infrared conductivity, decreases with increasing Zn concentration as a consequence of a suppression of short range spin correlations. (ii) In the case of one hole and one Ni impurity, the hole is---for realistic values of the model parameters---weakly bound to the Ni site. This causes a slight increase of ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{PG}}$ with respect to the pure case. (iii) Based on this result and further results for 1--2 holes and 1--2 Ni impurities, we suggest that in the real Ni substituted ${\mathrm{CuO}}_{2}$ plane ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{PG}}$ is larger than in the pure case due to the binding of the doped holes to the Ni sites and effective underdoping. Our findings clarify the trends observed in the $c\text{-axis}$ infrared conductivity data of Zn and Ni substituted (Sm,Nd)${\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ crystals.

DOI
10.1103/physrevb.93.094512

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The influence of Zn and Ni impurities on the normal-state pseudogap of underdoped high-Tc\text{high-}{T}_{c}high-Tc​ cuprate superconductors is studied using exact diagonalization of effective t\ensuremath−J-liket\ensuremath{-}J\text{-like}t\ensuremath−J-like Hamiltonians describing low energy electronic excitations of the CuO2{\mathrm{CuO}}_{2}CuO2​ plane with some of the copper ions replaced with Zn/Ni. The Ni case Hamiltonian has been obtained by a sequence of approximations from a more complete model involving Cu 3d3d3d, Ni 3d3d3d, and O 2p2p2p orbitals. Our main findings are: (i) The width \ensuremathΩPG{\mathrm{\ensuremath{\Omega}}}_{\mathrm{PG}}\ensuremathΩPG​ of the pseudogap occurring in the many body density of states, and manifesting itself also in the c-axisc\text{-axis}c-axis infrared conductivity, decreases with increasing Zn concentration as a consequence of a suppression of short range spin correlations. (ii) In the case of one hole and one Ni impurity, the hole is---for realistic values of the model parameters---weakly bound to the Ni site. This causes a slight increase of \ensuremathΩPG{\mathrm{\ensuremath{\Omega}}}_{\mathrm{PG}}\ensuremathΩPG​ with respect to the pure case. (iii) Based on this result and further results for 1--2 holes and 1--2 Ni impurities, we suggest that in the real Ni substituted CuO2{\mathrm{CuO}}_{2}CuO2​ plane \ensuremathΩPG{\mathrm{\ensuremath{\Omega}}}_{\mathrm{PG}}\ensuremathΩPG​ is larger than in the pure case due to the binding of the doped holes to the Ni sites and effective underdoping. Our findings clarify the trends observed in the c-axisc\text{-axis}c-axis infrared conductivity data of Zn and Ni substituted (Sm,Nd)Ba2Cu3O7\ensuremath−\ensuremathδ{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}Ba2​Cu3​O7\ensuremath−\ensuremathδ​ crystals.
We examine the electronic states in the hole- and electron-doped cuprates by using the t-t′-t″-J model. Numerically exact diagonalization method is employed for a 20-site square lattice under twisted boundary conditions. The density of states in the underdoped region clearly shows a pseudogap behavior near the Fermi level in both hole and electron dopings. In hole doping, the edge of the pseudogap in the occupied side exhibits a large weight that comes from a flat band near k=(π,0). In contrast, the weight near the gap edge in electron doping is larger for the unoccupied side than for the occupied side.
We study the interplay of quantum impurity, and collective spinon and holon dynamics in Zn doped high-Tc_cc​ cuprates in the normal state. The two-dimensional t-t′^{\prime}′-J models with one and a small amount of Zn impurity are investigated within a numerical method based on the double-time Green function theory. We study the inhomogeneities of holon density and antiferromagnetic correlation background in cases with different Zn concentrations, and obtain that doped holes tend to assemble around the Zn impurity with their mobility being reduced. Therefore a bound state of holon is formed around the nonmagnetic Zn impurity with the effect helping Zn to introduce local antiferromagnetism around itself. The incommensurate peaks we obtained in the spin structure factor indicate that Zn impurities have effects on mixing the q=(πππ, πππ) and q=0 components in spin excitations.
Motivated by similarities between cuprate superconductors and two-leg ladder copper-oxide compounds and in order to obtain a better understanding of optical properties of cuprate superconductors we have studied the c-axis (along the ladder) optical conductivity [Formula: see text] of a doped [Formula: see text] two-leg ladder. Using exact diagonalization, we have calculated the conductivity and related quantities for cyclic ladders of up to 13 rungs. In agreement with results of an early study by Hayward and coworkers (Hayward et al 1996 Phys. Rev. B 53 8863) we find that [Formula: see text] consists of a Drude peak at zero frequency and an absorption band in the infrared region that is separated from the former by a pseudogap. The width of the pseudogap [Formula: see text] increases with increasing J/t, in parallel with an increase of the magnitude [Formula: see text] of the gap in the quasiparticle excitation spectra. Our central finding is that [Formula: see text], where [Formula: see text] is the magnitude of the gap in the spin excitation spectra. We demonstrate that this approximate relation can be understood in terms of a phenomenological model involving a superconducting ladder and a coupling between charged quasiparticles and spin excitations. The relation is remarkably similar to the one between experimental values of the energy scale of a dip in the in-plane optical conductivity, the superconducting gap [Formula: see text] and the energy of the spin-resonance in cuprate superconductors (for a recent discussion of the optical data, see Šopík et al 2015 New J. Phys. 17 053022). Our findings support the point of view that low energy infrared active excited states of cuprate superconductors can be viewed as consisting of two charged quasiparticles connected with pair-breaking and a spin excitation.
In the hole-doped cuprates, the pseudogap refers to a suppression of the density of states at low energies, in the absence of superconducting long-range order. Numerous calculations of the Hubbard model show a pseudogap in the single-particle spectra, with striking similarities to photoemission and tunneling experiments on cuprates. However, no clear mechanism has been established. Here, we solve the Hubbard model on 2×22\times22×2 clusters by exact diagonalization, with integration over twisted boundary conditions. A pseudogap is found in the single-particle density of states with the following characteristics: a decreasing energy scale and onset temperature for increased hole-doping, closure at a critical hole doping near 15\%, absence upon electron-doping, particle-hole asymmetry indicated by the location of the gap center, and persistence in the strong-coupling limit of U/t→∞U/t \to \inftyU/t→∞. Studying the many-body excitation spectrum reveals that the pseudogap in single-particle spectra is due to orthogonality between bare electrons and the lowest energy excitations for U/t≳8U/t \gtrsim 8U/t≳8.
We present a theory for the lightly doped $t\text{\ensuremath{-}}J$ model that is of possible relevance for the normal state of underdoped cuprates. Starting from an arbitrary dimer covering of the plane, an exact representation of the $t\text{\ensuremath{-}}J$ Hamiltonian in terms of bond bosons and fermions can be derived. Since all dimer coverings must give identical results for observable quantities, we construct an approximate but translationally invariant Hamiltonian by averaging the bond particle Hamiltonian over all possible dimer coverings. Treating the resulting Hamiltonian in the mean-field approximation, we find Fermi pockets centered near $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ with a total area of x/2x/2x/2 (with xxx the hole concentration) and a gapped spin-wave-like band of triplet excitations.
Pseudogap phenomena are observed for the normal underdoped phase of different high-T c cuprates. Among others, the Bi2Sr2CaCu2O8 − δ (Bi2212) compound is one of the most studied experimentally. To describe the pseudogap regime in Bi2212, we use a novel generalized ab initio LDA + DMFT + Σk hybrid scheme. This scheme is based on the strategy of one of the most powerful computational tools for real correlated materials: the local density approximation (LDA) + dynamical mean-field theory (DMFT). Conventional LDA + DMFT equations are here supplied with an additional (momentum-dependent) self-energy Σk in the spirit of our recently proposed DMFT + Σk approach taking into account pseudogap fluctuations. In the present model, Σk describes nonlocal correlations induced by short-range collective Heisenberg-like antiferromagnetic spin fluctuations. The effective single-impurity problem of the DMFT is solved by the numerical renormalization group (NRG) method. Material-specific model parameters for the effective x 2 − y 2 orbital of Cu-3d shell of the Bi2212 compound, e.g., the values of intra-and interlayer hopping integrals between different Cu sites, the local Coulomb interaction U, and the pseudogap potential Δ were obtained within the LDA and LDA + DMFT schemes. Here, we report on the theoretical LDA + DMFT + Σk quasiparticle band dispersion and damping, Fermi surface renormalization, momentum anisotropy of (quasi)static scattering, densities of states, spectral densities, and angular-resolved photoemission (ARPES) spectra, taking into account pseudogap and bilayer splitting effects for normal (slightly) underdoped Bi2212 (δ = 0.15). We show that LDA + DMFT + Σk successfully describes strong (pseudogap) scattering close to Brillouin zone boundaries. Our calculated LDA + DMFT + Σk Fermi surfaces and ARPES spectra in the presence of pseudogap fluctuations are almost insensitive to the bilayer splitting strength. However, our LDA-calculated value of bilayer splitting is rather small to describe the experimentally observed peak-dip-hump structure. The results obtained are in good semiquantitative agreement with various recent ARPES experiments.