Topological Quasicrystals

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Science  26 Oct 2012:
Vol. 338, Issue 6106, pp. 445
DOI: 10.1126/science.338.6106.445-a

The discovery of topological order has changed the traditional view of phase transitions in condensed-matter physics. Topological phases are characterized by boundary states that are immune to certain types of perturbation and appear, for example, as edge states or surface states in two-dimensional (2D) and 3D systems, but are absent in 1D systems under most circumstances. Kraus et al. found evidence for topological boundary states in 1D quasicrystals—materials that can be viewed as a “projection” of periodic systems onto a lower-dimensional physical space. The experimental system consisted of parallel photonic waveguides engineered to realize a quasiperiodic Hamiltonian; when light was injected into a middle waveguide, it spilled over to its neighbors and beyond, whereas it stayed localized if injected into the leftmost guide, indicating a boundary state. In a modified setup, it was also possible to observe the adiabatic pumping of light between the boundaries. It is expected that the results can be generalized to 2D and 3D quasicrystals, which would have the topological properties of the higher dimensional spaces they are projected from.

Phys. Rev. Lett. 109, 106402 (2012).

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