Session B1: DCMP/DCOMP Prize Session

Curvature, chirality, and polar symmetry in liquid crystals

Charles Frank taught us the relationship between curvature and polarity in liquid crystals. He showed that polar ordering of dipolar molecules, with the polar axis parallel to the nematic director, would lead to spontaneous splay deformation of the otherwise uniaxial nematic state. Likewise, he showed that molecular chirality leads to spontaneous twisting of the director field, resulting in the helicoidal textures of chiral nematics. Augmenting Frank's insight on polarity induced splay with the realization that bend induces polarization perpendicular to the director, led to the concept of curvature induced polarization of liquid crystals, or flexoelectricity. The concepts of chirality induced twist and bend induced polarization became intimately combined in the case of chiral smectic C liquid crystals. The chirality induced twisting of the molecular tilt direction from layer to layer in the smectic produces a helical state incorporating both spontaneous twist and bend, and therefore inducing polarization in the smectic layers, normal to the molecular tilt direction. Thus, Frank's original insights led eventually to the discovery of ferroelectric liquid crystals. In fact, spontaneous polarization and helical order are independent consequences of molecular chirality in tilted smectics. The fundamental combination of monoclinic local symmetry in the smectic C phase with molecular chirality leads directly to spontaneous polarization, with no requirement of helical twisting. This realization leads to generalizations of ferroelectricity to include anti-ferroelectric and ferri-electric smectics, among the fascinating array of polar liquid crystal phases. The consequences of these concepts in fundamental science, materials development, and applications will be reviewed.   

Liquid Crystal Phases of Molecular Bananas: Polarity and Chirality as Broken Symmetries

The study of the interplay of chirality and polarity has been a particularly rich theme of soft matter science since Meyer's seminal discovery that tilted smectics of chiral molecules are macroscopically polar. This event, and the subsequent realization of polar domains and high-speed electro-optic switching in chiral smectics, engaged the liquid crystal community in a worldwide pursuit of novel smectics for applications, featured by the synthesis of more than 50,000 new liquid crystal compounds, and by a consequent broad diversification of the palette of liquid crystal phases and possibilities for supermolecular ordering. A current important activity in this scenario is the study of polar order in synthetically achiral molecules, for example, in molecular bananas, which, as their shape suggests, might be expected to organize in a polar way. Indeed they do, but beyond this, almost everything learned about them has been surprising, including their persistent tendency to exhibit chirality as a spontaneously broken symmetry. I will discuss some of these new phases and phenomena, including the discovery of fluid conglomerates (Pasteur's experiment in a fluid), triclinic fluid order, chiral twist grain boundary phases of achiral molecules, chirality flipping and field-induced deracemization, ferroelectric and antiferroelectric phases with supermolecular- scale polarization modulation, and chiral thermotropic sponge phases.   

Generating Coherent Phonons and Spin Excitations with Ultrafast Light Pulses

Recent work on the generation of coherent low-lying excitations by ultrafast laser pulses will be reviewed, emphasizing the microscopic mechanisms of light-matter interaction. The topics covered include long-lived phonons in ZnO [C. Aku-Leh, J. Zhao, R. Merlin, J. Men\'{e}ndez and M. Cardona, \textit{Phys. Rev.B }\textbf{71}, 205211 (2005)], squeezed magnons [J.~Zhao, A. V. Bragas, D. J. Lockwood and R. Merlin, \textit{Phys. Rev. Lett.} \textbf{93}, 107203 (2004)], spin- and charge-density fluctuations [J. M. Bao et al., \textit{Phys. Rev. Lett.} \textbf{92}, 236601 (2004)] and cyclotron resonance [J. K. Wahlstrand, D. M. Wang, P. Jacobs, J. M. Bao, R. Merlin, K. W. West and L. N. Pfeiffer, AIP Conference Proceedings \textbf{772 }(2005), p. 1313] in GaAs quantum wells. In addition, unpublished results on surface -avoiding phonons in GaAs-AlAs superlattices [M. Trigo et al., \textit{unpublished}] and magnons in ferromagnetic Ga$_{1-x}$Mn$_{x}$As [D. M. Wang et al., \textit{unpublished}] will be discussed. It will also be shown that frequencies can be measured using pump-probe techniques with a precision comparable to that of Brillouin scattering. It is now widely accepted that stimulated Raman scattering (SRS) is (often but not always) the mechanism responsible for the coherent coupling. Results will be presented showing that SRS is described by two separate tensors, one of which accounts for the excitation-induced modulation of the susceptibility, and the other one for the dependence of the amplitude of the oscillation on the light intensity [T. E. Stevens, J. Kuhl and R. Merlin, \textit{Phys. Rev.} B \textbf{65}, 144304 (2002)]. These tensors have the same real component, associated with \textit{impulsive }coherent generation, but different imaginary parts. If the imaginary term dominates, that is, for strongly absorbing substances, the mechanism for two-band processes becomes \textit{displacive }in nature, as in the DECP (displacive excitation of coherent phonons) model. It will be argued that DECP is not a separate mechanism, but a particular case of SRS. In the final part of the talk, an attempt will be made to identify emerging areas of research on coherent excitations and coherent control, relevant to condensed matter systems, that could benefit from ultrafast electron and x-ray diffraction studies.   

Berry Phases and Curvatures in Electronic-Structure Theory.

In the last fifteen years, Berry phases have been found to play an increasingly important role in electronic-structure theory. I will briefly review some of the important developments in which Berry phases have been involved, starting with the modern theory of polarization$^1$ and the closely related theory of Wannier functions and their Wannier centers.$^2$ Next, I will discuss the theory of insulators in finite electric fields,$^3$ in which the field is taken to couple linearly to the Berry-phase polarization. I will then conclude by discussing the role of Berry phases and Berry curvatures in systems in which time-reversal symmetry has been broken, and in particular, the theory of orbital magnetization$^4$ and the anomalous Hall effect in ferromagnets. \begin{itemize} \item[{[1]}] R.D.~King-Smith and D.~Vanderbilt, Phys. Rev. B {\bf 47}, 1651 (1993). \item[{[2]}] Nicola Marzari and D.~Vanderbilt, Phys. Rev. B {\bf 56}, 12847 (1997). \item[{[3]}] I.~Souza, J.~\'I\~niguez, and D.~Vanderbilt, Phys. Rev. Lett. {\bf 89}, 117602 (2002). \item[{[4]}] T.~Thonhauser, D.~Ceresoli, D.~Vanderbilt, and R.~Resta, Phys. Rev. Lett. {\bf 95}, 137205 (2005). \end{itemize}