The natural-heterostructure concept realized in delafossites highlights these layered oxides. While metallic, band- or Mott-insulating character may be associated with individual layers, inter-layer coupling still plays a decisive role. We review the correlated electronic structure of PdCoO$_2$, PdCrO$_2$ and AgCrO$_2$, showing that layer-entangled electronic states can deviate from standard classifications of interacting systems. This finding opens up possibilities for materials design in a subtle Mott-critical regime. Manipulated Hidden-Mott physics, correlation-induced semimetallicity, or Dirac/flat-band dispersions in a Mott background are emerging features. Together with achievements in the experimental preparation, this inaugurates an exciting research field in the arena of correlated materials.
Delafossites represent natural heterostructures which can host rather different electronic characteristics in their constituting layers. The design of novel heterostructure architectures highlighting the competition between such varying layer properties is promising from the viewpoint of basic research as well as for future technological applications. By means of the combination of density functional theory and dynamical mean-field theory, we here unveil the formation of highly correlated electron states in delafossite heterostructures build from metallic PdCrO$_2$ and insulating AgCrO$_2$. Du…
There has been a long-standing debate on the coexistence between itinerant electrons and localized spins in the PdCrO$_2$ delafossite. By means of the charge self-consistent combination of density functional theory and dynamical mean-field theory, it is corroborated that despite overall remarkable metallic response, the CrO$_2$ layers are indeed Mott insulating as suggested by previous experimental work. The resulting ${\bf k}$-resolved spectral function in the paramagnetic phase is in excellent agreement with available photoemission data. Subtle coupling between the itinerant and Mott-localiz…
Although they were first synthesized in chemistry laboratories nearly fifty years ago, the physical properties of the metals PdCoO2, PtCoO2 and PdCrO2 have only more recently been studied in detail. The delafossite structure contains triangular co-ordinated atomic layers, and electrical transport in the delafossite metals is strongly two-dimensional. Their most notable feature is their in-plane conductivity, which is amazingly high for oxide metals. At room temperature, the conductivity of non-magnetic PdCoO2 and PtCoO2 is higher per carrier than those of any alkali metal and even the most con…
Theory of doped Mott insulators is revisited in the light of recent understanding on the singular self-energy structure of the single-particle Green's function. The unique pole structure in the self-energy induces the high-temperature superconductivity in the anomalous part, while it generates Mott gap and pseudogap in the normal part. Here, we elucidate that fractionalization of electrons, which is exactly hold in the Mott insulator in the atomic limit, more generally produces the emergent Mott-gap fermion and dark (hidden) fermions. It does not require any spontaneous symmetry breaking. The …
Fe3-xGeTe2 is a layered magnetic van der Waals material of interest for both fundamental and applied research. Despite the observation of intriguing physical properties, open questions exist even on the basic features related to magnetism: is it a simple ferromagnet or are there antiferromagnetic regimes and are the moments local or itinerant. Here, we demonstrate that antiferromagnetic spin fluctuations coexist with the ferromagnetism through comprehensive elastic and inelastic neutron scattering and thermodynamic measurements. Our realistic dynamical mean-field theory calculations reveal tha…
We use scanning tunneling microscopy to study the temperature evolution of electronic structure in Ca3Cu2O4Cl2 parent Mott insulator of cuprates. We find that the upper Hubbard band moves towards the Fermi energy with increasing temperature, while the charge transfer band remains basically unchanged. This leads to a reduction of the charge transfer gap size at high temperatures, and the rate of reduction is much faster than that of conventional semiconductors. Across the Neel temperature for antiferromagnetic order, there is no sudden change in the electronic structure. These results shed new …
We show how the general and basic asymmetry between two fundamental degrees of freedom present in strongly correlated oxides, spin and orbital, has very profound repercussions on the elementary spin and orbital excitations. Whereas the magnons remain largely unaffected, orbitons become inherently coupled with spin fluctuations in spin-orbital models with antiferromagnetic and ferroorbital ordered ground states. The composite orbiton-magnon modes that emerge fractionalize again in one dimension, giving rise to spin-orbital separation in the peculiar regime where spinons are faster than orbitons…
We propose an energy-scale correspondence between the Mott physics and the Kondo lattice physics and construct a tentative phase diagram of their correlated electrons with two characteristic energy scales $ω^*$ and $Ω$ marking the upper boundary of a low-energy regime with well-developed long-range coherence and the lower boundary of localized spectral weight in the energy space, respectively. In between, there exists a crossover region with emergent but damped quasiparticle excitations. We argue that the presence of two separate energy scales is a generic property of correlated electrons on a…
Moiré super-potentials in two-dimensional materials allow unprecedented control of the ratio between kinetic and interaction energy. By this, they pave the way to study a wide variety of strongly correlated physics under a new light. In particular, the transition metal dichalcogenides (TMDs) are promising candidate "quantum simulators" of the Hubbard model on a triangular lattice. Indeed, Mott and generalized Wigner crystals have been observed in such devices. Here we theoretically propose to extend this model into the multi-orbital regime by focusing on electron doped systems at filling highe…
Nonequilibrium states induced by an applied bias voltage (V) and the corresponding current-voltage characteristics of one-dimensional models describing band and Mott insulators are investigated theoretically by using nonequilibrium Green's functions. We attach the models to metallic electrodes whose effects are incorporated into the self-energy. Modulation of the electron density and the scalar potential coming from the additional long-range interaction are calculated self-consistently within the Hartree approximation. For both models of band and Mott insulators with length L_C, the bias volta…
We consider the finite temperature metal-insulator transition in the half filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. A new method for calculating the Dynamical Mean Field Theory fixpoint surface in the phase diagram is presented and shown to be free from the convergence problems of standard forward recursion. The fixpoint equation is then analyzed using dynamical systems methods. On the fixpoint surface the eigenspectra of its Jacobian is used to characterize the hysteresis boundaries of the first order transition line and its second order critical end point. …
In a recent X-ray absorption study in boron doped diamond, Nakamura et al. have seen a well isolated narrow boron impurity band in non-superconducting samples and an additional narrow band at the chemical potential in a superconducting sample. We interpret the beautiful spectra as evidence for upper Hubbard band of a Mott insulating impurity band and an additional metallic `mid-gap band' of a conducting `self-doped' Mott insulator. This supports the basic framework of a recent theory of the present author of strongly correlated impurity band superconductivity (SCIBS) in a template of a wide-ga…
Special solutions of the Hartree-Fock (HF) problem for Coulomb interacting electrons, being described by a simple model of the Cu-O planes in La2CuO4, are presented. One of the mean field states obtained, is able to predict some of the basic properties of this material, such as its insulator character and the antiferromagnetic order. The natural appearance of pseudogaps in some states of this compound is also indicated by another of the HF states obtained. These surprising results follow after eliminating spin and crystal symmetry restrictions which are usually imposed on the single particle H…
This is extended version of a previously submitted paper, in which special solutions of the Hartree-Fock (HF) problem for Coulomb interacting electrons, being described by a simple model of the Cu-O planes in La2CuO4, are presented. One of the mean field states obtained, is able to predict some of the basic properties of this material, such as its insulator character and the antiferromagnetic order. The natural appearance of pseudogaps in some states of this compound is also indicated by another of the HF states obtained. These surprising results follow after eliminating spin and crystal symme…
We consider the orbitally degenerate 3-band Hubbard model with on-site interactions which favor low spin and low orbital angular momentum using standard second order perturbation theory in the large Hubbard-U limit. At even integer filling this model is a Mott insulator with a non-degenerate ground state that allows for a simple description of particle-hole excitations as well as gapped spin and orbital modes. We find that the Mott gap is generally indirect and that the single particle spectrum at low doping reappears close to even filling but rescaled by a factor 2/3 or 1/3. The model capture…
We review the basic ideas of the dynamical mean field theory (DMFT) and some of the insights into the electronic structure of strongly correlated electrons obtained by this method in the context of model Hamiltonians. We then discuss the perspectives for carrying out more realistic DMFT studies of strongly correlated electron systems and we compare it with existent methods, LDA and LDA+U. We stress the existence of new functionals for electronic structure calculations which allow us to treat situations where the single--particle description breaks down such as the vicinity of the Mott transiti…
We review the interplay of frustration and strong electronic correlations in quasi-two-dimensional organic charge transfer salts, such as k-(BEDT-TTF)_2X and Et_nMe_{4-n}Pn[Pd(dmit)2]2. These two forces drive a range of exotic phases including spin liquids, valence bond crystals, pseudogapped metals, and unconventional superconductivity. Of particular interest is that in several materials there is a direct transition as a function of pressure from a spin liquid Mott insulating state to a superconducting state. Experiments on these materials raise a number of profound questions about the quantu…
Various topics at the interface between condensed matter physics and the physics of ultra-cold fermionic atoms in optical lattices are discussed. The lectures start with basic considerations on energy scales, and on the regimes in which a description by an effective Hubbard model is valid. Qualitative ideas about the Mott transition are then presented, both for bosons and fermions, as well as mean-field theories of this phenomenon. Antiferromagnetism of the fermionic Hubbard model at half-filling is briefly reviewed. The possibility that interaction effects facilitate adiabatic cooling is disc…
Exploring the transport properties of different materials brings new avenue for basic understanding of emergent phenomena and practical applications in many different fields. Here, we report a program named as TRACK (TRAnsport properties for Correlated materials using Kubo formalism) which is written in Python 3 for calculating temperature dependent electrical conductivity, electronic part of thermal conductivity, Seebeck coefficient and Lorenz number. In this code, Kubo linear-response formalism is utilized for computing these parameters using both interacting and non-interacting electronic s…
The nonlinear transport properties of the Mott insulator are discussed with focus on the many-body Landau-Zener mechanism. After reviewing basic concepts such as the non-adiabatic geometric phase and the Schwinger mechanism, we study the decay of the insulating groundstate in strong electric fields using the time-dependent density matrix renormalization group. A short comment on the proposed mapping to the quantum walk model is added before discussing the relevance of the theory to experimental results. This article is a draft of a book chapter of the book entitled "Quantum and Semi-classical …
We propose that the electrons responsible for superconductivity in Li2Pd3B come from the palladium 4d-electrons. So, its electronic properties are likely to be dominated by strong electronic correlations. The basic unit in this material are Pd$_6$B octahedra which share vertices to form a 3-dimensional network. Due to the highly distorted nature of the Pd$_6$B octahedron, one far stretched Pd atom per octahedra becomes almost inactive for electronic conduction. Thus, the material escapes the fate of becoming a half- filled insulating Mott antiferromagnet by hiding extra charges at these inacti…
These are introductory lectures to some aspects of the physics of strongly correlated electron systems. I first explain the main reasons for strong correlations in several classes of materials. The basic principles of dynamical mean-field theory (DMFT) are then briefly reviewed. I emphasize the formal analogies with classical mean-field theory and density functional theory, through the construction of free-energy functionals of a local observable. I review the application of DMFT to the Mott transition, and compare to recent spectroscopy and transport experiments. The key role of the quasipart…
LDA+DMFT is a novel computational technique for ab initio investigations of real materials with strongly correlated electrons, such as transition metals and their oxides. It combines the strength of conventional band structure theory in the local density approximation (LDA) with a modern many-body approach, the dynamical mean-field theory (DMFT). In the last few years LDA+DMFT has proved to be a powerful tool for the realistic modeling of strongly correlated electronic systems. In this paper the basic ideas and the set-up of the LDA+DMFT(X) approach, where X is the method used to solve the DMF…
Many remarkable properties of quantum materials emerge from states with intricate coupling between the charge, spin and orbital degrees of freedom. Ultrafast photo-excitations of these materials hold great promise for understanding and controlling the properties of these states. Here we introduce time-resolved resonant inelastic X-ray scattering (trRIXS) as a means of measuring charge, spin and orbital excitations out of equilibrium. These excitations encode the correlations and interactions that determine the detailed properties of the states generated. After outlining the basic principles an…
Single-site and cluster dynamical mean-field methods are used to estimate the response of a doped Mott insulator to a charged impurity. The effect of correlations on the Thomas-Fermi screening properties is determined. The charge density, the on-site and near-neighbor spin-spin correlations in the vicinity of the impurity are compared to those far from it. The theory is used to address the question of the effect of the density perturbation induced by the muon charge on the local response functions of a high-temperature superconductor. For reasonable values of the background dielectric constant…
The concept of electronic correlations plays an important role in modern condensed matter physics. It refers to interaction effects which cannot be explained within a static mean-field picture as provided by Hartree-Fock theory. Electronic correlations can have a very strong influence on the properties of materials. For example, they may turn a metal into an insulator (Mott-Hubbard metal-insulator transition). In these lecture notes I (i) introduce basic notions of the physics of correlated electronic systems, (ii) discuss the construction of mean-field theories by taking the limit of high lat…
Electronic phase behavior in correlated-electron systems is a fundamental problem of condensed matter physics. We argue here that the change in the phase behavior near the surface and interface, i.e., {\em electronic reconstruction}, is the fundamental issue of the correlated-electron surface or interface science. Beyond its importance to basic science, understanding of this behavior is crucial for potential devices exploiting the novel properties of the correlated systems. % We present a general overview of the field, and then illustrate the general concepts by theoretical studies of the mode…
The 3$d$-5$d$ based double perovskites offer an ideal playground to study the interplay between electron correlation ($U$) and spin-orbit coupling (SOC) effect, showing exotic physics. The Sr$_2$FeIrO$_6$ is an interesting member in this family with ionic distribution of Fe$^{3+}$ (3$d^5$) and Ir$^{5+}$ (5$d^4$) where the later is believed to be nonmagnetic under the picture of strong SOC. Here, we report detailed investigation of structural, magnetic and electronic transport properties along with electronic structure calculations in (Sr$_{1-x}$Ca$_x$)$_2$FeIrO$_6$ series with $x$ from 0 to 1.…
