Hasan Research Group

Laboratory for Topological Quantum Matter & Advanced Spectroscopy

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 Pb_1-xSn_xTe 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 Pb_1-xSn_xTe, the mirror Chern number, n_M = -2. Our systematic measurements on a similar TCI material, Pb_1-xSn_xSe, 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.