Condensed Matter Theory

Abstract:

Applications for photonic crystals and metamaterials put stringent requirements on the characteristics of advanced optical materials, demanding tunability, high Q factors, applicability in visible range, and large-scale self-assembly. Exploiting the interplay between structural and optical properties, colloidal lattices embedded in liquid crystals (LCs) are promising candidates for such materials. Recently, stable two-dimensional colloidal configurations were demonstrated in nematic LCs. However, the question as to whether stable 3D colloidal structures can exist in an LC had remained unanswered. We show, by means of computer modeling, that colloidal particles can self-assemble into stable, 3D, periodic structures in blue phase LCs. The assembly is based on blue phases providing a 3D template of trapping sites for colloidal particles. The particle configuration is determined by the orientational order of the LC molecules: Specifically, face-centered cubic colloidal crystals form in type-I blue phases, whereas body-centered crystals form in type-II blue phases. For typical particle diameters (approximately 100 nm) the effective binding energy can reach up to a few 100 k(B)T, implying robustness against mechanical stress and temperature fluctuations. Moreover, the colloidal particles substantially increase the thermal stability range of the blue phases, for a factor of two and more. The LC-supported colloidal structure is one or two orders of magnitude stronger bound than, e.g., water-based colloidal crystals.

Abstract:

We perform numerical studies to determine if the fractional quantum Hall state observed at a filling factor of ν=5/2 is the Moore-Read wave function or its particle-hole conjugate, the so-called anti-Pfaffian. Using a truncated Hilbert space approach we find that, for realistic interactions, including Landau-level mixing, the ground state remains fully polarized and the anti-Pfaffian is strongly favored. © 2011 American Physical Society.

Abstract:

Based on the known physics of the excitonic superfluid or 111 state of the quantum Hall ν = 1/2 + 1/2 bilayer, we create a simple trial wavefunction ansatz for constructing a low-energy branch of (Goldstone) excitations by taking the overall ground state and boosting one layer with respect to the other. This ansatz works extremely well for any interlayer spacing. For small d, this is simply the physics of the Goldstone mode, whereas for large d, this is a reflection of composite fermion physics. We find hints that certain aspects of composite fermion physics persist to low d whereas certain aspects of Goldstone mode physics persist to high d. Using these results, we show nonmonotonic behavior of the Goldstone mode velocity as a function of d. Copyright 2011 Gunnar Mller and Steven H. Simon.