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

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.

/pdf/doping-a-mott-insulator-physics-of-high-temperature-55r49vtp31.pdf

Doping a Mott insulator: Physics of high-temperature superconductivity

The last decade witnessed significant progress in angle-resolved photoemission spectroscopy (ARPES) and its applications. Today, ARPES experiments with 2-meV energy resolution and $0.2\ifmmode^\circ\else\textdegree\fi{}$ angular resolution are a reality even for photoemission on solids. These technological advances and the improved sample quality have enabled ARPES to emerge as a leading tool in the investigation of the high-${T}_{c}$ superconductors. This paper reviews the most recent ARPES results on the cuprate superconductors and their insulating parent and sister compounds, with the purpose of providing an updated summary of the extensive literature. The low-energy excitations are discussed with emphasis on some of the most relevant issues, such as the Fermi surface and remnant Fermi surface, the superconducting gap, the pseudogap and $d$-wave-like dispersion, evidence of electronic inhomogeneity and nanoscale phase separation, the emergence of coherent quasiparticles through the superconducting transition, and many-body effects in the one-particle spectral function due to the interaction of the charge with magnetic and/or lattice degrees of freedom. Given the dynamic nature of the field, we chose to focus mainly on reviewing the experimental data, as on the experimental side a general consensus has been reached, whereas interpretations and related theoretical models can vary significantly. The first part of the paper introduces photoemission spectroscopy in the context of strongly interacting systems, along with an update on the state-of-the-art instrumentation. The second part provides an overview of the scientific issues relevant to the investigation of the low-energy electronic structure by ARPES. The rest of the paper is devoted to the experimental results from the cuprates, and the discussion is organized along conceptual lines: normal-state electronic structure, interlayer interaction, superconducting gap, coherent superconducting peak, pseudogap, electron self-energy, and collective modes. Within each topic, ARPES data from the various copper oxides are presented.

https://arxiv.org/pdf/cond-mat/0208504.pdf

Angle-resolved photoemission studies of the cuprate superconductors

This article reviews the effort to understand the physics of high temperature superconductors from the point of view of doping a Mott insulator. The basic electronic structure of the 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. We introduce Anderson's idea of the resonating valence bond (RVB) and argue that it gives a qualitative account of the data. The importance of phase fluctuation is discussed, leading to a theory of the transition temperature which is driven by phase fluctuation and thermal excitation of quasiparticles. We then describe the numerical method of projected wavefunction which turns out to be a very useful technique to implement 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-J model, with the goal of putting the RVB idea on a more formal footing. The slave-boson is introduced to enforce the constraint of no double occupation. The implementation of the local constraint leads naturally to gauge theories. We give a rather thorough discussion of the role of gauge theory in describing the spin liquid phase of the undoped Mott insulator. We next describe the extension of the SU(2) formulation to nonzero doping. We show that inclusion of gauge fluctuation provides a reasonable description of the pseudogap phase.

Doping a Mott Insulator: Physics of High Temperature Superconductivity

The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered a huge amount of innovative scientific inquiry. In the almost three decades since, much has been learned about the novel forms of quantum matter that are exhibited in these strongly correlated electron systems. A qualitative understanding of the nature of the superconducting state itself has been achieved. However, unresolved issues include the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the 'normal' state at elevated temperatures.

/pdf/from-quantum-matter-to-high-temperature-superconductivity-in-3vq16xcye2.pdf

From quantum matter to high-temperature superconductivity in copper oxides

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

Dissipative flux motion in high-temperature superconductors

Single crystal sof the 84-K superconductor ${\mathrm{Bi}}_{2.2}{\mathrm{Sr}}_{2}{\mathrm{Ca}}_{0.8}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ were characterized by x-ray diffraction, dc magnetic susceptibility, electrical resistivity, and microwave absorption. The structure has ${[\mathrm{Cu}{\mathrm{O}}_{2}]}_{\ensuremath{\infty}}$ planes separated by calcium atoms, edge-shared bismuth oxide double layers, and an incommensurate superlattice along $b$ with a period of 4.76. The in-plane resistivity above ${T}_{c}$ is linear in $T$, with ${\ensuremath{\rho}}_{\mathrm{RT}}=130$ \ensuremath{\mu}\ensuremath{\Omega} cm. Initial results on Pb substitution yielding ${T}_{c}'\mathrm{s}$ of 107 K are reported.

Structure and physical properties of single crystals of the 84-K superconductor Bi 2.2 Sr 2 Ca 0.8 Cu 2 O 8+δ

A new family of high-temperature superconductors is described, with the general formula Pb2Sr2ACu3O8+δ. Although they have the planes of CuO5 square pyramids characteristic of the other copper-oxide superconductors, the new compounds belong to a distinct structural series, with wide scope for elemental substitution. Their unusual electronic configuration also gives new insight into the role of charge distribution among the structural building blocks in controlling superconductivity.

Superconductivity near 70 K in a new family of layered copper oxides

The continuing drive towards miniaturization of electronic devices1 is motivating the search for new materials. Consider, for example, the case of the much-used dynamic random-access memory. The minimum capacitance per cell that can be tolerated is expected2 to remain at 30–40 fF, but as the cell area decreases, the corresponding reduction in geometric capacitance has to be compensated for. So far, this has been achieved by resorting to complex non-planar structures and/or using much thinner films of the dielectric insulator, amorphous silicon dioxide (a-SiOx), although the latter approach is limited by the electric fields that can be supported by a-SiOx before its insulating properties break down. An alternative strategy is to develop thin-film insulators that have a dielectric constant significantly greater than that of a-SiOx, reducing the size of the fields required for device operation. Here we show that a composition-spread technique allows for the efficient evaluating of materials with both a high dielectric constant and a high breakdown field. We apply this approach to the Zr–Sn–Ti–O system, and we find that compositions close to Zr0.15Sn0.3Ti0.55O2−δ are better thin-film dielectrics than high-quality deposited a-SiOx. Although detailed tests of the performance of these materials have not yet been carried out, our initial results suggest that they are likely to be comparable to the best alternatives (such as (Ba, Sr)TiO3) currently being considered for integrated-circuit capacitors.

/pdf/discovery-of-a-useful-thin-film-dielectric-using-a-4ookev4rf1.pdf

Lynn Schneemeyer

Papers

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

Dissipative flux motion in high-temperature superconductors

Structure and physical properties of single crystals of the 84-K superconductor Bi 2.2 Sr 2 Ca 0.8 Cu 2 O 8+δ

Superconductivity near 70 K in a new family of layered copper oxides

Discovery of a useful thin-film dielectric using a composition-spread approach