We systematically examine the asymmetry of the electronic states in the hole- and electron-doped cuprates by using a $t\text{\ensuremath{-}}J$ model with the second-neighbor hopping ${t}^{\ensuremath{'}}$ and third one ${t}^{\ensuremath{''}}$ (the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}{t}^{\ensuremath{''}}\text{\ensuremath{-}}J$ model). Numerically exact diagonalization method is employed for a 20-site square lattice. We impose twisted boundary conditions (BC) instead of standard periodic BC. For static and dynamical correlation functions, averaging procedure over the twisted BC is used to reduce the finite-size effect. We find that antiferromagnetic spin correlation remains strong in electron doping in contrast to the case of hole doping, being similar to the case of the periodic BC. This leads to a remarkable electron-hole asymmetry in the dynamical spin structure factor and two-magnon Raman scattering. By changing the twist, the single-particle spectral function is obtained for all momenta in the Brillouin zone. Examining the spectral function in detail, we find a gap opening at around the $\mathbf{k}=(\ensuremath{\pi},0)$ region for 10% doping of holes (the carrier concentration
x=0.1), leading to a Fermi arc that is consistent with experiments. In electron doping, however, a gap opens at around $\mathbf{k}=(\ensuremath{\pi}∕2,\ensuremath{\pi}∕2)$ and persists up to
x=0.2, being correlated with the strength of the antiferromagnetic correlation. We find that the magnitude of the gaps is sensitive to ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$. A pseudogap is also seen in the optical conductivity for electron doping, and its magnitude is found to be the same as that in the spectral function. We compare calculated quantities with corresponding experimental data, and discuss similarities and differences between them as well as their implications.
The influence of Zn and Ni impurities on the normal-state pseudogap of underdoped
high-Tc cuprate superconductors is studied using exact diagonalization of effective $t\ensuremath{-}J\text{-like}$ Hamiltonians describing low energy electronic excitations of the
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
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-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
CuO2 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-axis infrared conductivity data of Zn and Ni substituted (Sm,Nd)${\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ crystals.
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
2×2 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→∞. 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≳8.
We investigate the electronic states in the antiferromagnetic (AF) phase of electron-doped cuprates by using numerically exact diagonalization technique for a $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}\ensuremath{-}J$ model. When AF correlation develops with decreasing temperature, a gaplike behavior emerges in the optical conductivity. Simultaneously, the coherent motion of carriers due to the same sublattice hoppings is enhanced. We propose that the phase is characterized as an AF state with small Fermi surface around the momentum $\mathbf{k}=(\ensuremath{\pi},0)$ and $(0,\ensuremath{\pi}).$ This is a remarkable contrast to the behavior of hole-doped cuprates.
An exact diagonalization technique on small lattices is used to calculate the single-particle spectral function A(k,\ensuremath{\omega}) for one- and three-band Hubbard models at various parameter values and doping rates, thereby examining the low-energy electronic structure (or in-gap state) of the doped
CuO2 plane in high-
Tc superconducting cuprates. It is illustrated that, by carrier doping, the dispersive state of the charge excitation gap at half filling undergoes a strongly momentum-dependent spectral-weight transfer, and evolves into the new state with a free-electron-like dispersion that forms the in-gap state characteristic of a large Fermi surface consistent with Luttinger's sum rule. The quasiparticlelike band narrowing observed is shown to depend sensitively on the parameter values and doping rate.
Quantum Monte Carlo (QMC) and maximum-entropy techniques are used to study the spectral function $A(\mathbf{p},\ensuremath{\omega})$ of the one-band Hubbard model with strong coupling including a next-nearest-neighbor electronic hopping with amplitude ${t}^{\ensuremath{'}}/t=\ensuremath{-}0.35$. These values of parameters are chosen to improve the comparison of the Hubbard model with angle-resolved photoemission (ARPES) data for
Sr2CuO2Cl2. A narrow quasiparticle (qp) band is observed in the QMC analysis at the temperature of the simulation
T=t/3, both at and away from half-filling. Such a narrow band produces a large accumulation of weight in the density of states at the top of the valence band. As the electronic density
〈n〉 decreases further away from half-filling, the chemical potential travels through this energy window with a large number of states, and by $〈n〉\ensuremath{\sim}0.70$ it has crossed it entirely. The region near momentum $(0,\ensuremath{\pi})$ and $(\ensuremath{\pi},0)$ in the spectral function is more sensitive to doping than momenta along the diagonal from
(0,0) to $(\ensuremath{\pi},\ensuremath{\pi})$. The evolution with hole density of the quasiparticle dispersion contains some of the features observed in recent ARPES data in the underdoped regime. For sufficiently large hole densities the ``flat'' bands at $(\ensuremath{\pi},0)$ cross the Fermi energy, a prediction that could be tested with ARPES techniques applied to overdoped cuprates. The population of the qp band introduces a hidden density in the system which produces interesting consequences when the quasiparticles are assumed to interact through antiferromagnetic fluctuations and studied with the BCS gap-equation formalism. In particular, a region of extended
s-wave character is found to compete with the
d wave in the overdoped regime, i.e., when the chemical potential has almost entirely crossed the qp band as
〈n〉 is reduced. The present study also shows that previous ``real-space'' pairing theories for the cuprates, such as the antiferromagnetic Van Hove scenario, originally constructed based on information gathered at half-filling, do not change their predictions if hole dispersions resembling noninteracting electrons with renormalized parameters are used.