How simple can a useful topological system be? In this talk I try to answer this question based on our recent work on achieving topological states by simply deforming honeycomb lattice. We observe that honeycomb lattice is equivalent to triangle lattice of hexagons formed by six neighboring sites. When the triangle lattice is squeezed with the size and shape of hexagons fixed and C6 symmetry preserved, a gap is opened in the Dirac energy dispersion, and simultaneously a pseudo spin degree of freedom will be generated in the system, resulting in a topologically nontrivial state. The first implementation of this idea is a topological photonic crystal based on conventional dielectric material [1], such as silicon, which carries counter-propagations of electromagnetic waves with opposite pseudo spins on the sample edge. In the second example, we modify the electron hopping integral between nearest-neighboring sites of honeycomb lattice in a way to build Kekule hopping texture [2]. It is shown that an effective spin-orbit coupling (SOC) is generated, larger than the intrinsic SOC by several orders of magnitude, which may make helical edge currents available above room temperature. I will also discuss other possible implementations of this idea.

References:

[1] L.-H. Wu and X. Hu, Phys. Rev. Lett. 114, 223901 (2015)

[2] L.-H. Wu and X. Hu, arXiv:1509.00919