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Topological Crystalline Insulators

Nature Commun. 3, 1192 (2012)
Science 341, 1496 (2013)
Nature Physics 10, 572 (2014)

In a 3D Z2 TI, it is the protection of time-reversal symmetry that gives rise to the nontrivial Z2 topological invariant. With the explosion of research interest in 3D topological insulators, a new research topic that focused on finding new topologically nontrivial phases protected by other discrete symmetries emerged. In 2011, a new topological phase of matter, which is now usually referred to as the topological crystalline insulator (TCI), was theoretically proposed. In a TCI, the space group symmetries of a crystal replace the role of time-reversal symmetry in a Z2 TI. It was predicted that the properties of TCIs differed fundamentally from those of Z2 TIs because the point group symmetries played a crucial role. Such distinction leads to many exotic properties, such as higher order (non-linear) surface band crossings, topological states without spin-orbit coupling, and crystalline symmetry protected topological superconductivity or Chern currents.

We experimentally discovered the first TCI state in the Pb1-xSnxTe material system. Our ARPES measurements identified the existence of an even number of Dirac surface states that are protected by the mirror symmetry. Our critical spin-resolved APRES studies experimentally determines the topological invariant associated with the TCI state in Pb1-xSnxTe, the mirror Chern number, nM = -2. Our systematic measurements on a similar TCI material, Pb1-xSnxSe, revealed a novel quantum Lifshitz transition in its topological surface states, leading to a surface van Hove singularity that paves the way for correlated electronic phenomena on the surface of a topological material.

Observation of a topological crystalline insulator phase and topological phase transition in Pb1-xSnxTe
Published in Su-Yang Xu, Chang Liu, N. Alidoust, et al.,
Nature Commun. 3, 1192 (2012)

Nontrivial spin texture of the coaxial Dirac cones on the surface of topological crystalline insulator SnTe.
Y. J. Wang, W-F. Tsai, H. Lin, et al.;
Phys. Rev. B 87, 235317 (2013)

Observation of Dirac Node Formation and Mass Acquisition in a Topological Crystalline Insulator.
Y. Okada, M. Serbyn, H. Lin, et al.;
Science 341, 1496 (2013)

Theory of quasiparticle interference in mirror-symmetric two-dimensional systems and its application to surface states of topological crystalline insulators.
C. Fang, M. J. Gilbert, S.-Y. Xu, et al.;
Phys. Rev. B 88, 125141 (2013)

Mapping the unconventional orbital texture in topological crystalline insulators.
I. Zeljkovic, Y. Okada, C.-Y. Huang, et al.;
Nature Physics 10, 572 (2014)

Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators.
I. Zeljkovic, Y. Okada, M. Serbyn, et al.;
Nature Materials 14, 318 (2015)