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Institute: search.filters.UBSInstitut.Sonstige EinrichtungAuthor: search.filters.author.Trebin, Hans-Rainer

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    TRSS: a new version of program TRS for a different geometry
    (1992) Schmitz, Joachim; Trebin, Hans-Rainer; Rössler, Ulrich
    Quantum resonances in the bands of semiconductors under uniaxial stress provide very detailed information on the band parameters. However, the analysis of experimental data is difficult. Computer programs based on an adequate theoretical model make this task easier. Program TRSS calculates energy eigenvalues, wave functions and oscillator strengths for direct inter- and intraband dipole transitions. The magnetic field is applied parallel to the [001] crystal axis while the uniaxial stress is directed perpendicular [100] to it.
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    Liquid-crystalline blue phase III and structures of broken icosahedral symmetry
    (1993) Longa, Lech; Fink, Werner; Trebin, Hans-Rainer
    The structure of the liquid-crystalline blue phase III (BPIII) is still unknown and remains one of the mysteries of liquid-crystal physics. We take all icosahedral space-group symmetries of the reciprocal space for BPIII and study their thermodynamic stability within the frame of an extended de Gennes–Ginzburg–Landau free-energy expansion. The stability of the icosahedral structures is compared with that of the cholesteric phase and of the cubic blue phases. Strikingly, even though the extended model contains three extra parameters, we could not detect a region of parameter space where icosahedral structures are absolutely stable just below the isotropic phase.
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    Electrons and holes in InSb under crossed magnetic and stress fields. 1, Theory
    (1988) Trebin, Hans-Rainer; Wolfstädter, Bernd; Pascher, Harald; Häfele, Hans-Georg
    In a series of four papers magnetooptical transitions are presented for InSb crystals, which are subjected to uniaxial stress perpendicular to the magnetic field. Here, in the first paper, we establish an 8×8 k⋅p Hamiltonian matrix for stress Tǁ[100] and field Bǁ[001] and diagonalize it exactly. The dependence of valence and conduction states on stress and longitudinal momentum is discussed and compared with the geometry of parallel fields TǁBǁ[001]. Characteristic features are extracted for inter- and intraband transitions. Under crossed fields, the levels are separated much stronger with stress, yielding more insight than in the parallel configuration.
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    Theory of liquid crystalline phases in biaxial systems
    (1992) Longa, Lech; Trebin, Hans-Rainer
    General properties of SO(3) - symmetric free- energy expansion for biaxial systems are studied. In particular, all invariants in powers of a traceless and symmetric quadrupole tensor order parameter and a vector order parameter are identified and their relation to possible local structures are found. A new class of polar, chiral biaxial phases are predicted.
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    Spontaneous polarization in chiral biaxial liquid crystals
    (1990) Longa, Lech; Trebin, Hans-Rainer
    A phenomenological theory of polar structures in chiral biaxial liquid crystals is constructed exploiting the properties of a symmetric and traceless tensor order parameter field Q αβ(r) and of a polar field Pα(r). Full advantage is taken of the symmetry of the order parameters by systematic use of the method of integrity bases, which allows us to establish an expansion of the most general SO(3)-invariant free-energy density to arbitrary powers in the components Qαβ and Pα. A coordinate-independent parametrization of the invariants is introduced that yields a classification of local polar structures and some predictions about possible topologies of phase diagrams without the necessity of performing numerical calculations. As one prominent result, the theory predicts a polar, chiral biaxial state that exists due to a piezoelectric coupling of a chiral biaxial tensor field and the polarization field and which disappears if tensor is uniaxial. We then provide a general theory of flexopolarization in biaxial systems. A general biaxial system is described by 12 fundamental flexopolarization modes. Special cases, obtained by imposing symmetry restrictions to the tensor field Q, reduce the number of modes. Finally, the theory is applied to chiral phases. Simple polar chiral structures including cholesteric and smectic-C* liquid crystals are analyzed. In particular, it is shown that if the smectic-C* phase is stabilized due to the piezoelectric coupling between Q, P, and a density wave, then it must be described as a biaxial uniform spiral with at least two nonvanishing commensurate harmonics. The minimization of the quadratic part of the Landau–de Gennes energy supplemented by (flexo)polarization terms may give rise to incommensurate two- or three-dimensional polar structures that can be stabilized by cubic terms.
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    Electrons and holes in InSb under crossed magnetic and stress fields. 4, Stimulated Raman scattering in the valence bands
    (1988) Wolfstädter, Bernd; Trebin, Hans-Rainer; Pascher, Harald; Häfele, Hans-Georg
    In a series of four papers magnetooptical transitions are presented for InSb crystals, which are subjected to uniaxial stress perpendicular to the magnetic field. Here, in the first paper, we establish an 8×8 k⋅p Hamiltonian matrix for stress Tǁ[100] and field Bǁ[001] and diagonalize it exactly. The dependence of valence and conduction states on stress and longitudinal momentum is discussed and compared with the geometry of parallel fields TǁBǁ[001]. Characteristic features are extracted for inter- and intraband transitions. Under crossed fields, the levels are separated much stronger with stress, yielding more insight than in the parallel configuration.
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    Bond orientational order in the blue phases of chiral liquid crystals
    (1993) Longa, Lech; Trebin, Hans-Rainer
    It is proposed to describe blue phases by two order parameters: the standard alignment tensor field Q αβ(r) and a bond orientational tensor order parameter of octahedral point group symmetry scrO(432). The yet mysterious blue fog then emerges as a liquid of purely cubic bond orientational order. In the transition from the cubic blue phases to the blue fog the cubic space group symmetry is being reduced to its octahedral factor group. Because of the new order parameter the scrO 5(scrI432) structure, which in all previous calculations proved most stable, but never has been detected in experiment, is eliminated from the phase diagram.
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    Integrity basis approach to the elastic free energy functional of liquid crystals. 1, Classification of basic elastic modes
    (1989) Longa, Lech; Trebin, Hans-Rainer
    Using the method integrity basis, the most general SO(3)-invariant free energy density up to all powers in xβ and up to second order in Q xβ,y is established. The method provides all analytically independent elastic modes for nematics and cholesterics in the form of 33 so-called, irreducible invariants. Interestingly, among the irreducible invariants there are only three chiral terms (i.e. linear in Q δ,β,y ). They give rise locally to three independent helix modes in chiral, biaxial liquid crystals. This conclusion generalizes results of Trebin and Govers and Vertogen and contradicts a statement of Pleiner and Brandt, according to which only one twist term is supposed to exist. The most general free energy expansion can be written as sum of 39 additive invariants, which are multiplied by arbitrary polynomials in TrQ 2 and TrQ 3.
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    Diffusion in 2D quasi-crystals
    (1994) Joseph, Dieter; Baake, Michael; Kramer, Peter; Trebin, Hans-Rainer
    Self-diffusion induced by phasonic flips is studied in an octagonal model quasi-crystal. To determine the temperature dependence of the diffusion coefficient, we apply a Monte Carlo simulation with specific energy values of local configurations. We compare the results of the ideal quasi-periodic tiling and a related periodic approximant and comment on possible implications to real quasi-crystals.
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    Stability of monatomic and diatomic quasicrystals and the influence of noise
    (1990) Roth, Johannes; Schilling, Rolf; Trebin, Hans-Rainer
    The stability of quasicrystals endowed with atomic Lennard-Jones–like pair potentials was investigated with use of the method of steepest descent. Starting from two- and three-dimensional Penrose patterns, the basic units were decorated in various fashions with one or two sorts of atoms. In accord with previous studies, all monatomic two-dimensional quasicrystals decay to a hexagonal periodic crystal with defects; diatomic systems remain stable when the relative size of the atoms is suitably chosen. In three dimensions, the monatomic quasicrystalline unit-sphere packing was proven stable as well as the structure of truncated icosahedra, even if in the initial configuration the atoms were displaced statistically up to 7% and 25%, respectively, of the edge length (noise). A series of decorations (among them one involving Mackay icosahedra) relaxed to the amorphous state. In these transitions the atoms arrange in families of Fibonacci planes whose separations scale down to atomic distances in a self-similar fashion.