Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topological quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the $\ensuremath{\nu}=5∕2$ state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. Both the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the $\ensuremath{\nu}=5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.

Non-Abelian Anyons and Topological Quantum Computation

International Tables for X-Ray Crystallography (Published for the International Union of Crystallography.) Vol. 1: Symmetry Groups. Edited by Norman F. M. Henry and Kathleen Lonsdale. Pp. xi + 558. (Birmingham: Kynoch Press, 1952.) 105s.

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International Tables for X-Ray Crystallography

Organic thin-film transistors (OTFTs) have lived to see great improvements in recent years. This review presents new insight into conduction mechanisms and performance characteristics, as well as opportunities for modeling properties of OTFTs. The shifted focus in research from novel chemical structures to fabrication technologies that optimize morphology and structural order is underscored by chapters on vacuum-deposited and solution-processed organic semiconducting films. Finally, progress in the growing field of the n-type OTFTs is discussed in ample detail. The Figure, showing a pentacene film edge on SiO2, illustrates the morphology issue.

Organic Thin Film Transistors for Large Area Electronics

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

Frustrated magnets are materials in which localized magnetic moments, or spins, interact through competing exchange interactions that cannot be simultaneously satisfied, giving rise to a large degeneracy of the system ground state. Under certain conditions, this can lead to the formation of fluid-like states of matter, so-called spin liquids, in which the constituent spins are highly correlated but still fluctuate strongly down to a temperature of absolute zero. The fluctuations of the spins in a spin liquid can be classical or quantum and show remarkable collective phenomena such as emergent gauge fields and fractional particle excitations. This exotic behaviour is now being uncovered in the laboratory, providing insight into the properties of spin liquids and challenges to the theoretical description of these materials.

Spin liquids in frustrated magnets

The characters of hydrogen-bond of 2,2′-bi-1H-imidazole (H2BIM) system were examined from a viewpoint of the proton-transfer (PT) and electron-transfer (CT) interactions. To make the effects of the dibenzo substitution of H2BIM molecule clear, we prepared the charge-transfer complexes of dibenzo-2,2′-bi-1H-imidazole (H2BBIM) and H2BIM systems with 7,7,8,8- tetracyanoquinodimethane(TCNQ). The one-dimensional column of TCNQ was confirmed by the crystal structural analysis, however, the packing forms of the H2BIM and H2BBIM systems were entirely different to each other. The H2BBIM system in the TCNQ complex formed the one-dimensional column which is parallel to the TCNQ stack, while the H2BIM system was constructed by the hydrogen-bonded dimer unit along the perpendicular direction to the TCNQ column.

Hydrogen-Bond Character of 2,2′-Bi-1H-Imidazole Systems

A new ionic complex of C60 with decamethylchromocene, Cp*2Cr.C60(C6H4Cl2)2 (1), has been obtained. The fullerides are monomeric in 1 at room temperature, whereas they form a single-bonded (C60-)2 dimer at low temperatures, the structure of which has been studied by the X-ray diffraction on a single crystal at 100 K. The length of the intercage C-C bond is 1.597(7) A and the interfullerene distance is equal to 9.28 A. A phase transition attributed to the reversible C60*- dimerization is observed in the 220-200 K range. The transition is accompanied by changes in the unit cell parameters, the decrease of the magnetic moment from 4.20 muB (S = 3/2, 1/2) to 3.88 muB (S = 3/2) and the appearance of EPR signal from Cp*2Cr+, simultaneously.

The Reversible Formation of a Single‐Bonded (C60‐)2 Dimer in Ionic Charge Transfer Complex: Cp*2Cr×C60 (C6H4Cl2)2. The Molecular Structure of (C60‐)2.

Intramolecular charge transfer (CT) compounds (D δ+ -π-A δ− ) were synthesized by the reaction between enamine and TCNQ. The CT transition energy ( h ν CT ) showed the solvent dependence (solvatochromism). The ionicity of these compounds was deduced from the plot of h ν CT against the solvent polarity. The plot exhibited abnormal behavior.

Structure and Ionicity of Intramolecular Charge Transfer Zwitterions, D δ+ − π − A δ−

Ambient-pressure superconductivity of κ'-(BEDT-TTF)2Cu2(CN)3 realized by a carrier-doping into a mott-insulating state

Solid-state high-resolution 13C NMR study of the intermolecular interaction in organic semiconductors TTCn-TTF

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