The previously developed particle mesh Ewald method is reformulated in terms of efficient B‐spline interpolation of the structure factors This reformulation allows a natural extension of the method to potentials of the form 1/rp with p≥1 Furthermore, efficient calculation of the virial tensor follows Use of B‐splines in place of Lagrange interpolation leads to analytic gradients as well as a significant improvement in the accuracy We demonstrate that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N) For biomolecular systems with many thousands of atoms this method permits the use of Ewald summation at a computational cost comparable to that of a simple truncation method of 10 A or less

A smooth particle mesh Ewald method

We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

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

The Linac Coherent Light Source free-electron laser has now achieved coherent X-ray generation down to a wavelength of 1.2 A and at a brightness that is nearly ten orders of magnitude higher than conventional synchrotrons. Researchers detail the first operation and beam characteristics of the system, which give hope for imaging at atomic spatial and temporal scales.

First lasing and operation of an ångstrom-wavelength free-electron laser

Following the discovery of long-range antiferromagnetic order in the parent compounds of high-transition-temperature (high-T(c)) copper oxides, there have been efforts to understand the role of magnetism in the superconductivity that occurs when mobile 'electrons' or 'holes' are doped into the antiferromagnetic parent compounds. Superconductivity in the newly discovered rare-earth iron-based oxide systems ROFeAs (R, rare-earth metal) also arises from either electron or hole doping of their non-superconducting parent compounds. The parent material LaOFeAs is metallic but shows anomalies near 150 K in both resistivity and d.c. magnetic susceptibility. Although optical conductivity and theoretical calculations suggest that LaOFeAs exhibits a spin-density-wave (SDW) instability that is suppressed by doping with electrons to induce superconductivity, there has been no direct evidence of SDW order. Here we report neutron-scattering experiments that demonstrate that LaOFeAs undergoes an abrupt structural distortion below 155 K, changing the symmetry from tetragonal (space group P4/nmm) to monoclinic (space group P112/n) at low temperatures, and then, at approximately 137 K, develops long-range SDW-type antiferromagnetic order with a small moment but simple magnetic structure. Doping the system with fluorine suppresses both the magnetic order and the structural distortion in favour of superconductivity. Therefore, like high-T(c) copper oxides, the superconducting regime in these iron-based materials occurs in close proximity to a long-range-ordered antiferromagnetic ground state.

Magnetic order close to superconductivity in the iron-based layered LaO1-xFxFeAs systems

The scattering of x rays and neutrons from rough surfaces is calculated. It is split into specular reflection and diffuse scattering terms. These are calculated in the first Born approximation, and explicit expressions are given for surfaces whose roughness can be described as self-affine over finite length scales. Expressions are also given for scattering from liquid surfaces, where it is shown that ``specular'' reflections only exist by virtue of a finite length cutoff to the mean-square height fluctuations. Expressions are also given for the scattering from randomly oriented surfaces, as studied in a typical small-angle scattering experiment. It is shown how various well-known asymptotic power laws in S(q) are obtained from the above theory. The distorted-wave Born approximation is next used to treat the case where the scattering is large (e.g., near the critical angle for total external reflection), and its limits of validity are discussed. Finally, the theory is compared with experimental results on x-ray scattering from a polished Pyrex glass surface.

X-ray and neutron scattering from rough surfaces

Neutron-diffraction experiments on ceramic powders of YBa/sub 2/Cu/sub 3/O/sub 6+//sub x/ (nonsuperconducting, with x = 0.0 and 0.15) have confirmed the existence of long-range, three-dimensional, antiferromagnetic order of the Cu spins. The structure determination was aided by the use of uniaxially oriented powders. The ordering wave vector within a CuO/sub 2/ plane is (1/21/2) and the planes are coupled antiferromagnetically along the c axis. The Neel tempreature is 400 +- 10 K for the x = 0.15 +- 0.05 sample and approx. >500 K for x = 0.0.

Neutron-diffraction determination of antiferromagnetic structure of Cu ions in YBa2Cu

The structures of five phases in the ${\mathrm{Ba}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{K}}_{\mathit{x}}$${\mathrm{BiO}}_{3}$ system for 0\ensuremath{\le}x\ensuremath{\le}05 and temperatures below 473 K have been determined by neutron powder diffraction Bulk superconductivity occurs only in a cubic perovskite phase which exists for x\ensuremath{\ge}037 (at 10 K) At room temperature, as the potassium concentration is decreased, the cubic structure distorts first by ${\mathrm{BiO}}_{6}$ octahedral tilting and then by symmetric oxygen breathing-mode distortions Semiconducting behavior for the monoclinic phase at 0\ensuremath{\le}x\ensuremath{\le}01 can readily be explained on the basis of a commensurate charge-density wave The semiconducting orthorhombic phase, which extends from the monoclinic phase to the cubic superconducting phase, contains only octahedral tilting distortions that would not be expected to destroy metallic behavior Thus, this commensurate structure provides no explanation for the metal-insulator transition An incommensurate modulation extending across the semiconducting region of the phase diagram has been observed by electron diffraction, but is not observed by neutron diffraction It is not clear whether this incommensurate modulation is responsible for the nonmetallic behavior

Structural phase diagram of the Ba1-xKxBiO3 system.

X-ray scattering and surface tension measurements reveal the formation of a crystalline monolayer on the surface of liquid n-alkanes at about 3 \ifmmode^\circ\else\textdegree\fi{}C above the bulk solidification temperature. The molecules in the monolayer are hexagonally packed and oriented normal to the surface. The single solid monolayer persists down to the bulk solidification temperature, thus exhibiting a very limited partial wetting.

Surface crystallization of liquid normal-alkanes.

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.

S. K. Sinha

Papers

X-ray and neutron scattering from rough surfaces

Neutron-diffraction determination of antiferromagnetic structure of Cu ions in YBa2Cu

Structural phase diagram of the Ba1-xKxBiO3 system.

Surface crystallization of liquid normal-alkanes.

Antiferromagnetism in YBa2Cu