This article reviews the physics of high-temperature superconductors from the point of view of the doping of a Mott insulator. The basic electronic structure of cuprates is reviewed, emphasizing the physics of strong correlation and establishing the model of a doped Mott insulator as a starting point. A variety of experiments are discussed, focusing on the region of the phase diagram close to the Mott insulator (the underdoped region) where the behavior is most anomalous. The normal state in this region exhibits pseudogap phenomenon. In contrast, the quasiparticles in the superconducting state are well defined and behave according to theory. This review introduces Anderson's idea of the resonating valence bond and argues that it gives a qualitative account of the data. The importance of phase fluctuations is discussed, leading to a theory of the transition temperature, which is driven by phase fluctuations and the thermal excitation of quasiparticles. However, an argument is made that phase fluctuations can only explain pseudogap phenomenology over a limited temperature range, and some additional physics is needed to explain the onset of singlet formation at very high temperatures. A description of the numerical method of the projected wave function is presented, which turns out to be a very useful technique for implementing the strong correlation constraint and leads to a number of predictions which are in agreement with experiments. The remainder of the paper deals with an analytic treatment of the $t\text{\ensuremath{-}}J$ model, with the goal of putting the resonating valence bond idea on a more formal footing. The slave boson is introduced to enforce the constraint againt double occupation and it is shown that the implementation of this local constraint leads naturally to gauge theories. This review follows the historical order by first examining the U(1) formulation of the gauge theory. Some inadequacies of this formulation for underdoping are discussed, leading to the SU(2) formulation. Here follows a rather thorough discussion of the role of gauge theory in describing the spin-liquid phase of the undoped Mott insulator. The difference between the high-energy gauge group in the formulation of the problem versus the low-energy gauge group, which is an emergent phenomenon, is emphasized. Several possible routes to deconfinement based on different emergent gauge groups are discussed, which leads to the physics of fractionalization and spin-charge separation. Next the extension of the SU(2) formulation to nonzero doping is described with a focus on a part of the mean-field phase diagram called the staggered flux liquid phase. It will be shown that inclusion of the gauge fluctuation provides a reasonable description of the pseudogap phase. It is emphasized that $d$-wave superconductivity can be considered as evolving from a stable U(1) spin liquid. These ideas are applied to the high-${T}_{c}$ cuprates, and their implications for the vortex structure and the phase diagram are discussed. A possible test of the topological structure of the pseudogap phase is described.

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Doping a Mott insulator: Physics of high-temperature superconductivity

Background Since at least 400 C.E., when the Mayans first used layered clays to make dyes, people have been harnessing the properties of layered materials. This gradually developed into scientific research, leading to the elucidation of the laminar structure of layered materials, detailed understanding of their properties, and eventually experiments to exfoliate or delaminate them into individual, atomically thin nanosheets. This culminated in the discovery of graphene, resulting in a new explosion of interest in two-dimensional materials. Layered materials consist of two-dimensional platelets weakly stacked to form three-dimensional structures. The archetypal example is graphite, which consists of stacked graphene monolayers. However, there are many others: from MoS 2 and layered clays to more exotic examples such as MoO 3 , GaTe, and Bi 2 Se 3 . These materials display a wide range of electronic, optical, mechanical, and electrochemical properties. Over the past decade, a number of methods have been developed to exfoliate layered materials in order to produce monolayer nanosheets. Such exfoliation creates extremely high-aspect-ratio nanosheets with enormous surface area, which are ideal for applications that require surface activity. More importantly, however, the two-dimensional confinement of electrons upon exfoliation leads to unprecedented optical and electrical properties. Liquid exfoliation of layered crystals allows the production of suspensions of two-dimensional nanosheets, which can be formed into a range of structures. (A) MoS 2 powder. (B) WS 2 dispersed in surfactant solution. (C) An exfoliated MoS 2 nanosheet. (D) A hybrid material consisting of WS 2 nanosheets embedded in a network of carbon nanotubes. Advances An important advance has been the discovery that layered crystals can be exfoliated in liquids. There are a number of methods to do this that involve oxidation, ion intercalation/exchange, or surface passivation by solvents. However, all result in liquid dispersions containing large quantities of nanosheets. This brings considerable advantages: Liquid exfoliation allows the formation of thin films and composites, is potentially scaleable, and may facilitate processing by using standard technologies such as reel-to-reel manufacturing. Although much work has focused on liquid exfoliation of graphene, such processes have also been demonstrated for a host of other materials, including MoS 2 and related structures, layered oxides, and clays. The resultant liquid dispersions have been formed into films, hybrids, and composites for a range of applications. Outlook There is little doubt that the main advances are in the future. Multifunctional composites based on metal and polymer matrices will be developed that will result in enhanced mechanical, electrical, and barrier properties. Applications in energy generation and storage will abound, with layered materials appearing as electrodes or active elements in devices such as displays, solar cells, and batteries. Particularly important will be the use of MoS 2 for water splitting and metal oxides as hydrogen evolution catalysts. In addition, two-dimensional materials will find important roles in printed electronics as dielectrics, optoelectronic devices, and transistors. To achieve this, much needs to be done. Production rates need to be increased dramatically, the degree of exfoliation improved, and methods to control nanosheet properties developed. The range of layered materials that can be exfoliated must be expanded, even as methods for chemical modification must be developed. Success in these areas will lead to a family of materials that will dominate nanomaterials science in the 21st century.

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Liquid Exfoliation of Layered Materials

Herein we report on the synthesis of two-dimensional transition metal carbides and carbonitrides by immersing select MAX phase powders in hydrofluoric acid, HF. The MAX phases represent a large (>60 members) family of ternary, layered, machinable transition metal carbides, nitrides, and carbonitrides. Herein we present evidence for the exfoliation of the following MAX phases: Ti2AlC, Ta4AlC3, (Ti0.5,Nb0.5)2AlC, (V0.5,Cr0.5)3AlC2, and Ti3AlCN by the simple immersion of their powders, at room temperature, in HF of varying concentrations for times varying between 10 and 72 h followed by sonication. The removal of the “A” group layer from the MAX phases results in 2-D layers that we are labeling MXenes to denote the loss of the A element and emphasize their structural similarities with graphene. The sheet resistances of the MXenes were found to be comparable to multilayer graphene. Contact angle measurements with water on pressed MXene surfaces showed hydrophilic behavior.

Two-dimensional transition metal carbides.

Oxide pyrochlores — A review

MICROPOROUS inorganic materials such as zeolites find widespread application in heterogeneous catalysis, adsorption and ion-exchange processes. The rigidity and stability of such frameworks allow for shape- and size-selective inclusion of organic molecules and ions1–4. Analogous microporous structures based on organic building blocks have the potential for more precise rational design, through control of the shape, size and functionalization of the pores5–8. Here we report the synthesis of a metal–organic framework designed to bind aromatic guest molecules selectively. The basic building block is a symmetric organic molecule, which binds metal ions9,10 to form layers of the metal–organic compound alternating with layers whose composition is determined by the functionalization of the starting molecules. The layers create channels in which guest aromatic molecules may be selectively bound. We show that the crystal lattice thus formed is thermally stable up to 350 °C, even after removal of included guest molecules, and that the inclusions can be selectively readsorbed.

Selective binding and removal of guests in a microporous metal–organic framework

Interlayer chemistry between thick transition-metal oxide layers: synthesis and intercalation reactions of K[Ca2Nan-3NbnO3n+1] (3 .ltoreq. n .ltoreq. 7)

Electron Microscopy Study of Delamination in Dispersions of the Perovskite-Related Layered Phases K[Ca2Nan−3NbnO3n+1]: Evidence for Single-Layer Formation

Neutron diffraction has been used to study antiferromagnetic ordering in $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}$ as a function of $x$. Evidence for such ordering has been observed only in the tetragonal, nonsuperconducting phase ($x\ensuremath{\lesssim}0.4$). The magnetic origin of the superlattice reflections has been confirmed with polarized beam measurements. A single antiferromagnetic structure was observed throughout the ordered phase, with a maximum N\'eel temperature of \ensuremath{\sim}500 K and average ordered moment of ${(0.66\ifmmode\pm\else\textpm\fi{}0.07)}_{\mathrm{\ensuremath{\mu}}\mathit{B}}$ per magnetic Cu atom at $x\ensuremath{\approx}0$. Magnetic susceptibility measurements suggest that two-dimensional correlations are strong, as in ${\mathrm{La}}_{2}\mathrm{Cu}{\mathrm{O}}_{4\ensuremath{-}y}$, and may survive into the orthorhombic phase.

Antiferromagnetism in YBa2Cu

Molecular recognition of alcohols by layered compounds with alternating organic and inorganic layers

The alkali cations in the layered perovskites MCa 2 Nb 3 O 10 (M ≡ K, Rb, Cs) are exchanged by protons in aqueous acid in a topochemical reaction to give HCa 2 Nb 3 O 10 . The unit cell of HCa 2 Nb 3 O 10 , as determined from powder X-ray diffraction, is tetragonal with a = 3.851 A and c = 14.38 A and contains one formula unit. The anhydrous hydrogen compound hydrates to form a composition HCa 2 Nb 3 O 10 ·1.5H 2 O which is also tetragonal with a = 3.854 A and c = 16.23 A . The hydration-dehydration behavior at 24 °C as a function of the partial water pressure shows significant hysteresis as a result of the expansion and contraction of the unit cell along the c axis.

Joseph T. Lewandowski

Papers

Interlayer chemistry between thick transition-metal oxide layers: synthesis and intercalation reactions of K[Ca2Nan-3NbnO3n+1] (3 .ltoreq. n .ltoreq. 7)

Electron Microscopy Study of Delamination in Dispersions of the Perovskite-Related Layered Phases K[Ca2Nan−3NbnO3n+1]: Evidence for Single-Layer Formation

Antiferromagnetism in YBa2Cu

Molecular recognition of alcohols by layered compounds with alternating organic and inorganic layers

Ion Exchange of the Layered Perovskite KCa2Nb3O10 by Protons.