V. M. Zhilin

Polar smectic subphases: Phase diagrams, structures and X-ray scattering

We analyze a discrete phenomenological model accounting for phase transitions and structures of polar Smectic-C* liquid-crystalline phases. The model predicts a sequence of phases observed in experiment: antiferroelectric SmCA*–ferrielectric SmCFI1*–antiferroelectric SmCFI2* (three-and four-layer periodic, respectively)–incommensurate SmCα*–SmA. We find that, in the three-layer SmCFI1* structure, both the phase and the module of the order parameter (tilt angle) differ in smectic layers. This modulation of the tilt angle (and therefore of the layer spacing d) must lead to X-ray diffraction at the wave vectors Qs=2πs/d(s=n±1/3) even for the nonresonant scattering.

Ferrielectric smectic phase with a layer-by-layer change of the two-component order parameter

One of the most remarkable properties of smectics is the wide variety of possible equilibrium structures. In this paper, based on the Landau theory of the phase transitions, the transitions between ferroelectric and antiferroelectric phases and the structure formed by smectic layers with different azimuthal and polar orientations of the molecules were calculated. This unique structure has been predicted [P.V. Dolganov et al., JETP Lett. 76, 498 (2002)] using the minimization of the free energy with respect to the phase and modulus of the two-component order parameter, but never before detected. Recently, a nonresonant Bragg reflection, consistent with the predictions of the model, was found [P. Fernandes et al., Eur. Phys. J. E 20, 81 (2006)] in the ferrielectric smectic C*FI1(SmC*FI1) phase. In the three-layer ferrielectric structure with a macroscopic helical pitch, the modulus of the order parameter is larger in anticlinic-like layers and smaller in layers with mixed ordering. The values of the interlayer interactions were determined for smectic liquid-crystalline materials forming different polar structures.

Laws of formation of polar smectic phases under a frustrated interaction

The Landau theory of phase transitions with a two-component order parameter is used to systematically calculate the structures and phase diagrams of polar liquid crystals. Commensurate and incommensurate structures with a layer-type period form as a result of a frustration interaction. Phase diagrams are calculated when various short- and long-range interlayer interactions are sequentially introduced. As a result, the nature of formation of various structures is revealed. The calculated phase diagrams explain the formation of various phases, their temperature sequence (including so-called “unusual” sequence of phases), and the nature of forces responsible for the formation of a certain structure and the shape of a phase diagram.

Formation and structure of a soliton in an antiferroelectric liquid crystal in an electric field

The soliton structure in an antiferroelectric liquid crystal in an electric field is calculated in the discrete phenomenological Landau model for phase transitions. The anticlinic structure of the antiferroelectric crystal gives rise to nontrivial features of the soliton structure and the stability of the soliton. The soliton is topologically stable in a metastable state if the electric field is much higher than the field of antiferroelectric-helix unwinding. A structural transition with a step-like change in the orientation of molecules occurs as the soliton field varies. A peculiar soliton (synclinic pair) can be formed if the barrier between the anti- and ferroelectric structures is large. The calculation shows the possibility of a large electroclinic effect in the soliton, i.e., a variation in the molecular tilt angle in an electric field in the vicinity of the transition of the structure to the synclinic state.

Excitonic representation: Collective excitation spectra in the quantized Hall regime and spin biexciton

The excitonic representation method for describing collective excitations in the quantized Hall regime makes it possible to simplify analysis of the spectra and to obtain new results in the strong magnetic field limit, when EC≪ħωc (ωc is the cyclotron frequency and EC is the characteristic Coulomb energy). For an integer odd filling factor ν greater than unity (i.e., for ν = 3, 5, 7,...), the spectra of one-cyclotron magneto-plasma excitations are calculated. For unit filling factor, the existence of a spin biexciton (bound state of two spin waves) corresponding to excitation with a spin change (δS = δSz = −2) is proved. The exact equation determining the ground state of the biexciton is derived in the thermodynamic limit NΦ → ∞ (Nϕ is the system degeneracy). The exchange energy of this state is lower than for a single spin wave (with δS = δSz = −1) for the same value of the 2D wavevector q. In the limit q → ∞ corresponding to the decay of a biexciton into a pair of quasiparticles one of which is a trion with a spin of −3/2, the energy is found to be lower than the energy (e2/εlB)√π/2 required for exciting an electron-hole pair in the strictly 2D case (lB is the magnetic length and ε is the dielectric constant), although this energy is higher than another “classical” result (e2/εlB)√π/2, corresponding to the excitation of a skyrmion-antiskyrmion pair (|δS|=|δSz|≫1). The solution of the exact equation gives the trion binding energy and the activation gap for quasiparticles whose excitation corresponds to a change in the total spin by δS = δ Sz =−3. The energy of a spin biexciton is calculated for values of the wavevector such that qlB≫1.

Electric-field-induced unwinding of ferroelectric helix in thin smectic C* layers with soft and rigid anchoring of molecules

The unwinding of a helical structure in thin films of a ferroelectric smectic liquid crystal (LC) by an external electric field has been theoretically studied using a discrete model in which every LC layer is characterized by a two-dimensional vector ξi (describing the orientation of molecules) and by the polarization Pi. It is established that the unwinding of the LC helix in thin films significantly differs from the well-known behavior of thick samples. In particular, discrete intermediate states (differing by an integer or half-integer number of turns) are formed in thin films for both weak and strong anchoring of molecules to a substrate surface. The physical factor responsible for this behavior is the presence of near-surface regions with thicknesses below the helix pitch and the corresponding uncompensated polarization.

Spectral investigations of surface ordering in ultrathin molecular films

Surface molecular ordering in ultrathin molecular films is investigated. The optical transmission spectra of molecular films ranging in thickness from 2 to 13 smectic layers (6.7–43 nm) in the region of the electronic absorption bands in the smectic A phase of cyanobiphenyl CB9 are measured. The thickness and temperature dependences of the permittivity are determined. It is found that the orientational ordering of the molecules depends on the film thickness. The penetration depth of the surface molecular orientational order does not exceed two smectic layers (<7 nm).

Donors in a strong magnetic field and elastic magnetic-impurity resonance in diamondlike semiconductors

The possibility of resonance during elastic intravalley scattering in n-type semiconductors is investigated in connection with the crossing (due to anisotropy of the effective mass) of the energy levels of excited states of a shallow donor as functions of the magnetic field. The hybridization of states of different frequencies in the vicinity of a crossing is attributed to the emergence of a nonzero dipole moment of the excited impurity atom and, accordingly, a long-range potential, which creates carrier-transport anomalies. The lower part of the donor spectrum is calculated as a function of the magnetic field in Si with B∥〈001〉 and in Ge with B∥〈111〉 or B∥〈110〉. A crossing occurs in Ge in the field range 9.9 T<B<16.7 T and in Si in the field range 10.5 T<B<37.7 T. The characteristic longitudinal relaxation time and the transverse conductivity, which are determined by scattering at excited donors in the presence of the hybridization of states, are calculated.

Elastic magnetoimpurity resonance in diamond-like semiconductors (intravalley scattering)

The scattering by an excited neutral donor in Ge and Si near an energy-level crossing (on account of anisotropy of the effective mass) of the electronic states of the impurity as a function of the magnetic field is investigated. The crossing of the 2s-and 2p-like levels leads to the appearance of a nonzero dipole moment of the impurity atom and, therefore, a long-range potential, which is responsible for characteristic features in carrier transport. The transverse impurity conductivity is calculated.