The response of the worldwide scientific community to the discovery in 2008 of superconductivity at T c = 26 K in the Fe-based compound LaFeAsO1−x F x has been very enthusiastic. In short order, ot...

The puzzle of high temperature superconductivity in layered iron pnictides and chalcogenides

We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is tuned to a critical value are characterized by a dynamic exponent $z$ related to the energy and length scales $\Delta$ and $\xi$. Simple arguments based on an expansion to first order in the effective interaction allow to define an upper-critical dimension $D_{C}=4$ (where $D=d+z$ and $d$ is the spatial dimension) below which mean-field description is no longer valid. We emphasize the role of pertubative renormalization group (RG) approaches and self-consistent renormalized spin fluctuation (SCR-SF) theories to understand the quantum-classical crossover in the vicinity of the quantum critical point with generalization to the Kondo effect in heavy-fermion systems. Finally we quote some recent inelastic neutron scattering experiments performed on heavy-fermions which lead to unusual scaling law in $\omega /T$ for the dynamical spin susceptibility revealing critical local modes beyond the itinerant magnetism scheme and mention new attempts to describe this local quantum critical point.

https://arxiv.org/pdf/cond-mat/0102119.pdf

Quantum Phase Transitions

In the early 1970s, Wilson developed the concept of a fully nonperturbative renormalization group transformation. When applied to the Kondo problem, this numerical renormalization group (NRG) method gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG method was later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method, including some guidelines for calculating physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi-liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean-field theory.

http://www.physics.udel.edu/~bnikolic/QTTG/NOTES/NRG/BULLA=numerical_renormalization_group_method_for_quantum_impurity_systems.pdf

Numerical renormalization group method for quantum impurity systems

The recently discovered Fe-pnictide and chalcogenide superconductors display low-temperature properties suggesting superconducting gap structures which appear to vary substantially from family to family, and even within families as a function of doping or pressure. We propose that this apparent nonuniversality can actually be understood by considering the predictions of spin fluctuation theory and accounting for the peculiar electronic structure of these systems, coupled with the likely 'sign-changing s-wave' (s?) symmetry. We review theoretical aspects, materials properties and experimental evidence relevant to this suggestion, and discuss which further measurements would be useful to settle these issues.Satisfactoriness has to be measured by a multitude of standards, of which some, for aught we know, may fail in any given case; and what is more satisfactory than any alternative in sight, may to the end be a sum of pluses and minuses, concerning which we can only trust that by ulterior corrections and improvements a maximum of the one and a minimum of the other may some day be approached.??????????????????????William James, Meaning of Truth

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Gap symmetry and structure of Fe-based superconductors

We review studies of the electromagnetic response of various classes of correlated electron materials including transition metal oxides, organic and molecular conductors, intermetallic compounds with $d$- and $f$-electrons as well as magnetic semiconductors. Optical inquiry into correlations in all these diverse systems is enabled by experimental access to the fundamental characteristics of an ensemble of electrons including their self-energy and kinetic energy. Steady-state spectroscopy carried out over a broad range of frequencies from microwaves to UV light and fast optics time-resolved techniques provide complimentary prospectives on correlations. Because the theoretical understanding of strong correlations is still evolving, the review is focused on the analysis of the universal trends that are emerging out of a large body of experimental data augmented where possible with insights from numerical studies.

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Electrodynamics of correlated electron materials

We generalize the dynamical-mean field (DMFT) approximation by including into the DMFT equations some length scale $\ensuremath{\xi}$ via a momentum dependent external self-energy ${\ensuremath{\Sigma}}_{\mathbf{k}}$. This external self-energy describes nonlocal dynamical correlations induced by the short-ranged collective spin density wave--like antiferromagnetic spin (or the charge density wave--like charge) fluctuations. At high enough temperatures these fluctuations can be viewed as a quenched Gaussian random field with a finite correlation length. This generalized $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with the nearest and the next nearest neighbor hopping. The effective single impurity problem in this generalized $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ is solved by the numerical renormalization group. Both types of the strongly correlated metals, namely: (i) The doped Mott insulator and (ii) the case of the bandwidth $W\ensuremath{\lesssim}U$ ($U$---value of the local Coulomb interaction) are considered. The densities of states, the spectral functions, and the angle resolved photoemission spectra calculated within the $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ show a pseudogap formation near the Fermi level of the quasiparticle band.

/pdf/pseudogaps-in-strongly-correlated-metals-a-generalized-3xy6oekg0i.pdf

Pseudogaps in strongly correlated metals: A generalized dynamical mean-field theory approach

We have performed ab initio LDA calculations of the electronic structure of newly discovered prototype high-temperature superconductors AFe2As2 (A = Ba, Sr) and compared it with the previously calculated electronic spectra of ReOFeAs (Re = La, Ce, Pr, Nd, Sm). In all cases, we obtain almost identical densities of states in a rather wide energy interval (up to 1 eV) around the Fermi level. Energy dispersions are also very similar and almost two dimensional in this energy interval, leading to the same basic (minimal) model of the electronic spectra, determined mainly by Fe d orbitals of the FeAs layers. The other constituents, such as A ions or rare-earth Re (or oxygen states) are more or less irrelevant for superconductivity. LDA Fermi surfaces for AFe2As2 are also very similar to that of ReOFeAs. This makes the more simple AFe2As2 a generic system to study the high-temperature superconductivity in FeAs-layered compounds.

Electronic structure of prototype AFe2As2 and ReOFeAs high-temperature superconductors: A comparison

This review discusses the generalization of dynamical mean-field theory (DMFT) for strongly correlated electronic systems to include additional interactions necessary for the correct description of physical effects in such systems. Specifically, the additional interactions include: (1) the interaction of electrons with antiferromagnetic (or charge) order-parameter fluctuations in high-temperature superconductors leading to the formation of a pseudogap state; (2) scattering on static disorder and its role in the general picture of the Anderson-Hubbard metal-insulator transition, and (3) electron-phonon interaction and the features of electronic spectra in strongly correlated systems. The proposed DMFT+ approach incorporates the above interactions by introducing into the general DMFT model an additional (generally momentum-dependent) self-energy which is calculated in a self-consistent way without violating the general structure of the DMFT iteration cycle. The paper formulates a general calculational scheme for both one-particle (spectral functions and densities of states) and two-particle (optical conductivity) properties. The problem of pseudogap formation is examined, including Fermi arc formation and partial destruction of the Fermi surface, as are the metal-insulator transition in the disordered Anderson-Hubbard model, and the general picture of kink formation in the electronic spectra of strongly correlated systems. A generalization of the DMFT+ approach to realistic materials with strong electron-electron correlations is presented based on the LDA+DMFT method. The general model of the LDA+DMFT method is reviewed, as are some of its applications to real systems. The generalized LDA+DMFT+ approach is employed to calculate pseudogap states in electron- and hole-doped HTSC cuprates. Comparisons with angle-resolved photoemission spectroscopy (ARPES) results are presented.

https://iopscience.iop.org/article/10.3367/UFNe.0182.201204a.0345/pdf

Generalized dynamical mean-field theory in the physics of strongly correlated systems

We present results of it ab initio LDA calculations of electronic structure of "next generation" layered ironpnictide High-Tc superconductor LiFeAs (Tc=18K). Obtained electronic structure of LiFeAs is very similar to recently studied ReOFeAs (Re=La,Ce,Pr,Nd,Sm) and AFe2As2 (A=Ba,Sr) compounds. Namely close to the Fermi level its electronic properties are also determined ma inly by Fe 3d-orbitals of FeAs4 two-dimensional layers. Band dispersions of LiFeAs are very similar to the LaOFeAs and BaFe2As2 systems as well as the shape of the Fe-3d density o f states and Fermi surface.

Electronic Structure of New LiFeAs High-Tc Superconductor

We present LDA band structure of novel hole doped high temperature superconductors (Tc ∼ 30 K) KxFe2Se2 and CsxFe2Se2 and compare it with previously studied electronic structure of isostructural FeAs superconductor BaFe2As2 (Ba122). We show that stoichiometric KFe2Se2 and CsFe2Se2 have rather different Fermi surfaces as compared with Ba122. However at about 60% of hole doping Fermi surfaces of novel materials closely resemble those of Ba122. In between these dopings we observe a number of topological Fermi surface transitions near the Γ point in the Brillouin zone. Superconducting transition temperature Tc of new systems is apparently governed by the value of the total density of states (DOS) at the Fermi level.

Mikhail V. Sadovskii

Papers

Pseudogaps in strongly correlated metals: A generalized dynamical mean-field theory approach

Electronic structure of prototype AFe2As2 and ReOFeAs high-temperature superconductors: A comparison

Generalized dynamical mean-field theory in the physics of strongly correlated systems

Electronic Structure of New LiFeAs High-Tc Superconductor

Electronic structure, topological phase transitions and superconductivity in (K, Cs)xFe2Se2