A Short Proof of Stability of Topological Order under Local Perturbations

Recently, the stability of certain topological phases of matter under weak perturbations was proven. Here, we present a short, alternate proof of the same result. We consider models of topological quantum order for which the unperturbed Hamiltonian H ₀ can be written as a sum of local pairwise commuting projectors on a D-dimensional lattice. We consider a perturbed Hamiltonian H = H ₀ + V involving a generic perturbation V that can be written as a sum of short-range bounded-norm interactions. We prove that if the strength of V is below a constant threshold value then H has well-defined spectral bands originating from the low-lying eigenvalues of H ₀. These bands are separated from the rest of the spectrum and from each other by a constant gap. The width of the band originating from the smallest eigenvalue of H ₀ decays faster than any power of the lattice size.     

Grüneisen parameter for HCP iron at extreme compression

The Thomas–Fermi approximation gives the Grüneisen parameter γ=γ_∞=1/2 for all materials at extreme compression (P→∞ or V→0). After re-analyzing the existing experimental data of volume dependence of Grüneisen parameter γ of hexagonal close-packed (HCP) iron, we find that γ=1/2+a(V/V ₀)^1/3+b(V/V ₀) ⁿ , where a, b and n are constants. Based on this new form of γ, the second Grüneisen parameter q, the Debye temperature θ_D and the shear sound velocity v _s of HCP iron are discussed in the present work. It is found that the zero pressure second Grüneisen parameter q ₀=0.654, which is consistent with the previously determined value of HCP iron for Earth's core physics from Dubrovinsky et al. The calculations for the Debye temperature and the shear sound velocity are also found to be in good agreement with the experimental data.     

Electronic theory for impurity segregation at lattice defects in metals

A tight-binding type electronic theory is used to study the impurity segregation at lattice defects in metals. It is shown that the heat of segregation E_segr results from a simple physical origin: It is roughly proportional to the difference in the diagonal matrix elements (V_i-V₀) of impurity potentials, where V_i (V₀) is determined for atomic sites in the vicinity of lattice defects (for a perfect lattice site). Applications to impurity segregation at cleaved surfaces, screw dislocations and tilt grain boundaries are discussed.     

Electrostatic properties and stability of Coulomb crystals

We calculate the electrostatic properties of more than 20 different Coulomb crystals and study their resistance to small oscillations of the ions around their equilibrium positions (phonon oscillations). We discuss the stability of multicomponent crystals against separation into set of one-component lattices and for some cases, the influence of energy of the zero-point vibrations. It is confirmed that the body-centred cubic (bcc) lattice possesses the lowest electrostatic energy among all one-component (one type of ion in the elementary cell) crystals. For systems composed of two types of ions (their charge and density numbers are Z₁, n₁ and Z₂, n₂, respectively) and for n₁ = n₂, it is found that the formation of a binary bcc lattice is possible at 1/2.4229 < α < 2.4229, where α ≡ Z₂/Z₁. Under the same conditions, the NaCl lattice forms at α > 5.197 and α < 0.192. While for n₂ = 2n₁, the MgB₂ lattice is found be stable at 0.1 < α < 0.32. For multicomponent lattices with hexagonal structure (binary hexagonal close-packed, MgB₂ and some others lattices), it is shown that their properties depend on the distance between hexagonal layers and this distance changes with α.     

Thermal property of binary tetrahedral semiconductors

In this paper we present an expression relating the lattice thermal expansion coefficient α_L (10⁻⁶ K⁻¹) for the A^IIIB^V and A^IIB^VI semiconductors with the product of ionic charges (Z₁Z₂), melting temperature (T_m) and nearest neighbor distance d (Å). The lattice thermal expansion coefficient of these compounds exhibit a linear relationship when plotted on a log–log scale against the melting temperature (T_m), but fall on different straight lines according to the ionic charge product of the compounds. A good agreement has been found between the experimental and calculated values of the lattice thermal expansion coefficient for A^IIIB^V and A^IIB^VI semiconductors.     

Transition of expanded liquid iron to the nonmetallic state under supercritical pressure

A transition of expanded liquid iron to the nonmetallic state under high pressures (30–100 kbar) at high temperatures (of about 1 eV) is discovered. The result is obtained by direct measurement of the dependence of resistivity on the specific internal energy and volume. Measurements are taken in the specific volume range from the melting curve to values six times higher than the normal specific volume V ₀ in the solid state. It is shown that iron remains in the metallic state up to a relative volume of V/V ₀ = 3–4, at which the resistivity attains a value of about 3–4 μΩ m and becomes almost independent of temperature, while the conduction electron mean free path decreases to the atomic spacing. For V/V ₀ = 4–5, a transition to the nonmetallic state takes place, for which the temperature coefficient of resistance becomes negative and its absolute value becomes much higher than in the metallic state.     

Electric Field Gradients in Metal Diborides

Systematic calculations of the electric field gradient V _zz with the FLAPW code WIEN97 have been performed for the metal diborides MB₂ (M = Mg–Al, Sc–Fe, Y–Mo, Lu–W) with the hexagonal C32 structure, where with knowledge of the lattice constants a, c all atomic positions are fixed. For V _zz (B) good agreement with the experimental result is found in all cases. The case of the recently discovered superconductor MgB₂ is discussed as representative example. This revised version was published online in September 2006 with corrections to the Cover Date.     

Comparative investigations of the P-V-T relationship of NaCl at high pressure and temperature

Two different potential models of molecular dynamics (MD) simulations have been applied to investigate the pressure-volume-temperature (P-V-T) relationship and lattice parameter of NaCl under high pressure and temperature. The first one is the shell model (SM) potentials in which due to the short-range interaction pairs of ions are moved together as is the case in polarization of a crystal due to the motion of the positive and negative ions, and the second one is the two-body rigid-ion Born-Mayer-Huggins-Fumi-Tosi (BMHFT) potentials with full treatment of long-range Coulomb forces. The P-V relationship at 300 K, T-V relationship at zero pressure, and lattice parameter a, have been obtained and compared with the available experimental data and other theoretical results. Compared with SM potentials, the MD simulation with BMHFT potentials is very successful in reproducing accurately the measured volumes of NaCl. At an extended pressure and temperature ranges, P-V relationship under different isotherms at selected temperatures, T-V relationship under different pressures, and lattice parameter a have also been predicted. The properties of NaCl are summarized in the pressure range 0-30 GPa and the temperature up to 2000 K.     

The Pion Form Factor on the Lattice at Zero and Finite Temperature

We calculate the electromagnetic form factor of the pion in quenched lattice QCD. The non-perturbatively improved Sheikoleslami-Wohlert lattice action is used together with the consistently -improved current. We calculate the pion form factor for masses down to m_π = 360 MeV, extract the charge radius, and extrapolate toward the physical pion mass. In the second part, we discuss results for the pion form factor and charge radius at 0.93 T_c and compare with zero temperature results.     

Spontaneous magnetization of the vacuum and the strength of the magnetic field in the hot Universe

Intergalactic magnetic fields are assumed to have been spontaneously generated at the reheating stage of the early Universe, due to vacuum polarization of non-Abelian gauge fields at high temperature. The fact that the screening mass of this type of fields has zero value was discovered recently. A procedure to estimate their field strengths, B(T), at different temperatures is here developed, and the value B(T _ew)∼10¹⁴ G at the electroweak phase transition temperature is derived by taking into consideration the present value of the intergalactic magnetic field strength, B ₀∼10⁻¹⁵ G, coherent on the ∼1 Mpc scale. As a particular case, the standard model is considered and the field scale at high temperature is estimated in this case. Model-dependent properties of the phenomena under investigation are briefly discussed, too.     

Internal cooling efficiency of a junction diode

The three thermal rate equations were built newly up at both ends and at the junction of a p–n diode, in order to derive analytically the temperature difference ΔT (between a junction and both ends) and the internal cooling efficiency η defined newly for a homojunction diode. The maxima ΔT and η of a diode were derived analytically as a function of V _j within the short-length approximation and calculated numerically as a function of V _j or V _bi, where V _j is a voltage across the junction and V _bi is a built-in voltage at the junction. As a result, ΔT increases abruptly with an increase of V _j below V _j=0.050 V or of V _bi below V _bi=0.10 V, while above their values, it increases slowly with an increase of V _j or V _bi to saturate a certain value. For example, ΔT was estimated as 14.6 K for Hg_0.8Cd_0.2Te diode with V _bi=0.36 V. η has a local maximum of 63% at V _j≈0.01 V or at V _bi≈0.03 V, while above their respective values, it decreases abruptly with an increase of V _j or V _bi and falls to 4.4% at V _bi=0.80 V which is equivalent to that of a diode emitting a laser for fiber optical communication. However, the greater enhancements in ΔT and η of a diode are required to apply the internal cooling system to a laser-emitting diode which needs the exact control of temperature. These results should be useful for the application of the internal cooling system to the double heterojunction diode used in the optical communication.     

Effect of poly silicon thickness on the formation of Ni-FUSI gate by using atomic layer deposited nickel film

The effect of poly-Si thickness on silicidation of Ni film was investigated by using X-ray diffraction, auger electron spectroscopy, cross-sectional scanning transmission electron microscopy, resistivity, I–V, and C–V measurements. The poly-Si films with various thickness of 30–200 nm were deposited by LPCVD on thermally grown 50 nm thick SiO₂, followed by deposition of Ni film right after removing the native oxide. The Ni film was prepared by using atomic layer deposition with a N²-hydroxyhexafluoroisopropyl-N¹ (Bis-Ni) precursor. Rapid thermal process was then applied for a formation of fully silicide (FUSI) gate at temperature of 500 °C in N₂ ambient during 30 s. The resultant phase of Ni-silicide was strongly dependent on the thickness of poly-Si layer, continuously changing its phase from Ni-rich (Ni₃Si₂) to Si-rich (NiSi₂) with increasing the thickness of the poly-Si layer, which is believed to be responsible for the observed flat band voltage shift, ΔV_FB, in C–V curves.     

Titanium Doping to Enhance Thermoelectric Performance of 19-Electron VCoSb Half-Heusler Compounds with Vanadium Vacancies

The 19-electron VCoSb compounds are actually composites of an off-stoichiometric half-Heusler phase and impurities. Here the compositional adjustment is systematically studied in V_1−xCoSb to obtain single-phase V_0.955CoSb. Hall measurements suggest that such a V vacancy, as well as Ti doping, can optimize the carrier concentration, which decreases from ≈11.3 × 10²¹ cm⁻³ for VCoSb to ≈6.3 × 10²¹ cm⁻³ for V_0.755Ti_0.2CoSb. Low sound velocity contributes to the intrinsically low lattice thermal conductivity for VCoSb-based materials. The high Ti-dopant content results in enhanced point-defect scattering, which further decreases the lattice thermal conductivity. Finally, the optimized n-type V_0.855Ti_0.1CoSb is found to reach a peak ZT of ≈0.7 at 973 K. The work demonstrates that the VCoSb-based half-Heuslers are promising thermoelectric materials.     

Quasiteilchen und Eigenwerte des Lippmann-Schwinger-Kerns

In the following we investigate several properties of the eigenvalues of the Lippmann-Schwinger kernel for potentials of Yukawa-type. In particular we derive the analogue of the Dashen-Frautschi formula, which was recently used for the calculation of the neutron-proton mass difference, and extend the result to resonances. We then use the eigenvalues of the Lippmann-Schwinger kernel to obtain a necessary and sufficient condition for the quotient of two Jost functions (corresponding to distinct potentialsV ₁,V ₂) to be the Jost function corresponding to the difference of their potentials (V ₁-V ₂). The result leads to separable potentials. Finally we examine the classical analogues of the vertex and wave-function renormalization constants and discuss the relationship betweenWeinberg's theory of quasiparticles andBohr's compound model of the atomic nucleous.     

Structural and elastic properties of Ce2O3 under pressure from LDA+U method

We investigate the structural and elastic properties of hexagonal Ce₂O₃ under pressure using LDA+U scheme in the frame of density functional theory (DFT). The obtained lattice constants and bulk modulus agree well with the available experimental and other theoretical data. The pressure dependences of normalized lattice parameters a/a ₀ and c/c ₀, ratio c/a, and normalized primitive volume V/V ₀ of Ce₂O₃ are obtained. Moreover, the pressure dependences of elastic properties and three anisotropies of elastic waves of Ce₂O₃ are investigated for the first time. We find that the negative value of C ₄₄ is indicative of the structural instability of the hexagonal structure Ce₂O₃ at zero temperature and 30 GPa. Finally, the density of states (DOS) of Ce₂O₃ under pressure is investigated.     

Wegner-type Bounds for a Two-particle Lattice Model with a Generic “Rough” Quasi-periodic Potential

In this paper, we consider a class of two-particle tight-binding Hamiltonians, describing pairs of interacting quantum particles on the lattice ℤ ^d , d ≥ 1, subject to a common external potential V(x) which we assume quasi-periodic and depending on auxiliary parameters. Such parametric families of ergodic deterministic potentials (“grands ensembles”) have been introduced earlier in Chulaevsky (2007), in the framework of single-particle lattice systems, where it was proved that a non-uniform analog of the Wegner bound holds true for a class of quasi-periodic grands ensembles. Using the approach proposed in Chulaevsky and Suhov (Commun Math Phys 283(2):479–489, 2008), we establish volume-dependent Wegner-type bounds for a class of quasi-periodic two-particle lattice systems with a non-random short-range interaction.     

Atomic displacements due to interstitial hydrogen in Cu and Pd

The density functional theory (DFT) is used to study the atomic interactions in transition metal-based interstitial alloys. The strain field is calculated in the discrete lattice model using Kanzaki method. The total energy and hence atomic forces between interstitial hydrogen and transition metal hosts are calculated using DFT. The norm-conserving pseudopotentials for H, Cu and Pd are generated self-consistently. The dynamical matrices are evaluated considering interaction up to first nearest neighbors whereas impurity-induced forces are calculated with M₃₂H shell (where M = Cu and Pd). The atomic displacements produced by interstitial hydrogen at the octahedral site in Cu and Pd show displacements of 7.36% and 4.3% of the first nearest neighbors respectively. Both Cu and Pd lattices show lattice expansion due to the presence of hydrogen and the obtained average lattice expansion ΔV/V = 0.177 for Cu and 0.145 for Pd.      

The quadrupole interaction at181Ta in Zn

The quadrupole interaction (QI) in hexagonal close packed zinc lattice was measured using the 482 keV, 10.6 ns probe state of¹⁸¹Ta employing the time-differential perturbed angular correlation technique. The electric field gradient (EFG) at¹⁸¹Ta in Zn was derived from the measured quadrupole interaction frequency at room temperature asV _zz =12.202×10¹⁷ V/cm². The quadrupole interaction measured at various temperatures displayed normal temperature dependence similar to that seen by this probe in many non-cubic hosts.     

Directional solidification of Ti–49 at.%Al alloy

Ti–49Al (at.%) alloy was directionally solidified in Bridgman-type directional solidification furnace. The specimens were directionally solidified under an argon atmosphere with the different growth rate (V=5–30 μm/s) at a constant temperature gradient (G=12.1 K/mm), and with the different temperature gradient (G=2.8–12.1 K/mm) at a constant growth rate (V=10 μm/s). The dendritic spacings (λ ₁) were measured from both transverse and longitudinal sections of the specimens. The dependence of λ ₁ on the growth rate (V) and temperature gradient (G) were determined by using linear regression analysis. According to the experimental results, the value of λ ₁ decreases with the increase of values of V and G. The experimental results were compared with the current theoretical and numerical models, and similar previous experimental results.