Stability of Two-Dimensional Soft Quasicrystals

The relative stability of two-dimensional soft quasicrystals is examined using a recently developed projection method which provides a unified numerical framework to compute the free energy of periodic crystal and quasicrystals. Accurate free energies of numerous ordered phases, including dodecagonal, decagonal and octagonal quasicrystals, are obtained for a simple model, i.e. the Lifshitz-Petrich free energy functional, of soft quasicrystals with two length-scales. The availability of the free energy allows us to construct phase diagrams of the system, demonstrating that, for the Lifshitz-Petrich model, the dodecagonal and decagonal quasicrystals can become stable phases, whereas the octagonal quasicrystal stays as a metastable phase.Comment: 11 pages, 7 figure

Anomalous Electron Trajectory in Topological Insulators

We present a general theory about electron orbital motions in topological insulators. An in-plane electric field drives spin-up and spin-down electrons bending to opposite directions, and skipping orbital motions, a counterpart of the integer quantum Hall effect, are formed near the boundary of the sample. The accompanying Zitterbewegung can be found and controlled by tuning external electric fields. Ultrafast flipping electron spin leads to a quantum side jump in the topological insulator, and a snake-orbit motion in two-dimensional electron gas with spin-orbit interactions. This feature provides a way to control electron orbital motion by manipulating electron spin.Comment: 5 pages and 4 figures for the letter, 6 pagers for the online supplemental materia