Complete asymptotic expansion of the integrated density of states of multidimensional almost-periodic pseudo-differential operators

We obtain a complete asymptotic expansion of the integrated density of states of operators of the form H =(-\Delta)^w +B in R^d. Here w >0, and B belongs to a wide class of almost-periodic self-adjoint pseudo-differential operators of order less than 2w. In particular, we obtain such an expansion for magnetic Schr\"odinger operators with either smooth periodic or generic almost-periodic coefficients.Comment: 47 pages. arXiv admin note: text overlap with arXiv:1004.293

Symmetric achromatic low-beta collider interaction region design concept

We present a new symmetry-based concept for an achromatic low-beta collider interaction region design. A specially-designed symmetric Chromaticity Compensation Block (CCB) induces an angle spread in the passing beam such that it cancels the chromatic kick of the final focusing quadrupoles. Two such CCBs placed symmetrically around an interaction point allow simultaneous compensation of the 1st-order chromaticities and chromatic beam smear at the IP without inducing significant 2nd-order aberrations to the particle trajectory. We first develop an analytic description of this approach and explicitly formulate 2nd-order aberration compensation conditions at the interaction point. The concept is next applied to develop an interaction region design for the ion collider ring of an electron-ion collider. We numerically evaluate performance of the design in terms of momentum acceptance and dynamic aperture. The advantages of the new concept are illustrated by comparing it to the conventional distributed-sextupole chromaticity compensation scheme.Comment: 12 pages, 17 figures, to be submitted to Phys. Rev. ST Accel. Beam

Titanium trisulfide monolayer: A new direct-gap semiconductor with high and anisotropic carrier mobility

A new two-dimensional (2D) layered material, namely, titanium trisulfide (TiS$_3$) monolayer sheet, is predicted to possess desired electronic properties for nanoelectronic applications. On basis of the first-principles calculations within the framework of density functional theory and deformation theory, we show that the TiS$_3$ 2D crystal is a direct gap semiconductor with a band gap of 1.06 eV and high carrier mobility. More remarkably, the in-plane electron mobility of the 2D TiS$_3$ is highly anisotropic, amounting to $\sim$10,000 cm$^2$V$^{-1}$s$^{-1}$ in the \emph{b} direction, which is higher than that of the MoS$_2$ monolayer. Meanwhile, the hole mobility is about two orders of magnitude lower. We also find that bulk TiS$_3$ possesses lower cleavage energy than graphite, indicating high possibility of exfoliation for TiS$_3$ monolayers or multilayers. Both dynamical and thermal stability of the TiS$_3$ monolayer is examined via phonon-spectrum calculation and Born-Oppenheimer molecular dynamics simulation in \emph{NPT} ensemble. The predicted novel electronic properties render the TiS$_3$ monolayer an attractive 2D material for applications in future nanoelectronics.Comment: 4 figure

Energy bands of atomic monolayers of various materials: Possibility of energy gap engineering

The mobility of graphene is very high because the quantum Hall effects can be observed even at room temperature. Graphene has the potential of the material for novel devices because of this high mobility. But the energy gap of graphene is zero, so graphene can not be applied to semiconductor devices such as transistors, LEDs, etc. In order to control the energy gaps, we propose atomic monolayers which consist of various materials besides carbon atoms. To examine the energy dispersions of atomic monolayers of various materials, we calculated the electronic states of these atomic monolayers using density functional theory with structural optimizations. The quantum chemical calculation software "Gaussian 03" was used under periodic boundary conditions. The calculation method is LSDA/6-311G(d,p), B3LYP/6-31G(d), or B3LYP/6-311G(d,p). The calculated materials are C (graphene), Si (silicene), Ge, SiC, GeC, GeSi, BN, BP, BAs, AlP, AlAs, GaP, and GaAs. These atomic monolayers can exist in the flat honeycomb shapes. The energy gaps of these atomic monolayers take various values. Ge is a semimetal; AlP, AlAs, GaP, and GaAs are indirect semiconductors; and others are direct semiconductors. We also calculated the change of energy dispersions accompanied by the substitution of the atoms. Our results suggest that the substitution of impurity atoms for monolayer materials can control the energy gaps of the atomic monolayers. We conclude that atomic monolayers of various materials have the potential for novel devices.Comment: This paper was first presented at the 14th International Conference on Modulated Semiconductor Structures (MSS14) held in Kobe, Japan, on 23 July 200