We consider how electron-phonon interaction influences the insulator-metal transitions driven by doping in the strongly correlated system. Using the polaronic version of the generalized tight-binding method, we investigate a multiband two-dimensional
model taking into account both Holstein and Su-Schrieffer-Heeger types of electron-lattice contributions. For adiabatic ratio of the hopping parameter and the phonon field energy, different types of band structure evolution are observed in a wide electron-phonon parameter range. We demonstrate the relationship between transition features and such properties of the system as the polaron and bipolaron crossovers, pseudogap behavior of various origin, orbital selectivity, and the redistribution of the spectral weight due to the electron-phonon interaction.
Electron-phonon coupling, diagonal in a real space formulation, leads to polaron paradigm of smoothly varying properties. However, fundamental changes, namely the singular behavior of polarons, occur if non-diagonal pairing is involved into considera
tion. The study of polaron transformations and related properties of matter is of particular interest for realistic models, since competition between diagonal and non-diagonal electron-phonon contributions in the presence of other strong interactions can result in unconventional behavior of the system. Here we consider the multiband pd-model of cuprate superconductors with electron-phonon interaction and analyze the features of the systems that are caused by the competition of diagonal and non-diagonal electron-phonon contributions in the limit of strong electron correlations. Using the polaronic version of the generalized tight-binding method, we describe the evolution of the band structure, Fermi surface, density of states at Fermi level, and phonon spectral function in the space of electron-phonon parameters ranging from weak to strong coupling strength of the adiabatic limit. On the phase diagram of polaron properties we reveal two quantum phase transitions and show how electron-phonon interaction gives rise to Fermi surface transformation (i) from hole pockets to Fermi arcs and (ii) from hole to electron type of conductivity. We also demonstrate the emergence of new states in the phonon spectral function of the polaron and discuss their origin.
The multielectron LDA+GTB approach has been developed to calculate electronic structure of strongly correlated cuprates. At low energies the effective Hamiltonian of the $t - t - t - {t_ bot } - {J^ * } - {J_ bot }$-model has been derived with parame
ters coming from the ab initio calculation for LSCO. The electronic structure of LSCO has been calculated self-consistently with the short-range antiferromagnetic order for various doping level. Two Lifshitz-type quantum phase transitions with Fermi surface topology changes have been found at dopings $x_{c1}=0.15$ and $x_{c2}=0.24$. Its effect on normal and superconducting properties has been calculated. The interatomic exchange parameter and its pressure dependence has been calculated within LDA+GTB scheme. The magnetic mechanisms of d-wave pairing induced by static and dynamical spin correlations are discussed. Simultaneous treatment of magnetic and phonon pairing results in the conclusion that both contributions are of the same order. For two layer cuprates like YBCO the interlayer hopping and exchange effects on the electronic structure and doping dependence of $T_c$ is discussed as well as the Coulomb interaction induced mechanism of pairing.
In many cases the standard perturbation approach appears to be too simple to describe precisely the angle resolved photoemission spectrum of strongly correlated electron system. In particular, to describe the momentum asymmetry observed in photoemiss
ion spectra of high-Tc cuprates a phenomenological approach based on extremely correlated Fermi-liquid model has been recently introduced. In this paper we analyze the general structure of the Green function of quasiparticles in strongly correlated electron systems and stress that it is defined not only by the self-energy of Hubbard quasiparticles but also by a strength operator. We show that the later leads to an additional odd momentum contribution to the spectral function and alone can explain the observed asymmetry. So, the asymmetry of the ARPES spectra can be a measure of the strength of electron correlations in materials.
We present ab initio results for the electron-phonon interaction of the Gamma-point phonons in the tetragonal high-temperature phase of La2CuO4. Eigenfrequencies and eigenvectors for the symmetry-allowed phonon modes are calculated with the full-pote
ntial augmented plane wave+local orbitals method using the frozen phonon approach. It is found that the Gamma-point phonons with the strongest electron-phonon interaction are the A{2u} modes with 236 cm^{-1}, 131 cm^{-1} and 476 cm^{-1}. To take effect of strong electron on-site interaction into account we use generalized tight-binding method that results in the interaction of phonons with Hubbard fermions forming quasiparticles band structure. Finally, the matrix elements of Hubbard fermion-phonon interaction and their reduction due to strong electron correlation are obtained.
We study the doping evolution of the electronic structure in the normal phase of high-$T_c$ cuprates. Electronic structure and Fermi surface of cuprates with single CuO$_2$ layer in the unit cell like La$_{2-x}$Sr$_x$CuO$_4$ have been calculated by t
he LDA+GTB method in the regime of strong electron correlations (SEC) and compared to ARPES and quantum oscillations data. We have found two critical concentrations, $x_{c1}$ and $x_{c2}$, where the Fermi surface topology changes. Following I.M. Lifshitz ideas of the quantum phase transitions (QPT) of the 2.5-order we discuss the concentration dependence of the low temperature thermodynamics. The behavior of the electronic specific heat $delta(C/T) sim (x - x_c)^{1/2}$ is similar to the Loram and Cooper experimental data in the vicinity of $x_{c1} approx 0.15$.
Several experimental and theoretical studies indicate the existence of a critical point separating the underdoped and overdoped regions of the high-T_c cuprates phase diagram. There are at least two distinct proposals on the critical concentration an
d its physical origin. First one is associated with the pseudogap formation for p<p*, with p~0.2. Another one relies on the Hall effect measurements and suggests that the critical point and the quantum phase transition (QPT) take place at optimal doping, p_{opt}~0.16. Here we have performed a precise density of states calculation and found that there are two QPTs and the corresponding critical concentrations associated with the change of the Fermi surface topology upon doping.
Strong electron correlations are responsible both for the insulator ground state of undoped La$_2$CuO$_4$ and strong antiferromagnetic coupling $J$ between neighbouring spins. We consider magnetic mechanism of superconducting pairing in the effective
low energy $t - t - t - J^*$ model with all parameters calculated {it ab initio}. Interaction of strongly correlated electrons with different phonon modes is also incorporated. In a BCS type theory the $d_{x^2 - y^2}$ gap is given by a sum of magnetic and phonon contributions. The phonon coupling parameter $lambda = f(x)G$, where $G$ is a combination of bare electron-phonon couplings for all modes and the function $f$ depends on the hole concentration $x$ due to strong electron correlations. The main contribution to the only fitting parameter $G$ is determined by a competition of the breathing and buckling modes. Fitting the parameter $G$ from the isotope effect we obtain that magnetic and phonon contributions to the critical temperature $T_c $ work together and are of the same order of magnitude.
