Trigonal warping of the Fermi surface in n-Bi2Se3

Shubnikov-de Haas investigations on n-type Bi₂Se₃ single crystals were performed in magnetic fields up to 10.5 Tesla (105 kG). The shape of the single-valley Fermi surfaces is almost an ellipsoid of revolution around the trigonal k_c-axis, the longest main axis of the Fermi surface. There is a small amount of flattening in the direction of the k_c-axis and of trigonal warping around the k_c-axis, caused by higher order terms than [k²] in the ?(k) relation.     

Calculations of mass and moment of inertia for neutron stars

Masses and moments of inertia for slowly-rotating neutron stars are calculated from the Tolman-Oppenheimer-Volkoff equations and various equations of state for neutron-star matter. We have also obtained pressure and density as a function of the distance from the centre of the star. Generally, two different equations of state are applied for particle densities n > 0.47 fm^?3 and n < 0.47 fm^?3.The maximum mass is, in our calculations for all equations of state except for the unrealistic non-relativistic ideal Fermi gas, given by 1.50 M_⊙ < M < 1.82 M_⊙, which agrees very well with “experimental results”. Corresponding results for the maximum moment of inertia are 9.5 × 10⁴⁴ g · cm² < I < 1.58 × 10⁴⁵ g · cm², which also seem to agree very well with “experimental results”. The radius of the star corresponding to maximum mass and maximum moment of inertia is given by 8.2 km < R < 10.0 km, but a smaller central density ρ_c will give a larger radius.     

Anderson localization and superconducting transition temperature in two-dimensional systems

Effects of the Anderson localization on superconducting transition temperature T_c are examined by calculating a two-electron propagator K rigorously up to 0[(?_Fτ₀)^?1ln(Tτ₀)], where τ₀ is the electron life time due to impurity scattering and ?_F the Fermi energy. The results show that in K the pair-breaking terms cancel out among themselves exactly and the remaining terms which contribute to the correction to the density of states and to the renormalization of electron-electron interaction by impurity scattering lead to the changes in T_c of 0[{ln(Tτ₀)}²] and of 0[{ln(Tτ₀)}³], respectively.     

Nuclear matter approach to the heavy-ion optical potential: (II). Imaginary part

The heavy-ion optical potentials are constructed in a nuclear matter approach, for the ¹⁶O + ¹⁶O, ⁴⁰Ca + ¹⁶O and ⁴⁰Ca + ⁴⁰Ca elastic scattering at the incident energies per nucleon E^lab/A ? 45 MeV. The energy density formalism is employed assuming that the complex energy density of colliding heavy ions is a functional of the nucleon density ?(r), the intrinsic kinetic energy density τ⁽²⁾(r) and the average momentum of relative motion per nucleon K_r(≦ 1.5 fm^?1). The complex energy density is numerically evaluated for the two units of colliding nuclear matter with the same values of ρ, τ⁽²⁾ and K_r. The Bethe-Goldstone equation is solved for the corresponding Fermi distribution in momentum space using the Reid soft-core interaction. The “self-consistent” single-particle potential for unoccupied states which is continuous at the Fermi surface plays a crucial role to produce the imaginary part. It is found that the calculated optical potentials become more attractive and absorptive with increasing incident energy. The elastic scattering and the reaction cross sections are in fair agreement with the experimental data.     

Supersymmetric approach to heavy-fermion systems

We present a new supersymmetric approach to the Kondo lattice model in order to describe simultaneously the quasiparticle excitations and the low-energy magnetic fluctuations in heavy-Fermion systems. This approach mixes the fermionic and the bosonic representation of the spin following the standard rules of superalgebra. Our results show the formation of a bosonic band within the hybridization gap reflecting the spin collective modes. The density of states at the Fermi level is strongly renormalized while the Fermi surface sum rule includes n _c + 1 states. The dynamical susceptibility is made of a Fermi liquid superimposed on a localized magnetism contribution.     

Observation of possible production and decay of short-living heavy neutral particles in the SKAT neutrino experiment

In the SKAT bubble chamber neutrino experiment production of a short-living neutral particle with mass (1.4?m?2.5) GeV/c² and lifetime τ≈6×10^?12 s has been detected. The event may be interpreted as production and decay of the heavy lepton M⁰→μ^?+e⁺+ν_e with mass (1.4?m_M⁰?2.1) GeV/c². It might also be the production of a charmed particle D⁰→e⁺+τ^?+ν_e (D⁰→e⁺+π^?+ν_e) with mass 1.4?m_D⁰?2.5) GeV/c² in a non-diagonal neutral current. The probability to interpret the event as other possible processes is very low.     

Large magnetoresistance in an inhomogeneous magnetic semiconductor

A new way of attaining large values of magnetoresistance in a magnetic semiconductor was investigated. The mechanism of magnetoresistance is based on the formation of a space charge, a depletion layer, and a contact potential U _c at the interface between two semiconductors with different Fermi levels E _n ^F and E _p ^f and on the dependence of U _c, the electrical resistivity, and the size of the depletion layer in the magnetic semiconductor on the magnetic field strength. The model proposed was experimentally verified using a microstructure consisting of an HgCr₂Se₄ n-layer with a thickness of up to several tens of microns deposited on the surface of a bulk p-HgCr₂Se₄ single crystal. Depending on microstructure parameters, a sharp (up to ～30 times) rise in the current flowing through the n-layer was observed in the region of Curie temperature upon switching on a magnetic field (H～15 kOe).     

Anisotropic superconductivity in UPt3

A consistent picture of conventional superconductivity in UPt₃ is presented which explains qualitatively the gap anisotropy, the dependence of T_c on crystal perfection, the low value of the specific heat discontinuity at T_c and the induced magnetic form factor. The model obtained is based on results of a local density band calculation for UPt₃ which are in excellent agreement with photoemission experiments and on estimates of the strength and anisotropy of the electron-phonon interaction. The key feature is anisotropy of the superconducting energy gap which arises from the variation of the electronic mass on the Fermi surface.     

Natural orbitals,diatomic molecules and ERD

The effects of molecular motions on spin-echo signals (2n + 1)90°_y—τ—90°_x:—Acq(t) in nuclear spin systems with dipolar interactions have been investigated. It was found that in the case of a rigid lattice (M₂τ² _c: >> 1) and a motionally narrowed NMR line (M₂τ² _c,<< 1) a maximum of echo signals is observed at t_e = 2τ + t₂—t₁/2, where t₁ and t₂ are the widths of the RF pulses. It also was found that in the slow motion region (M₂τ² _c ? 1) an amplitude of the dipolar echo signal is reduced and the maximum of the echo signal is shifted to the end of the second pulse. The theory developed is confirmed by the experimental results obtained for C₆H₆.     

de Haas van Alphen (dHvA) effect in two-dimensional (2D) conductors: susceptibility oscillations

A new scheme for analyzing the de Haas van Alphen (dHvA) effect in nearly two dimensional (2D) metals (i.e. with nearly cylindrical Fermi surface) is presented. The envelope of the magnetic susceptibility oscillations is calculated in the entire range of magnetic fields and temperatures. The resulting envelope function is found to be proportional to a universal function of the dimensionless parameter Q=hω_c/k _B T. The upper (i.e. paramagnetic) branch of the susceptibility envelope has a maximum at a certain Q = 5.45. This universal value may be useful for determining the effective cyclotron mass and the Fermi energy of nearly 2D metals. A simple relation between magnetization oscillations amplitude and calculated susceptibility amplitudes is derived. The corresponding limiting formulae for the magnetization oscillations envelope are found to match smoothly around the value X = 2π²/Q?2 of the Lifshitz-Kosevich (LK) smearing parameter. The influence of Fermi surface sheets with open orbits on magneto-quantum oscillations is considered. Triangle-like rather than saw-tooth-like oscillations at ultralow temperatures are obtained and substantially diminished magnetization and susceptibility amplitudes are calculated. This suggests the possibility of estimating the band structure parameters of Fermi surface sheets from magneto-quantum oscillations measurements.     

Measurement of the spectral functions of vector current hadronic tau decays

A measurement of the spectral functions of non-strange τ vector current final states is presented, using 124 358 τ pairs recorded by the ALEPH detector at LEP during the years 1991 to 1994. The spectral functions of the dominant two- and four-pion τ decay channels are compared to published results of e ⁺ e ^- annihilation experiments via isospin rotation. A combined fit of the pion form factor from τ decays and e ⁺ e ^- data is performed using different parametrizations. The mass and the width of the ρ ^±(770) and the ρ ⁰(770) are separately determined in order to extract possible isospin violating effects. The mass and width differences are measured to be M _ρ ^± ₍₇₇₀₎ - M _ρ ⁰ ₍₇₇₀₎ = (0.0 ± 1.0) MeV/c ² and Γ _ρ ^± ₍₇₇₀₎ - Γ _ρ ⁰ ₍₇₇₀₎ = (0.1 ± 1.9) MeV/c ².     

The metal insulator transition in two-dimensional systems with charged impurities

The motion of interacting electrons in an array of charged impurities in two dimensions is discussed within a generalized selfconsistent current relaxation theory. The ratio of impurity density n_i to electron density n_c, where the metal insulator transition takes place, is shown to depend on n_c and varies between 0.2 and 10. A comparison of the theory with mobility measurements of Na⁺ drift experiments in inversion layers is made.     

Influence des marches atomiques sur le transport de matière à la surface du nickel

Surface atomic transport on Ni was measured by mass transport technique on a sinusoidal profile. One of the studied surfaces was within 15' of a singular (001) orientation. Others were vicinal surfaces. Kinetic damping coefficients $\text{1}\text{τ}$ are shown to be dependent on the profile parameters, i.e. of the density n_tot, of all the monoatomic steps and also of the density σ_c of kinks of the monoatomic steps. If the parameter describes the random motion of adatoms on isolated terraces and if α and k are two coefficients linked to adsorption/emission processes from steps and kinks, a sinusoidal profile with 5 μm periodicity obeys to the relation: $\text{1}\text{τ}\text{= (}\text{1}\text{τ}\text{)}{}_{\mathrm{T}}\text{[1+αn}{}_{\mathrm{tot}}{}^2\text{(1+ kσ}{}^2{}_{\mathrm{c}}\text{)]}$. This result demonstrates the importance of surface atomic structure which has been neglected in Mullins' theory, which may be non-negligible in all processes where surface mass transport is involved.     

Anomalous behavior of the surface tension at the interface of the metallic and insulating phases in the vicinity of the metal-insulator phase transition in a magnetic field

Mean-field equations describing the metal-insulator (MI) transition are formulated. They involve two coupled order parameters characterizing this transition: (i) a scalar order parameter describing the density change accompanying the transition from the insulating state to the metallic one and (ii) an order parameter (a two-component vector) describing the electron density in the metallic or semimetallic phase affected by the applied magnetic field. Two components of this vector correspond to different possible spin states of electrons in the applied magnetic field. The transition in the density of metallic and insulating phases being a first order phase transition is treated in terms of the Cahn-Hilliard-type gradient expansion. The transition in the electron density is a second order phase described by the Ginzburg-Landau-type functional. The coupling of these two parameters is described by the term linearly dependent on the electron density n in the metal with the proportionality factor being a function of the density of the metallic phase. The derived equations are solved in the case of the MI interface in the presence of both parallel and perpendicular uniform magnetic fields. The calculated surface tension Σ_mi between the metallic and insulating phases has a singular behavior. In the limit of zero electron density n ? 0, Σ_mi ～ n ^3/2. Near the MI transition point T _c(h) in the applied magnetic field, Σ_mi ～ [T - T _c(h)]^3/2. The singular behavior of the surface tension at the MI interface results in the clearly pronounced hysteresis accompanying the transition from the insulating to metallic state and vice versa.     

From the Bose-Einstein to fermion condensation

The appearance of the fermion condensation, which can be compared to the Bose-Einstein condensation, in different Fermi liquids is considered; its properties are discussed; and a large amount of experimental evidence in favor of the existence of the fermion condensate (FC) is presented. We show that the appearance of FC is a signature of the fermion condensation quantum phase transition (FCQPT), which separates the regions of normal and strongly correlated liquids. Beyond the FCQPT point, the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other, FC, localized at the Fermi level. In the superconducting state, the quasiparticle dispersion in systems with FC can be represented by two straight lines, characterized by effective masses M _FC ^* and M _L ^* and intersecting near the binding energy E₀, which is of the order of the superconducting gap. The same quasiparticle picture and the energy scale E₀ persist in the normal state. We demonstrate that fermion systems with FC have features of a “quantum protectorate” and show that strongly correlated systems with FC, which exhibit large deviations from the Landau Fermi liquid behavior, can be driven into the Landau Fermi liquid by applying a small magnetic field B at low temperatures. Thus, the essence of strongly correlated electron liquids can be controlled by weak magnetic fields. A reentrance into the strongly correlated regime is observed if the magnetic field B decreases to zero, while the effective mass M* diverges as \(M^ * \propto {1 \mathord{\left/ {\vphantom {1 {\sqrt B }}} \right. \kern-\nulldelimiterspace} {\sqrt B }}\). The regime is restored at some temperature \(T^ * \propto \sqrt B \). The behavior of Fermi systems that approach FCQPT from the disordered phase is considered. This behavior can be viewed as a highly correlated one, because the effective mass is large and strongly depends on the density. We expect that FCQPT takes place in trapped Fermi gases and in low-density neutron matter, leading to stabilization of the matter by lowering its ground-state energy. When the system recedes from FCQPT, the effective mass becomes density independent and the system is suited perfectly to be conventional Landau Fermi liquid.     

Structural and magnetic properties of Ti12M clusters (M=Sc to Zn)

The geometries, electronic, and magnetic properties of the 3d atom doped icosahedron (ICO) Ti₁₂M (M=Sc to Zn), where a dopant atom replaces either the centra l(Ti₁₂M^c) or surface (Ti₁₂M^s) Ti atom in ICO Ti₁₃ cluster, have been systematically investigated by using the density functional theory. The structures of all the optimized Ti₁₂M^c and Ti₁₂M^s clusters are distorted ICO. Sc, Ni, Cu, and Zn atoms prefer to displace surface Ti atom, V, Cr, Mn, and Fe atoms prefer to displace central Ti atom. The position of impurity atom depends on the strength of the interaction between the central atom and the surface atoms. As compared to the pure Ti₁₃ cluster, Ti₁₂M^c and Ti₁₂M^s (M=V, Fe, Co, and Ni) clusters are more stable, Ti₁₂M^c and Ti₁₂M^s (M=Sc, Cr, Mn, Cu, and Zn) are less stable. Both Ti₁₂Ni^s and Ti₁₂Ni^c are magic clusters, which originate from their electronic as well as geometric closed shells. Because the exchange interaction prevails over the crystal field in Ti₁₂M clusters, the valence electrons fill molecular orbitals in terms of Hund’s rule of maximum spin.     

On the dynamic conductivity for an electron-impurity system

The correlation function formula for the dynamic conductivity of a system of non-interacting electrons in the field of impurities is analyzed in terms of proper connected diagrams. By selecting those diagrams appropriate in the region of weak coupling and low impurity concentration, a set of coupled equations for the energy broadening γ (ω, ε, n_s) and the energy shift Δ(ω, ε, n_s) is derived, where both γ and Δ depend on the frequency ω of a probing field, the energy ε of the electron, and the concentration, n_g, of impurities. With the assumption of a finite range potential, these equations are solved. It is found that γ (ω, n_s) is smaller than that extrapolated value which the conventional expression γ₀ for the low-concentration collision frequency would predict, in the entire region studied, that the difference γ₀-γ becomes appreciable when the ratio of the average time between scatterings, τ_c, to the average duration of a scattering, τ_d, is 100 or less, that γ (ω, n_s) decreases monotonically from its static value γ (0, n_s), and becomes vanishingly small in the region ω≈1/τ_d, and that in the static limit (ω=0), γ=γ₀[1?(2/π) (γ₀τ_d)+…], that the energy shift Δ is positive, and increases from 0 and reach a peak of magnitude γ₀ as ω is raised from 0. By using the γ and Δ obtained, the dynamic conductivity σ(ω, n_s) for degenerated electrons is calculated. The deviation, σ-σ₀, from the conventional expression σ₀=(?i) (n_ee²/M) [ω-iΓ₀]^?1, (n_e]=number density of electrons), for 0°K, is appreciable when the ratio τ_c/τ_d is 100 or less. The field-term correction, which arises from the modification of the scattering due to the probing field, is found to be negligible in the entire region studied.     

NMR and NQR studies of spin dynamics and superconductivity in High-T c oxides

The magnetic and superconducting properties in the high-T _c cuprates have been investigated over a wide hole doping range by⁶³Cu,¹⁷O and²⁰⁵Tl NMR and NQR in the lightly-doped La_2?xSr_xCuO₄ (LSCO), the heavily-doped Tl₂Ba₂CuO_6+y (TBCO) and the Zn-doped YBa₂Cu₃O₇ (YBCO₇). In low doping region, the large antiferromagnetic (AF) spin correlation around the zone boundary (q=Q) causes the Curie-Weiss behavior of⁶³(1/T ₁ T) associated with that of the staggered susceptibility χ_O(T) in LSCO. In the vicinity of the hole content whereT _c has a peak, the AF spin correlation still survives, although the magnetic coherence length ξ_M is considerably short being presumably (ξ_M/a) ～ 1. The further doping destroys progressively the AF spin correlation, which is no longer present is non-superconducting TBCO compounds. These NMR evidences signify that there is an intimate relation between the presence of the AF spin correlation and the onset of the superconductivity. The local collapse of AF spin correlation is a primary cause for the unexpected strong reduction ofT _c in case of the substitution of Zn impurities into the CuO₂ plane. The superconducting properties clarified by NMR experiments cannot be accounted for by the conventional BCS model or other isotropic s-wave models. A d-wave model is applicable in interpreting consistently most of the NMR results, if the finite density of states at the Fermi level is taken into consideration and is associated with the pair breaking effect. There are increasing evidences that the magnetic mechanism for the superconductivity is promising in high-T _c cuprates.     

Thermodynamics of SU(3) lattice gauge theory

The pressure and the energy density of the SU(3) gauge theory are calculated on lattices with temporal extent N_τ = 4, 6 and 8 and spatial extent N_σ = 16 and 32. The results are then extrapolated to the continuum limit. In the investigated temperature range up to five times T_c we observe a 15% deviation from the ideal gas limit. We also present new results for the critical temperature on lattices with temporal extent N_τ = 8 and 12. At the corresponding critical couplings the string tension is calculated on 32⁴ lattices to fix the temperature scale. An extrapolation to the continuum limit yields T_c/√σ = 0.629(3). We furthermore present results on the electric and magnetic condensates as well as the temperature dependence of the spatial string tension. These observables suggest that the temperature dependent running coupling remains large even at T ≅ 5T_c. For the spatial string tension we find √σ_s/T=0.566(13)g²2(T) with g² (5T_c) ≅ 1.5.     

The quantum field as a quantum computer

It is supposed that at very small scales a quantum field is an infinite homogeneous quantum computer. On a quantum computer the information cannot propagate faster than c=a/τ, a and τ being the minimum space and time distances between gates, respectively. For one space dimension it is shown that the information flow satisfies a Dirac equation, with speed v=ζc and ζ=ζ(m) mass-dependent. For c the speed of light ζ−1 is a vacuum refraction index that increases monotonically from ζ−1(0)=1 to ζ−1(M)=∞, M being the Planck mass for 2a the Planck length. The Fermi anticommuting field can be entirely qubitized, i.e. it can be written in terms of local Pauli matrices and with the field interaction remaining local on qubits. Extensions to larger space dimensions are discussed.