Universität Stuttgart
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Item Open Access Electrons and holes in InSb under crossed magnetic and stress fields. 1, Theory(1988) Trebin, Hans-Rainer; Wolfstädter, Bernd; Pascher, Harald; Häfele, Hans-GeorgIn 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.Item Open Access Temperature dependence of the elastic constants for biaxial nematic liquid crystals(1989) Monselesan, Didier; Trebin, Hans-RainerThe elastic constants K ij of the Frank-Oseen energy density for uniaxial nematic liquid crystals depend on the Maier-Saupe order parameter S and hence on temperature. Longa et al. recently used an extended Landau-Ginzburg-de Gennes theory to expand the functions K ij(S) up to fourth order in S. Here, a similar procedure is applied for the elastic energy density of biaxial nematic liquid crystals. The three chiral and 15 achiral constants are expressed as fourth-order polynomials in the order parameter S and the degree of biaxiality T. Via the temperature dependence of the quantities S and T also the temperature dependence of the elastic constants is fixed.Item Open Access Metallic glasses and chiral nematic liquid crystals(1987) Trebin, Hans-Rainer; Longa, Lech; Salzgeber, BennoGeometrical frustration exists in both metallic glasses and chiral nematic liquid crystals. Applying results from the Landau-Ginzburg theory of liquid crystals and from polytope models for the amorphous state, a frustrated free-energy density for metallic glasses is derived. It is expressed in terms of an order parameter that characterizes the bond orientation of neighbouring atoms.Item Open Access Structure of the elastic free energy for chiral nematic liquid crystals(1989) Longa, Lech; Trebin, Hans-RainerIn Landau–de Gennes theory, the free energy f of liquid crystals is expanded into powers of a symmetric, traceless tensor order parameter Q αβ and its derivatives Q αβ,γ. The expansion is subject to the condition that f is a scalar, i.e., invariant under all rotations of the group SO(3). Using the method of integrity basis, we have established the most general SO(3)-invariant free-energy density up to all powers in Q αβ and up to second order in Q αβ,γ. It turns out that this free-energy density is composed of 39 invariants, which are multiplied by arbitrary polynomials in TrQ 2 and TrQ 3. On the other hand, these 39 invariants can be expressed as polynomials of 33 so-called irreducible invariants. Interestingly, among the irreducible invariants there are only three chiral terms (i.e., linear in Q αβ,γ). They locally give rise to three independent helix modes in chiral, biaxial liquid crystals. This conclusion generalizes results of Trebin [J. Phys. (Paris) 42, 1573 (1981)] and Govers and Vertogen [Phys. Rev. A 31, 1957 (1985); 34, 2520 (1986)] and contradicts a statement of Pleiner and Brand [Phys. Rev. A 24, 2777 (1981); 34, 2528 (1986)], according to which only one twist term is supposed to exist.Item Open Access Integrity basis approach to the elastic free energy functional of liquid crystals. 1, Classification of basic elastic modes(1989) Longa, Lech; Trebin, Hans-RainerUsing 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.Item Open Access Disclinations in quasicrystals [Erratum](1987) Bohsung, Jörg; Trebin, Hans-RainerThe most significant feature in the transition from the quasicrystalline to the amorphous state is the loss of long-range bond-orientational order. Disclinations are candidates for elementary excitations which destroy angular correlations. Generalizing the topological defect classification, we investigate point singularities in two-dimensional pentagonal quasicrystals and construct disclinations, dislocations, and disclination dipoles.Item Open Access 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-GeorgIn 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.Item Open Access Flüssigkristalline Blaue Phasen : 100 Jahre Flüssigkristalle(1988) Trebin, Hans-RainerVor hundert Jahren hat man erstmals Flüssigkeiten als eigenständige Phasen identifiziert, die wie ein Kristall das Licht doppelt brechen und daher flüssige Kristalle genannt werden. Noch besser trifft diese Bezeichnung zu auf die sog. Blauen Phasen, die ebenfalls schon vor hundert Jahren durch eine Lichterscheinung auffielen, deren Struktur aber erst in den letzten zehn Jahren aufgeklärt wurde. Die Moleküle der Blauen Phasen bilden nämlich mit ihren Anisotropieachsen ein dreidimensionales periodisches Orientierungsmuster. Die Einheitszelle von ca. 300 nm Durchmesser ist flüssig und faßt 10 7 Moleküle. Man beobachtet Phänomene wie bei atomaren Kristallen: selektive Lichtstreuung (aber im sichtbaren Spektrum), Facettenwachstum, Versetzungen.Item Open Access An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals(1987) Longa, Lech; Monselesan, Didier; Trebin, Hans-RainerUsing angular momentum representation a method is proposed that allows the systematic construction of a generalized Landau-de Gennes elastic free energy of liquid crystals, in powers of a symmetric and traceless tensor order parameter, polarization field, of external fields and all respective derivatives. By this method all linearly independent elastic invariants and surface terms are constructed for nematics and cholesterics up to fourth order terms. In particular it is shown that up to fourth order in the tensor order parameter there are nineteen bulk elastic constants and four surface terms in the free energy of a general, biaxial nematic. In addition, the stability of this expansion is studied in detail. Some special cases of the elastic free energy of liquid crystals, already discussed in the literature, are reexamined and discrepancies with our results are emphasized. Finally, a thermo-dynamically correct way of establishing contact between the generalized de Gennes elastic free energy and other theories, like those of Oseen-Frank or Meyer, is proposed by applying fluctuation theory. Thus, the degeneracy of splay and bend elastic constants is removed even when these are calculated from the standard de Gennes free energy. Restrictions on higher order elastic constants are also obtained by comparing mean field relations and stability conditions with available experimental data.Item Open Access Electrons and holes in InSb under crossed magnetic and stress fields. 3, Magnetoreflection(1988) Wolfstädter, Bernd; Trebin, Hans-Rainer; Pascher, Harald; Häfele, Hans-GeorgIn 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. We have investigated the electronic interband transitions close to the band gap of InSb by observing magnetoreflectivity under uniaxial stress. The sensitivity of the experiment was increased by application of a magnetic-field-modulation technique. By this method we can resolve transitions from the conduction band to various valence-band Landau levels. The measurements were carried out with light polarized linearly along and perpendicular to the magnetic induction B (EǁB and E⊥B). In addition to well-known electric dipole resonances we observed new transitions induced by stress. These additional lines are connected with transition matrix elements which arise from lowering the symmetry. The observed transition energies are compared with band-structure calculations.