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

A detailed study of doped LaMn${\mathrm{O}}_{3}$ with fixed carrier concentration reveals a direct relationship between the Curie temperature ${T}_{c}$ and the average ionic radius of the La site $〈{r}_{A}〉$, which is varied by substituting different rare earth ions for La. With decreasing $〈{r}_{A}〉$, magnetic order and significant magnetoresistance occur at lower temperatures with increasing thermal hysteresis, and the magnitude of the magnetoresistance increases dramatically. These results show that the notion of ``double exchange'' must be generalized to include changes in the Mn-Mn electronic hopping parameter as a result of changes in the Mn-O-Mn bond angle.

Lattice effects on the magnetoresistance in doped lamno3

We have prepared and identified as a single phase the high-temperature superconducting compound in the chemical system Y-Ba-Cu-O, an orthorhombic, distorted oxygen-deficient perovskite of stoichiometry ${\mathrm{Ba}}_{2}$${\mathrm{YCu}}_{3}$${\mathrm{O}}_{9\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ (\ensuremath{\delta}\ensuremath{\simeq}2.1). Samples exhibit zero resistance at 91 K, with a transition width of 1.5 K. The Meissner effect attains a value of 76% of the independently measured diamagnetic susceptibility. We estimate parameters that characterize this superconductor, e.g., \ensuremath{\gamma}\ensuremath{\simeq}3--5 mJ (mole Cu${)}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{K}}^{\mathrm{\ensuremath{-}}2}$. The critical current density at 77 K and H=0 exceeds 1100 A/${\mathrm{cm}}^{2}$.

https://link.aps.org/pdf/10.1103/PhysRevLett.58.1676

Bulk superconductivity at 91 K in single-phase oxygen-deficient perovskite Ba 2 YCu 3 O 9 − δ

THE attainment of unprecedentedly high transition temperatures (Tcs) in the copper oxide superconductors illustrates how working with more complex chemical systems allows greater opportunity to balance opposing forces within a single chemical compound, leading to a better optimization of physical properties. For many desired properties, materials with optimal chemical complexity have undoubtedly not yet been found. This appears to be the case for the intermetallic superconductors, whose study has languished in recent years, and which almost never show Tcs above 15 K. These are almost all binary compounds with substitution-type additives, or, rarely, true ternary compounds such as LuRh4B4 (Tc = 11.7 K; refs 1, 2). If, as some argue (refs 3, 4), materials such as AXC60 (ref. 5) and Ba0.6K0.4BiO3 (refs 6, 7) are conventional electron–phonon superconductors with Jcs of ~30 K, then the absence of higher Tcs in intermetallic compounds may mean only that more complex materials have not been sufficiently explored. We have recently found superconductivity at 23 K (a Tc equal to that of the previous intermetallic record holder, Nb3Ge; ref. 9) in the quaternary intermetallic system yttrium–palladium–boron–carbon8, but we were unable to identify the superconducting phase. Here we report superconductivity at temperatures up to 16.6 K for the single-phase quaternary intermetallic compounds LnNi2B2C (where Ln stands for Y, Tm, Er, Ho or Lu). The presence of the 3d transition metal nickel, and the layered crystal structure10 raise intriguing questions about the origin of the superconductivity, and the relatively high Tcs of these and the Y–Pd–B–C superconductor suggest that there may yet be more surprises in store.

Superconductivity in the quaternary intermetallic compounds LnNi 2 B 2 C

A new dissipation behavior is reported in superconducting Bi2.2Sr2Ca0.8Cu2Oa+δfor all temperatures belowTc and all magnetic fields exceeding Hc1. The current-independent electrical resistivity is thermally activated and can be described by an Arrhenius law with a single prefactor and a magnetic-field-and orientation-dependent activation energyU 0 (H,o).This behavior is markedly different from past observations and will be discussed in terms of flux creep and flux flow. This thermally activated behavior implies a finite resistance at all temperatures and all fields exceeding H c1 determined by the activation energy as the only parameter.

/pdf/thermally-activated-dissipation-in-bi2-2sr2ca0-8cu2o8-d-3gc0z58l7n.pdf

Thermally activated dissipation in Bi2.2Sr2Ca0.8Cu2O8+δ

The dissipation below ${\mathit{T}}_{\mathit{c}}$ has been studied for representatives of all classes of cuprate high-temperature superconductors, including ${\mathrm{Ba}}_{2}$${\mathrm{YCu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$, and Bi and Tl compounds. The results are parametrized in the framework of flux creep, with the largest activation energies found in ${\mathrm{Ba}}_{2}$${\mathrm{YCu}}_{3}$${\mathrm{O}}_{7}$. It is argued that the magnitude of dissipative flux motion is more related to the electronic anisotropy of the material than the actual defect structure. The thermally activated flux creep model, whose parameters are extracted from dc measurements, consistently describes also dynamic measurements, including the irreversibility line and the melting transition. Finally, the similarities in dissipative behavior are emphasized between high-${\mathit{T}}_{\mathit{c}}$ materials, very thin films, and layered low-${\mathit{T}}_{\mathit{c}}$ superconductors.

/pdf/dissipative-flux-motion-in-high-temperature-superconductors-1k71lm9xlm.pdf

Bertram Batlogg

Papers

Lattice effects on the magnetoresistance in doped lamno3

Bulk superconductivity at 91 K in single-phase oxygen-deficient perovskite Ba 2 YCu 3 O 9 − δ

Superconductivity in the quaternary intermetallic compounds LnNi 2 B 2 C

Thermally activated dissipation in Bi2.2Sr2Ca0.8Cu2O8+δ

Dissipative flux motion in high-temperature superconductors