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

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

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The electronic properties of graphene

A ferroelectric crystal exhibits a stable and switchable electrical polarization that is manifested in the form of cooperative atomic displacements. A ferromagnetic crystal exhibits a stable and switchable magnetization that arises through the quantum mechanical phenomenon of exchange. There are very few 'multiferroic' materials that exhibit both of these properties, but the 'magnetoelectric' coupling of magnetic and electrical properties is a more general and widespread phenomenon. Although work in this area can be traced back to pioneering research in the 1950s and 1960s, there has been a recent resurgence of interest driven by long-term technological aspirations.

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Multiferroic and magnetoelectric materials

Graphene devices on standard SiO(2) substrates are highly disordered, exhibiting characteristics that are far inferior to the expected intrinsic properties of graphene. Although suspending the graphene above the substrate leads to a substantial improvement in device quality, this geometry imposes severe limitations on device architecture and functionality. There is a growing need, therefore, to identify dielectrics that allow a substrate-supported geometry while retaining the quality achieved with a suspended sample. Hexagonal boron nitride (h-BN) is an appealing substrate, because it has an atomically smooth surface that is relatively free of dangling bonds and charge traps. It also has a lattice constant similar to that of graphite, and has large optical phonon modes and a large electrical bandgap. Here we report the fabrication and characterization of high-quality exfoliated mono- and bilayer graphene devices on single-crystal h-BN substrates, by using a mechanical transfer process. Graphene devices on h-BN substrates have mobilities and carrier inhomogeneities that are almost an order of magnitude better than devices on SiO(2). These devices also show reduced roughness, intrinsic doping and chemical reactivity. The ability to assemble crystalline layered materials in a controlled way permits the fabrication of graphene devices on other promising dielectrics and allows for the realization of more complex graphene heterostructures.

Boron nitride substrates for high-quality graphene electronics

The capability to probe the dispersion of elementary spin, charge, orbital, and lattice excitations has positioned resonant inelastic x-ray scattering (RIXS) at the forefront of photon science. Here we develop the scattering theory for RIXS on superconductors, calculating its momentum-dependent scattering amplitude. Considering superconductors with different pairing symmetries, we show that the low-energy scattering is strongly affected by the superconducting gap and coherence factors. This establishes RIXS as a tool to disentangle pairing symmetries and to probe the elementary excitations of unconventional superconductors.

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Resonant Inelastic X-Ray Scattering as a Probe of the Phase and Excitations of the Order Parameter of Superconductors

The fractional quantum Hall effect has been predicted to occur in the absence of magnetic fields and at high temperature in lattice systems that have flat bands with a nonzero Chern number. We demonstrate that orbital degrees of freedom in frustrated lattice systems lead to a narrowing of topologically nontrivial bands. This robust effect does not rely on fine-tuned long-range hopping parameters and is directly relevant to a wide class of transition-metal compounds.

Narrowing of topological bands due to electronic orbital degrees of freedom.

We study the interplay of quantum statistics, strong interactions, and finite temperatures in the twocomponent spinor Bose gas with repulsive delta-function interactions in one dimension. Using the Thermodynamic Bethe Ansatz, we obtain the equation of state, population densities, and local density correlation numerically as a function of all physical parameters interaction, temperature, and chemical potentials, quantifying the full crossover between low-temperature ferromagnetic and high-temperature unpolarized regimes. In contrast to the single component, Lieb-Liniger gas, nonmonotonic behavior of the local density correlation as a function of temperature is observed.

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Polarization Suppression and Nonmonotonic Local Two-Body Correlations in the Two-Component Bose Gas in One Dimension

Compound Bi14Rh3I9 consists of ionic stacks of intermetallic [(Bi4Rh)3I]2+ and insulating [Bi2I8]2– layers and has been identified to be a weak topological insulator. Scanning tunneling microscopy revealed the robust edge states at all step edges of the cationic layer as a topological fingerprint. However, these edge states are found 0.25 eV below the Fermi level, which is an obstacle for transport experiments. Here, we address this obstacle by comparing results of density functional slab calculations with scanning tunneling spectroscopy and angle-resolved photoemission spectroscopy. We show that the n-type doping of the intermetallic layer is intrinsically caused by the polar surface and is well-screened toward the bulk. In contrast, the anionic “spacer” layer shows a gap at the Fermi level, both on the surface and in the bulk; that is, it is not surface-doped due to iodine desorption. The well-screened surface dipole implies that a buried edge state, probably already below a single spacer layer, is loca...

Electronic Structure of the Dark Surface of the Weak Topological Insulator Bi14Rh3I9.

For 4d1 and 5d1 spin–orbit-coupled electron configurations, the notion of nonmagnetic j=3/2 quartet ground state discussed in classical textbooks is at odds with the observed variety of magnetic properties. Here we throw fresh light on the electronic structure of 4d1 and 5d1 ions in molybdenum- and osmium-based double-perovskite systems and reveal different kinds of on-site many-body physics in the two families of compounds: although the sizable magnetic moments and g-factors measured experimentally are due to both metal d–ligand p hybridisation and dynamic Jahn–Teller interactions for 4d electrons, it is essentially d−p covalency for the 5d1 configuration. These results highlight the subtle interplay of spin–orbit interactions, covalency and electron–lattice couplings as the major factor in deciding the nature of the magnetic ground states of 4d and 5d quantum materials. Cation charge imbalance in the double-perovskite structure is further shown to allow a fine tuning of the gap between the t2g and eg levels, an effect of much potential in the context of orbital engineering in oxide electronics. The metal-oxygen hybridization and lattice vibrations stabilize a finite magnetic polarization in a presumably nonmagnetic configuration. An international team of researchers led by Liviu Hozoi at Institute for Theoretical Solid State Physics at Dresden calculated the electronic structure of Mo5+ and Os7+ ions coordinated with six oxygen ligands forming a double-perovskite structure of metal-oxygen octahedra. The valence orbitals of the metal ion hybridizing those of the adjacent oxygen ligands induces magnetic polarization at the metal site, which can be further enhanced by oxygen-ion vibrational modes. This phenomenon appears even in a perfectly cubic environment where the Mo5+/Os7+ ions are normally assumed nonmagnetic. This result highlights the interplay among multiple interactions involving charge, orbital, spin and lattice degrees of freedom in determining emergent phenomena and sheds light on understanding the puzzling variety of magnetic properties observed in recent experiments.

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Jeroen van den Brink

Papers

Resonant Inelastic X-Ray Scattering as a Probe of the Phase and Excitations of the Order Parameter of Superconductors

Narrowing of topological bands due to electronic orbital degrees of freedom.

Polarization Suppression and Nonmonotonic Local Two-Body Correlations in the Two-Component Bose Gas in One Dimension

Electronic Structure of the Dark Surface of the Weak Topological Insulator Bi14Rh3I9.

Covalency and vibronic couplings make a nonmagnetic j=3/2 ion magnetic