We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

BACKGROUND Materials by design is an appealing idea that is very hard to realize in practice. Combining the best of different ingredients in one ultimate material is a task for which we currently have no general solution. However, we do have some successful examples to draw upon: Composite materials and III-V heterostructures have revolutionized many aspects of our lives. Still, we need a general strategy to solve the problem of mixing and matching crystals with different properties, creating combinations with predetermined attributes and functionalities. ADVANCES Two-dimensional (2D) materials offer a platform that allows creation of heterostructures with a variety of properties. One-atom-thick crystals now comprise a large family of these materials, collectively covering a very broad range of properties. The first material to be included was graphene, a zero-overlap semimetal. The family of 2D crystals has grown to includes metals (e.g., NbSe 2 ), semiconductors (e.g., MoS 2 ), and insulators [e.g., hexagonal boron nitride (hBN)]. Many of these materials are stable at ambient conditions, and we have come up with strategies for handling those that are not. Surprisingly, the properties of such 2D materials are often very different from those of their 3D counterparts. Furthermore, even the study of familiar phenomena (like superconductivity or ferromagnetism) in the 2D case, where there is no long-range order, raises many thought-provoking questions. A plethora of opportunities appear when we start to combine several 2D crystals in one vertical stack. Held together by van der Waals forces (the same forces that hold layered materials together), such heterostructures allow a far greater number of combinations than any traditional growth method. As the family of 2D crystals is expanding day by day, so too is the complexity of the heterostructures that could be created with atomic precision. When stacking different crystals together, the synergetic effects become very important. In the first-order approximation, charge redistribution might occur between the neighboring (and even more distant) crystals in the stack. Neighboring crystals can also induce structural changes in each other. Furthermore, such changes can be controlled by adjusting the relative orientation between the individual elements. Such heterostructures have already led to the observation of numerous exciting physical phenomena. Thus, spectrum reconstruction in graphene interacting with hBN allowed several groups to study the Hofstadter butterfly effect and topological currents in such a system. The possibility of positioning crystals in very close (but controlled) proximity to one another allows for the study of tunneling and drag effects. The use of semiconducting monolayers leads to the creation of optically active heterostructures. The extended range of functionalities of such heterostructures yields a range of possible applications. Now the highest-mobility graphene transistors are achieved by encapsulating graphene with hBN. Photovoltaic and light-emitting devices have been demonstrated by combining optically active semiconducting layers and graphene as transparent electrodes. OUTLOOK Currently, most 2D heterostructures are composed by direct stacking of individual monolayer flakes of different materials. Although this method allows ultimate flexibility, it is slow and cumbersome. Thus, techniques involving transfer of large-area crystals grown by chemical vapor deposition (CVD), direct growth of heterostructures by CVD or physical epitaxy, or one-step growth in solution are being developed. Currently, we are at the same level as we were with graphene 10 years ago: plenty of interesting science and unclear prospects for mass production. Given the fast progress of graphene technology over the past few years, we can expect similar advances in the production of the heterostructures, making the science and applications more achievable.

2D materials and van der Waals heterostructures

http://sces.phys.utk.edu/mostcited/mc1_1114.pdf

Colossal Magnetoresistant Materials: The Key Role of Phase Separation

The ternary iron arsenide ${\mathrm{BaFe}}_{2}{\mathrm{As}}_{2}$ becomes superconducting by hole doping, which was achieved by partial substitution of the barium site with potassium. We have discovered bulk superconductivity at ${T}_{c}=38\text{ }\text{ }\mathrm{K}$ in $({\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{K}}_{x}){\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$ with $x\ensuremath{\approx}0.4$. The parent compound ${\mathrm{BaFe}}_{2}{\mathrm{As}}_{2}$ crystallizes in the tetragonal ${\mathrm{ThCr}}_{2}{\mathrm{Si}}_{2}$-type structure, which consists of $(\mathrm{FeAs}{)}^{\ensuremath{\delta}\ensuremath{-}}$ iron arsenide layers separated by ${\mathrm{Ba}}^{2+}$ ions. ${\mathrm{BaFe}}_{2}{\mathrm{As}}_{2}$ is a poor metal and exhibits a spin density wave anomaly at 140 K. By substituting ${\mathrm{Ba}}^{2+}$ for ${\mathrm{K}}^{+}$ ions we have introduced holes in the $(\mathrm{FeAs}{)}^{\ensuremath{-}}$ layers, which suppress the anomaly and induce superconductivity. The ${T}_{c}$ of 38 K in $({\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}){\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$ is the highest in hole doped iron arsenide superconductors so far. Therefore, we were able to expand this class of superconductors by oxygen-free compounds with the ${\mathrm{ThCr}}_{2}{\mathrm{Si}}_{2}$-type structure.

Superconductivity at 38 K in the iron arsenide (Ba1-xKx)Fe2As2.

FOLLOWING the discovery of superconductivity at ∼30 K in La2−xBaxCuO4 (ref. 1), a large number of related compounds have been found that are superconducting at relatively high temperatures. The feature common to all of these materials is a layered crystal structure based on a perovskite template and containing planar networks of copper and oxygen. This raises the question of whether superconductivity can occur in layered perovskites that do not contain copper. To the best of our knowledge, no such material has been found to date, despite nearly a decade of searching. We describe here the discovery of superconductivity in Sr2RuO4, a layered perovskite isostructural with La2−xBaxCuO4 (Fig. 1). Our results demonstrate that the presence of copper is not a prerequisite for the existence of superconductivity in a layered perovskite. But the low value of the superconducting transition temperature (Tc = 0.93 K) points towards a special role for copper in the high-temperature superconductors.

Superconductivity in a layered perovskite without copper

The crystal structures, magnetic susceptibilities, and electrical resistivities of the quaternary intermetallic compounds ${\mathrm{LaRh}}_{2}$${\mathrm{B}}_{2}$C and ${\mathrm{LaIr}}_{2}$${\mathrm{B}}_{2}$C are reported. Although isostructural with the recently reported superconductors L${\mathrm{Ni}}_{2}$${\mathrm{B}}_{2}$C and L${\mathrm{Pt}}_{2}$${\mathrm{B}}_{2}$C (L=La and Y), they are not superconducting at temperatures above 1.4 K. The magnetic-susceptibility measurements reveal densities of states at the Fermi level intermediate to the Ni- and Pt-based compounds.

Elementary physical properties and crystal structures of LaRh2B2C and LaIr2B2C.

Structural, magnetic and superconducting properties of rare earth/superconductor multilayer films

The normal state transport properties (resistivity, Hall effect) of La2−xSrxCuO4 have been studied over wide ranges of Sr doping and temperature. The familiar T-linear resistivity and the strongly T dependent Hall effect RH(T) are found only near the optimal hole concentration (x ≈ 0.15–0.18). The charge dynamics changes significantly in the non-superconducting overdoped range with RH(T) becoming constant above a characteristic temperature T*, and p(T) ∝ Tn (n > 1; n ≈ 1.5±0.1). The temperature scale T*, decreasing with increasing hole concentration, provides a link between transport and magnetic properties.

Charge dynamics in (La, Sr)2CuO4: from underdoping to overdoping

Quantitative studies of ultrasound absorption in the heavy-fermion state of UPt/sub 3/ and UBe/sub 13/ are reported. The magnitude of the absorption due to electrons in the normal state is not enhanced compared to that of ordinary metals, indicating a cancellation of the mass enhancement by a reduction of the electron-phonon coupling parameter. This implies that the mass enhancement is described by a different Landau Fermi-liquid parameter than in /sup 3/He. The T/sup 2/ variation of the normal-state sound velocity at lowest temperatures is consistent with the large electronic specific heat.

/pdf/unrenormalized-ultrasound-attenuation-in-the-heavy-fermion-1lw3ad91cq.pdf

Unrenormalized ultrasound attenuation in the heavy-fermion state.

A reply to the comment on oxygen isotope effect in high temperature YBaCuO perovskite uperconductors is presented. (AIP)

Bertram Batlogg

Papers

Elementary physical properties and crystal structures of LaRh2B2C and LaIr2B2C.

Structural, magnetic and superconducting properties of rare earth/superconductor multilayer films

Charge dynamics in (La, Sr)2CuO4: from underdoping to overdoping

Unrenormalized ultrasound attenuation in the heavy-fermion state.

Batlogg, Cava, and Stavola reply.