Motivated by recent progress in understanding the interplay between lattice and electronic topological phases, we consider quantum-melting transitions of weak quantum liquid crystals, a crystal and a nematic phase, in which electrons form a quantum Hall state. In certain classes of Chern band insulators and quantum Hall phases, it has been previously demonstrated that there are topological Chern-Simons terms such as a Hall viscosity term and a gravitational Chern-Simons term for local lattice deformations. The Chern-Simons terms can induce anyonic statistics for the topological lattice defects and, furthermore, dress the defects with certain symmetry quantum numbers. On the other hand, the melting transitions of such liquid-crystalline orders are driven by the condensation of lattice defects. Based on these observations, we show how the topological terms can change the nature of the proximate disordered phases of the quantum liquid-crystalline phases. We derive and study the effective dual field theories for the liquid-crystalline phases with the geometric Chern-Simons terms, and carefully examine the symmetry quantum numbers and statistics of defects. We show that a crystal may go through a continuous phase transition into another crystal with the different discrete translational symmetries because the dislocation, the topological defect in the crystal, carries nonzero crystal momentum due to the Hall viscosity term. For the nematic phase, the disclination will condense at the phase transition to the isotropic phase, and we show that the isotropic phase may support a deconfined fractionally charged excitation due to the Wen-Zee term, and thus the isotropic phase and the nematic phase have different electromagnetic Hall responses.
|Original language||English (US)|
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|State||Published - Jan 20 2015|
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics