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The interplay between topology and crystalline symmetries in materials can lead to a variety of topological crystalline insulator (TCI) states. Despite significant effort towards their experimental realization, so far only Pb_1–xSn_xTe has been confirmed as a mirror-symmetry-protected TCI. In this work, based on first-principles calculations combined with a symmetry analysis, we identify a rotational-symmetry-protected TCI state in the transition metal dipnictide RX₂ family, where R = Ta or Nb and X = P, As, or Sb. Taking TaAs₂ as an exemplar system, we show that its low-energy band structure consists of two types of bulk nodal lines in the absencemore » of spin-orbit coupling (SOC) effects. Turning on the SOC opens a continuous band gap in the energy spectrum and drives the system into a C₂T -symmetry-protected TCI state. On the (010) surface, we show the presence of rotationalsymmetry- protected nontrivial Dirac cone states within a local bulk energy gap of ~300 meV. Interestingly, the Dirac cones have tilted energy dispersion, realizing a type-II Dirac fermion state in a topological crystalline insulator. Our results thus indicate that the TaAs₂ materials family provides an ideal setting for exploring the unique physics associated with type-II Dirac fermions in rotational-symmetry-protected TCIs.« less

Here we discuss how topological semimetals can support one-dimensional Fermi lines or zero-dimensional Weyl points in momentum space, where the valence and conduction bands touch. While the degeneracy points in Weyl semimetals are robust against any perturbation that preserves translational symmetry, nodal lines require protection by additional crystalline symmetries such as mirror reflection. Here we report, based on a systematic theoretical study and a detailed experimental characterization, the existence of topological nodal-line states in the non-centrosymmetric compound PbTaSe₂ with strong spin-orbit coupling. Remarkably, the spin-orbit nodal lines in PbTaSe₂ are not only protected by the reflection symmetry but also characterizedmore » by an integer topological invariant. Our detailed angle-resolved photoemission measurements, first-principles simulations and theoretical topological analysis illustrate the physical mechanism underlying the formation of the topological nodal-line states and associated surface states for the first time, thus paving the way towards exploring the exotic properties of the topological nodal-line fermions in condensed matter systems.« less