Condensed Matter Theory

Abstract:

Colloidal assembly in strongly confined cholesteric structures is demonstrated using phenomenological modelling. Particle trapping sites and trapping potentials, which are intrinsically imposed by the strongly anisotropic orientational profile of the confined blue phases, are calculated. Locations of the trapping sites and profiles of the trapping potentials are shown to depend importantly on the particle size, and the array of trapping sites can even change symmetry. Trapping sites provide robust binding of various colloidal structures with binding energy of ∼100kT for ∼100 nm particles. Maximising the filling of the trapping sites by particles proves to lower the full free energy of the system, offering means for thermodynamic stabilisation of confined blue phases. Finally, we present formation of disclination cages, formed as a three-dimensional closed network of defect lines surrounding sufficiently large particles with strong homeotropic anchoring. © 2011 The Royal Society of Chemistry.

Abstract:

Colloids with patchy metal coating under laser irradiation could act as local sources of heat due to the absorption of light. While for asymmetric colloids this could induce self-propulsion, it also leads to the generation of a slowly decaying temperature profile that other colloids could interact with. The collective behavior of a dilute solution of such thermally active particles is studied using a stochastic formulation. It is found that when the Soret coefficient is positive, the system could be described in stationary-state by the nonlinear Poisson-Boltzmann equation and could adopt density profiles with significant depletion in the middle region when confined. For colloids with negative Soret coefficient, the system can be described as a dissipative equivalent of a gravitational system. It is shown that in this case the thermally active colloidal solution could undergo an instability at a critical laser intensity, which has similarities to supernova explosion.

Abstract:

We consider the Chalker-Coddington network model for the integer quantum Hall effect, and examine the possibility of solving it exactly. In the supersymmetric path integral framework, we introduce a truncation procedure, leading to a series of well-defined two-dimensional loop models with two loop flavors. In the phase diagram of the first-order truncated model, we identify four integrable branches related to the dilute Birman-Wenzl-Murakami braid-monoid algebra and parameterized by the loop fugacity n. In the continuum limit, two of these branches (1,2) are described by a pair of decoupled copies of a Coulomb-gas theory, whereas the other two branches (3,4) couple the two loop flavors, and relate to an SU(2)r×SU(2)r/SU(2)2r Wess-Zumino-Witten (WZW) coset model for the particular values n=−2cos[π/(r+2)], where r is a positive integer. The truncated Chalker-Coddington model is the n=0 point of branch 4. By numerical diagonalization, we find that its universality class is neither an analytic continuation of the WZW coset nor the universality class of the original Chalker-Coddington model. It constitutes rather an integrable, critical approximation to the latter.