On temperature versus doping phase diagram of high critiical temperature superconductors

The attempt to describe the bell-shape dependence of the critical temperature of high-$T_{c}$ superconductors on charge carriers density is made. Its linear increase in the region of small densities (underdoped regime) is proposed to explain by the role of the order parameter phase 2D fluctuations which become less at this density growth. The critical temperature suppression in the region of large carrier densities (overdoped regime) is connected with the appearance (because of doping) of the essential damping of long-wave bosons which in the frame of the model proposed define the mechanism of indirect inter-fermion attraction.Comment: 15 pages, 3 figures, EMTE

Time-dependent density-functional theory for electronic excitations in materials: basics and perspectives

Time-dependent density-functional theory (TDDFT) is widely used to describe electronic excitations in complex finite systems with large numbers of atoms, such as biomolecules and nanocrystals. The first part of this paper will give a simple and pedagogical explanation, using a two-level system, which shows how the basic TDDFT formalism for excitation energies works. There is currently an intense effort underway to develop TDDFT methodologies for the charge and spin dynamics in extended systems, to calculate optical properties of bulk and nanostructured materials, and to study transport through molecular junctions. The second part of this paper highlights some challenges and recent advances of TDDFT in these areas. Two examples are discussed: excitonic effects in insulators and intersubband plasmon excitations in doped semiconductor quantum wells.Comment: 15 pages, 2 figures, International Conference on Materials Discovery and Databases: Materials Informatics and DF

Inhomogeneous spectral moment sum rules for the retarded Green function and self-energy of strongly correlated electrons or ultracold fermionic atoms in optical lattices

Spectral moment sum rules are presented for the inhomogeneous many-body problem described by the fermionic Falicov-Kimball or Hubbard models. These local sum rules allow for arbitrary hoppings, site energies, and interactions. They can be employed to quantify the accuracy of numerical solutions to the inhomogeneous many-body problem like strongly correlated multilayered devices, ultracold atoms in an optical lattice with a trap potential, strongly correlated systems that are disordered, or systems with nontrivial spatial ordering like a charge density wave or a spin density wave. We also show how the spectral moment sum rules determine the asymptotic behavior of the Green function, self-energy, and dynamical mean field, when applied to the dynamical mean-field theory solution of the many body problem. In particular, we illustrate in detail how one can dramatically reduce the number of Matsubara frequencies needed to solve the Falicov-Kimball model, while still retaining high precision, and we sketch how one can incorporate these results into Hirsch-Fye quantum Monte Carlo solvers for the Hubbard (or more complicated) models. Since the solution of inhomogeneous problems is significantly more time consuming than periodic systems, efficient use of these sum rules can provide a dramatic speed up in the computational time required to solve the many-body problem. We also discuss how these sum rules behave in nonequilibrium situations as well, where the Hamiltonian has explicit time dependence due to a driving field or due to the time-dependent change of a parameter like the interaction strength or the origin of the trap potential.Comment: (28 pages, 6 figures, ReVTeX) Paper updated to correct equations 11, 24, and 2

Non-equilibrium properties of the S=1/2 Heisenberg model in a time-dependent magnetic field

The time-dependent behavior of the Heisenberg model in contact with a phonon heat bath and in an external time-dependent magnetic field is studied by means of a path integral approach. The action of the phonon heat bath is taken into account up to the second order in the coupling to the heath bath. It is shown that there is a minimal value of the magnetic field below which the average magnetization of the system does not relax to equilibrium when the external magnetic field is flipped. This result is in qualitative agreement with the mean field results obtained within $\phi^{4}$-theory.Comment: To be published in Physica

Spectral moment sum rules for strongly correlated electrons in time-dependent electric fields

We derive exact operator average expressions for the first two spectral moments of nonequilibrium Green's functions for the Falicov-Kimball model and the Hubbard model in the presence of a spatially uniform, time-dependent electric field. The moments are similar to the well-known moments in equilibrium, but we extend those results to systems in arbitrary time-dependent electric fields. Moment sum rules can be employed to estimate the accuracy of numerical calculations; we compare our theoretical results to numerical calculations for the nonequilibrium dynamical mean-field theory solution of the Falicov-Kimball model at half-filling.Comment: (16 pages, submitted to Phys. Rev. B

Fluctuating order parameter in doped cuprate superconductors

We discuss static fluctuations of the d-wave superconducting order parameter $\Delta$ in CuO$_2$ planes, due to quasiparticle scattering by charged dopants. The analysis of two-particle anomalous Green functions at $T = 0$ permits to estimate the mean-square fluctuation $\delta^2 = - ^2$, averaged in random dopant configurations, to the lowest order in doping level $c$. Since $\Delta$ is found to saturate with growing doping level while $\delta$ remains to grow, this can explain the collapse of $T_c$ at overdoping. Also we consider the spatial correlations $$ for order parameter in different points of the plane.Comment: RevTex4, 3 pages, to be published in Proceedings of New3SC-4 International Conference, San Diego, California, January 15-21, 200

Superconducting properties of a boson-exchange model of doped graphene

We study the superconducting properties of a doped one-layer graphene by using a model in which the interparticle attraction is caused by a boson (phonon-like) excitations. We study the dependencies of the superconducting gap D and the mean-field critical temperature TcMF on the carrier density, attraction strength and the characteristic (Debye) bosonic frequency. In addition, we study the temperature-carrier density phase diagram of the model by taking into account the thermal fluctuations of the order parameter. We show that the fluctuations result in a significant suppression of TcMF, such that the real (Berezinskii– Kosterlitz–Thouless) critical temperature Tc is much lower than TcMF. The region Tc < T < TcMF is characterized by a finite density of states at the Fermi level (the pseudogap phase). We show that the width of the temperature interval of the pseudogap phase strongly depends on the model parameters—carrier concentration, attraction amplitude, and boson frequency