2D Cuprates Research Articles

Magnetic Interaction in Doped 2D Perovskite Cuprates with Nanoscale Inhomogeneity: Lattice Nonlocal Effects vs. Superexchange

We have studied the superexchange interaction Jij in doped 2D cuprates. The AFM interaction strongly depends on the state of the lattice of a CuO2 layer surrounded by two LaO rock salt layers. In a static U and D stripe nanostructure, the homogeneous AFM interaction is impossible due to the U/D/U… periodic stripe sequence and TN=0. In a dynamic stripe nanostructure, the ideal CuO2 layer with nonlocal effects and the homogeneous AFM interaction are restored. However, the interaction Jij decreases by the exponential factor due to partial dynamic quenching. The meaning of the transition from the dynamic to the static cases lies in the spontaneous θ-symmetry breaking with respect to the rotation of all the tilted CuO6 octahedra by an orientation angle δθ=n·45° (where n=1÷4) in the U and D stripe nanostructure of the CuO2 layer. Moreover, the structural features help to study various experimental data on the charge inhomogeneity, Fermi level pinning in the p type cuprates only and time reversal symmetry breaking from a unified point of view.

Particle-hole asymmetry in the dynamical spin and charge responses of corner-shared 1D cuprates

Although many experiments imply that oxygen orbitals play an essential role in the high-temperature superconducting cuprates, their precise role in collective spin and charge excitations and superconductivity is not yet fully understood. Here, we study the doping-dependent dynamical spin and charge structure factors of single and multi-orbital (pd) models for doped one-dimensional corner-shared spin-chain cuprates using several numerically exact methods. In doing so, we determine the orbital composition of the collective spin and charge excitations of cuprates, with important implications for our understanding of these materials. For example, we observe a particle-hole asymmetry in the orbital-resolved charge excitations, which is directly relevant to resonant inelastic x-ray scattering experiments and not captured by the single-band Hubbard model. Our results imply that one must explicitly include the oxygen degrees of freedom in order to fully understand some experimental observations on cuprate materials.

Electron–Hole Dimers in the Parent Phase of Quasi–2D Cuprates

The key feature of parent cuprates of the La2CuO4 type, in addition to their high ionic polarizability and closeness to polarization catastrophe, is identified as their instability against charge transfer that is accompanied by the formation of a system of metastable dipole-active Mott–Hubbard excitons, i.e., electron–hole (EH) dimers. This feature determines the behavior of cuprates upon nonisovalent substitution. Within the simplest model equivalent to a system of composite bosons, nonisovalent substitution shifts the phase equilibrium toward condensation of EH dimers and the formation of inhomogeneous EH liquid. To describe the electronic state of doped cuprates effectively, we propose to use the pseudospin S = 1 formalism. It enables us to treat cardinally new charged states such as Anderson’s RVB phases. Recombination of EH dimers at a critically low energy of local and nonlocal correlations drives the system into the state of a Fermi liquid.

Topological Structures in Unconventional Scenario for 2D Cuprates

Numerous experimental data point to cuprates as d-d charge transfer unstable systems whose description implies the inclusion of the three many-electron valence states CuO $_{4}^{7-,6-,5-}$ (nominally Cu1+,2+,3+) on an equal footing as a well-defined charge triplet. We introduce a minimal model to describe the charge degree of freedom in cuprates with the on-site Hilbert space reduced to only the three states and make use of the S = 1 pseudospin formalism. The formalism constitutes a powerful method to study complex phenomena in interacting quantum systems characterized by the coexistence and competition of various ordered states. Overall, such a framework provides a simple and systematic methodology to predict and discover new kinds of orders. In particular, the pseudospin formalism provides the most effective way to describe different topological structures, in particular, due to a possibility of a geometrical two-vector description of the on-site states. We introduce and analyze effective pseudospin Hamiltonian with on-site and inter-site charge correlations, two types of a correlated one-particle transfer and two-particle, or the composite boson transfer. The latter is of a principal importance for the HTSC perspectives. The 2D S = 1 pseudospin system is prone to a creation of different topological structures, which form topologically protected inhomogeneous distributions of the eight local S = 1 pseudospin order parameters. We present a short overview of localized topological structures, typical for S = 1 (pseudo)spin systems, focusing on unexpected antiphase domain walls in parent cuprates and so-called quadrupole skyrmion, which are believed to be candidates for a topological charge excitation in parent or underdoped cuprates. Puzzlingly, these unconventional structures can be characterized by an uniform distribution of the mean on-site charge, that makes these invisible for X-rays. Quasi-classical approximation and computer simulation are applied to analyze localized topological defects and evolution of the domain structures in “negative-U” model under charge order-superfluid phase transition.

Effect of Doping on the Electron Spectral Function of One-Dimensional Spin-Charge-Well-Separated Systems

The electron spectral function has been studied based on a model suitable for one-dimensional (1D) systems with spin and charge degrees of freedom well-separated. The result can permit a qualitative description of the spin-charge separated spectral feature observed in 1D cuprates. We find that the electron chemical potential shifts downward rapidly with hole doping, making the separated spectral feature harder and harder to be entirely detected in an angle-resolved photoemission (ARPES) measurement, which explains the ARPES result strangely observed in the 1/4-filled Cu–O chains in PrBa2Cu4O8. Additionally, doping evolution of the spectral function is found to show rich physics, and an essential feature is that a new coherent band gradually appears with hole doping just about the top of the lower Hubbard band, which is very similar to that observed in two-dimensional cuprates.

Doping dependence of magnetic excitations of one-dimensional cuprates as probed by resonant inelastic x-ray scattering

We study the dynamical, momentum dependent two- and four-spin response functions in doped and undoped 1D cuprates, as probed by resonant inelastic x-ray scattering, using an exact numerical diagonalization procedure. In the undoped $t-J$ system the four-spin response vanishes at $\pi$, whereas the two-spin correlator is peaked around $\pi/2$, with generally larger spectral weight. Upon doping spectra tend to soften and broaden, with a transfer of spectral weight towards higher energy. However, the total spectral weight and average peak position of either response are only weakly affected by doping up to a concentration of 1/8. Only the two-spin response at $\pi$ changes strongly, with a large reduction of spectral weight and enhancement of excitation energy. At other momenta the higher-energy, generic features of the magnetic response are robust against doping. It signals the presence of strong short-range antiferromagnetic correlations, even after doping mobile holes into the system. We expect this to hold also in higher dimensions.

Effect of electron–phonon interaction on optical response in one-dimensional cuprates

We examine the single-particle excitation and linear optical absorption spectra in the one-dimensional (1D) extended Hubbard–Holstein model. We perform dynamical density matrix renormalization group calculations with use of pseudo-site representation of phonons. We focus on the interplay among phonons and elementary excitations in 1D Mott insulators. The excitations in the Mott insulators are easily modified by the phonons. We discuss implications of the present results in light of spectroscopic measurements in 1D cuprates.

Third-order nonlinear optical spectroscopy in the two-dimensional cupratesNd2CuO4andLa2CuO4

We have measured third-order nonlinear susceptibility $({\ensuremath{\chi}}^{(3)})$ spectra of the two-dimensional (2D) cuprates ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ and ${\mathrm{Nd}}_{2}{\mathrm{CuO}}_{4}$ by third-harmonic generation. The $|{\ensuremath{\chi}}^{(3)}|$ spectra exhibit broad peaks with maximum values of $0.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\mathrm{esu}$ in ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ and $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\mathrm{esu}$ in ${\mathrm{Nd}}_{2}{\mathrm{CuO}}_{4}.$ These peaks are attributable to three-photon resonance to the charge transfer (CT) excited state. The ${\ensuremath{\chi}}^{(3)}$ phase spectrum of ${\mathrm{Nd}}_{2}{\mathrm{CuO}}_{4}$ has revealed that the two-photon resonance to the even CT state are hidden on the high-energy side of the ${\ensuremath{\chi}}^{(3)}$ peak. The difference in ${\ensuremath{\chi}}^{(3)}$ values between the 2D and 1D cuprates is discussed by considering differences in spin-charge coupling and in charge configurations between the 2D and 1D cases.

Momentum-resolved charge excitations in a prototype one-dimensional mott insulator.

We report momentum-resolved charge excitations in a one-dimensional (1D) Mott insulator studied using high resolution inelastic x-ray scattering over the entire Brillouin zone for the first time. Excitations at the insulating gap edge are found to be highly dispersive (momentum dependent) compared to excitations observed in two-dimensional Mott insulators. The observed dispersion in 1D cuprates ( SrCuO2 and Sr2CuO3) is consistent with charge excitations involving holons which is unique to spin-1/2 quantum chain systems. These results point to the potential utility of momentum-resolved inelastic x-ray scattering in providing valuable information about electronic structure of strongly correlated insulators.

Effect of four-spin interaction on magnetic excitation in ladder and 2D insulating cuprates

We investigate the effect of the cyclic four-spin interaction J cyc on the magnetic excitation spectra in two-leg ladder and two-dimensional (2D) insulating cuprates. The dynamical spin-correlation function S( q, ω) is calculated by using the numerically exact diagonalization method. For the ladder system, we find that the dispersion of spin wave along momentum q =(0, π) to (π/2,π) flattens by introducing J cyc. This feature is consistent with the experimental results of recent inelastic neutron-scattering measurement. For the 2D system, we find that the J cyc reduces effectively the magnetic interactions between nearest-neighbor (NN) Cu spins by about 20%. Moreover, it is found that the dispersion along the magnetic zone boundary from q =( π,0) to (π/2,π/2) has a finite width. This behavior can be understood by considering that the J cyc gives effectively a ferromagnetic diagonal interaction between next NN Cu spins. In order to verify the effect of J cyc, the inelastic neutron-scattering experiment at high-energy region will be highly desirable for 2D cuprates.

Systematic study of magnetic interactions in insulating cuprates

The magnetic interactions in one-dimensional, two-dimensional (2D) and ladder cuprates are evaluated systematically by using small CuO clusters. We find that the superexchange interaction J between nearest neighbor Cu spins strongly depends on CuO structure through the Madelung potential, and in 2D and ladder cuprates there is a four-spin interaction J cyc, with magnitude of 10% of J. We show that J cyc has a strong influence on the magnetic excitation in the high-energy region of 2D cuprates.

Hole-density evolution of the one-particle spectral function in doped ladders

The spectral function $A({\bf q}, \omega)$ of doped $t-J$ ladders is presented on clusters with up to $2 \times 20$ sites at zero temperature applying a recently developed technique that uses up to $\sim 6 \times 10^6$ rung-basis states. Similarities with photoemission results for the 2D cuprates are observed, such as the existence of a gap at $(\pi,0)$ near half-filling (caused by hole pair formation) and flat bands in its vicinity. These features should be observable in ARPES experiments on ladders. The main result of the paper is the nontrivial evolution of the spectral function from a narrow band at $x=0$, to a quasi-noninteracting band at $x \geq 0.5$. It was also observed that the low-energy peaks of a cluster spectra acquire finite line-widths as their energies move away from the chemical potential.

Crystal growth of pure and substituted low-dimensionality cuprates CuGeO 3, La 2CuO 4, SrCuO 2, Sr 2CuO 3 and Sr 14Cu 24O 41 by the floating zone and travelling solvent zone methods

The travelling solvent zone method has proven to be one of the most efficient techniques to grow high-quality centimetric size single crystals of compounds exhibiting non-congruent melting behavior. The method has been sucessfully applied to growth of various 1D and 2D cuprates: superconducting La 2− x Sr x CuO 4, chain cuprates SrCuO 2 and Sr 2CuO 3 and spin-ladder Sr 14Cu 24O 41. Growth conditions and crystalline perfection assessment of these crystals are presented and discussed together with data relative to growth by the floating-zone method of congruent melting spin-Peierls cuprate CuGeO 3.

Magnetic Interaction in Insulating Cuprates

We examine two-spin (2S) and cyclic four-spin (4S) magnetic interactions in insulating ladder and two-dimensional (2D) cuprates. By a comparison of eigenstates between d-p and Heisenberg models, we evaluate magnitudes of these interactions. We find that the 4S interaction is ∼10 % of nearest neighboring 2S interaction, and a diagonal 2S interaction is considerably small. The 4S interaction for a ladder cuprate is larger than that for 2D one, and plays an important role in the low-energy excitation. The Heisenberg ladder with the obtained 2S and 4S interactions reproduces very well the experimental result of the temperature dependence of the magnetic susceptibility.

Superexchange interaction in cuprates

Recent experiments have shown that the superexchange interaction $J$ in one-dimensional (1D) cuprates is larger than that in two-dimensional (2D) ones. We investigate a microscopic origin of the difference of $J$ in the 1D and 2D cuprates. The hopping matrix elements between $\mathrm{Cu}3d$ and $\mathrm{O}2p$ orbitals and between $\mathrm{O}2p$ orbitals are considerably influenced by the Madelung potential, which is a function of crystal structure, and these values in the 1D cuprates are enhanced as compared with those for the 2D ones, resulting in larger values of $J.$ The same mechanism is applied to hopping matrix elements in the ladder cuprates. The elements between $\mathrm{O}2p$ orbitals are found to be responsible for the anisotropic $J$'s along leg and rung of the ladder; i.e., ${J}_{leg}g{J}_{\mathrm{rung}}.$ We find a unique dependence of the electronic structure of cuprates on the dimensionality.

Spin and charge excitations and photoemission spectra in 1D and 2D cuprates

We study spin and charge excitations and photoemission spectra in 1D and 2D cuprates by using the numerically exact diagonalization method on small clusters of the t– J model. We identify the bands with small and large dispersion recently observed in the angle-resolved photoemission spectroscopy (ARPES) experiments of the 1D cuprate SrCuO 2 by Him et al. as those of spinon and holon with their energy scaled by t and J, respectively. The data are quantitatively analyzed by the numerical calculation based on the t– J model. The calculation is applied to the 2D cuprates. We find that in 2D, the ARPES spectrum depends strongly on the electron concentration: far away from half-filling, the spectrum is not much different from that in the Fermi liquid picture. On the other hand, near half-filling it becomes similar to that in 1D. We argue that the umklapp scattering causes the characteristic features in the spectrum near half-filling.