There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Fabrication techniques developed for graphene research allow the disassembly of many layered crystals (so-called van der Waals materials) into individual atomic planes and their reassembly into designer heterostructures, which reveal new properties and phenomena. Andre Geim and Irina Grigorieva offer a forward-looking review of the potential of layering two-dimensional materials into novel heterostructures held together by weak van der Waals interactions. Dozens of these one-atom- or one-molecule-thick crystals are known. Graphene has already been well studied but others, such as monolayers of hexagonal boron nitride, MoS2, WSe2, graphane, fluorographene, mica and silicene are attracting increasing interest. There are many other monolayers yet to be examined of course, and the possibility of combining graphene with other crystals adds even further options, offering exciting new opportunities for scientific exploration and technological innovation. Research on graphene and other two-dimensional atomic crystals is intense and is likely to remain one of the leading topics in condensed matter physics and materials science for many years. Looking beyond this field, isolated atomic planes can also be reassembled into designer heterostructures made layer by layer in a precisely chosen sequence. The first, already remarkably complex, such heterostructures (often referred to as ‘van der Waals’) have recently been fabricated and investigated, revealing unusual properties and new phenomena. Here we review this emerging research area and identify possible future directions. With steady improvement in fabrication techniques and using graphene’s springboard, van der Waals heterostructures should develop into a large field of their own.

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Van der Waals heterostructures

We report the experimental discovery of intrinsic ferromagnetism in Cr 2 Ge 2 Te 6 atomic layers by scanning magneto-optic Kerr microscopy. In this 2D van der Waals ferromagnet, unprecedented control of transition temperature is realized via small magnetic fields.

Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals

Graphene and other two-dimensional materials, such as transition metal dichalcogenides, have rapidly established themselves as intriguing building blocks for optoelectronic applications, with a strong focus on various photodetection platforms The versatility of these material systems enables their application in areas including ultrafast and ultrasensitive detection of light in the ultraviolet, visible, infrared and terahertz frequency ranges These detectors can be integrated with other photonic components based on the same material, as well as with silicon photonic and electronic technologies Here, we provide an overview and evaluation of state-of-the-art photodetectors based on graphene, other two-dimensional materials, and hybrid systems based on the combination of different two-dimensional crystals or of two-dimensional crystals and other (nano)materials, such as plasmonic nanoparticles, semiconductors, quantum dots, or their integration with (silicon) waveguides

http://www-g.eng.cam.ac.uk/nms/publications/pdf/nnano.2014.215.pdf

Photodetectors based on graphene, other two-dimensional materials and hybrid systems

We review the problem of electron-electron interactions in graphene. Starting from the screening of long range interactions in these systems, we discuss the existence of an emerging Dirac liquid of Lorentz invariant quasi-particles in the weak coupling regime, and strongly correlated electronic states in the strong coupling regime. We also analyze the analogy and connections between the many-body problem and the Coulomb impurity problem. The problem of the magnetic instability and Kondo effect of impurities and/or adatoms in graphene is also discussed in analogy with classical models of many-body effects in ordinary metals. We show that Lorentz invariance plays a fundamental role and leads to effects that span the whole spectrum, from the ultraviolet to the infrared. The effect of an emerging Lorentz invariance is also discussed in the context of finite size and edge effects as well as mesoscopic physics. We also briefly discuss the effects of strong magnetic fields in single layers and review some of the main aspects of the many-body problem in graphene bilayers. In addition to reviewing the fully understood aspects of the many-body problem in graphene, we show that a plethora of interesting issues remain open, both theoretically and experimentally, and that the field of graphene research is still exciting and vibrant.

Electron-Electron Interactions in Graphene: Current Status and Perspectives

We examine the conditions necessary for the presence of localized magnetic moments on adatoms with inner shell electrons in graphene. We show that the low density of states at the Dirac point, and the anomalous broadening of the adatom electronic level, lead to the formation of magnetic moments for arbitrarily small local charging energy. As a result, we obtain an anomalous scaling of the boundary separating magnetic and nonmagnetic states. We show that, unlike any other material, the formation of magnetic moments can be controlled by an electric field effect.

Localized Magnetic States in Graphene

We address the effective tight-binding Hamiltonian that describes the insulating Mott state of twisted graphene bilayers at a magic angle. In that configuration, twisted bilayers form a honeycomb superlattice of localized states, characterized by the appearance of flat bands with fourfold degeneracy. After calculating the maximally localized superlattice Wannier wave functions, we derive the effective spin model that describes the Mott state. We suggest that the system is an exotic ferromagnetic Mott insulator, with well-defined experimental signatures.

Ferromagnetic Mott state in Twisted Graphene Bilayers at the Magic Angle.

We study the problem of Coulomb field-induced charging of the ground state in a system of two-dimensional (2D) massive Dirac particles---gapped graphene. As in its 3D QED counterpart, the critical Coulomb coupling is renormalized to higher values compared to the massless case. We find that in gapped graphene, a different supercritical regime is possible, where the screening charge is comparable to the impurity charge; thus, leading to suppression of the Coulomb field at nanometer scales. We corroborate this with a numerical solution of the tight-binding problem on the honeycomb lattice.

Supercritical Coulomb impurities in gapped graphene

Raman light scattering of the two-dimensional quantum spin system ${\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}$ shows a rich structure in the magnetic excitation spectrum, including several well-defined bound state modes at low temperature, and a scattering continuum and quasielastic light scattering contributions at high temperature. The key to the understanding of the unique features of ${\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}$ is the presence of strong interactions between well-localized triplet excitations in the network of orthogonal spin dimers realized in this compound.

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Valeri N. Kotov

Papers

Electron-Electron Interactions in Graphene: Current Status and Perspectives

Localized Magnetic States in Graphene

Ferromagnetic Mott state in Twisted Graphene Bilayers at the Magic Angle.

Supercritical Coulomb impurities in gapped graphene

Collective Singlet Excitations and Evolution of Raman Spectral Weights in the 2D Spin Dimer Compound SrCu 2 \(BO 3 \) 2