### Hsin Lin (Graphene Research Centre and Department of Physics, National University of Singapore)

#### Topological Crystalline Insulators: A New Phase of Quantum Matter

The recently discovered topological crystalline insulators harbor multiple Dirac surface states protected by a discrete set of crystalline space group symmetries and show immense promise for novel quantum applications. In this talk, I will present a first principles investigation as well as a model Hamiltonian of the nontrivial surface states and their spin and orbital texture in the topological crystalline insulator SnTe and related compounds. The (001) surface states exhibit two distinct energy regions of the Fermi surface topology separated by a Van-Hove singularity at the Lifshitz transition point. The surface state band structure around X(pi,0)-point consists of two “parent” Dirac cones centered at X and vertically offset in energy. When they intersect, the hybridization between the electron-branch of the lower parent Dirac cone and the hole-branch of the upper parent Dirac cone opens a gap at all points except along the mirror line, leading to the formation of a pair of lower-energy “child” Dirac points shifted away in momentum space from the time-reversal-invariant point X. Interestingly, the two parent Dirac cones must have different orbital character since they were found to be associated with orbitals with opposite sign of mirror eigenvalues in order to deliver the correct spin texture and band dispersion. Such nontrivial spin and orbital texture of the Dirac cones, which are of immense importance in determining a variety of materials’ properties, have been confirmed recently by spin- and angle-resolved photoemission and Fourier-transform scanning tunneling spectroscopy. In particular, the intensity and energy dependences of interference patterns show distinct characteristics which can directly be attributed to orbital effects. I will also discuss the breaking of crystal symmetry and mass acquisition of Dirac fermions.

References:

Y. J. Wang, et al. “Nontrivial spin texture of the coaxial Dirac cones on the surface of topological crystalline insulator SnTe” Phys. Rev. B 87, 235317 (2013).

Y. Okada, et al. “Observation of Dirac Node Formation and Mass Acquisition in a Topological Crystalline Insulator” Science 341, 1496 (2013).

S.-Y. Xu, et al., Nat. Commun. 3, 1192 (2012).

T. H. Hsieh, et al., Nat. Commun. 3, 982 (2012).

I. Zeljkovic, et al, “Mapping the unconventional orbital texture in topological crystalline insulators”. Arxiv:1312.0164.