Discovery of $${\hat{\boldsymbol{C}}}_2$$ rotation anomaly in topological crystalline insulator SrPb

Abstract

Topological crystalline insulators (TCIs) are insulating electronic states with nontrivial topology protected by crystalline symmetries. Recently, theory has proposed new classes of TCIs protected by rotation symmetries $$\hat C_n$$ C ̂ n , which have surface rotation anomaly evading the fermion doubling theorem, i.e., n instead of 2n Dirac cones on the surface preserving the rotation symmetry. Here, we report the first realization of the $$\hat C_2$$ C ̂ 2 rotation anomaly in a binary compound SrPb. Our first-principles calculations reveal two massless Dirac fermions protected by the combination of time-reversal symmetry $$\hat T$$ T ̂ and $$\hat C_{2y}$$ C ̂ 2 y on the (010) surface. Using angle-resolved photoemission spectroscopy, we identify two Dirac surface states inside the bulk band gap of SrPb, confirming the $$\hat C_2$$ C ̂ 2 rotation anomaly in the new classes of TCIs. The findings enrich the classification of topological phases, which pave the way for exploring exotic behavior of the new classes of TCIs.

Ferromagnetism with in-plane magnetization, Dirac spin-gapless semiconducting properties, and tunable topological states in two-dimensional rare-earth metal dinitrides

“…When 𝒎 ̂ is parallel to the C2−/C2y/C2+ axis, the C2 symmetry can be protected, leading to two pairs of Weyl-like points in the corresponding parallel high-symmetry paths. [57][58][59][60][61][62] When there is an angle  between 𝒎 ̂ and the C2−/C2y/C2+ symmetry axis, the C2 symmetry can be broken, leading to the absence of Weyl-like points with the opening of a band gap in the corresponding parallel high-symmetry paths. The value of the band gap (G) depends on the degree of the broken C2 symmetry, and it can be accurately described by 2g sin G…”

Topology and Symmetry in Quantum Materials

“…Recently, SrPb has been confirmed as the first twofold rotational symmetry C 2 y ‐protected TCI with rotational invariant 2. [ 70 ] Here, two gapless Dirac cone surface states are observed lying on the (010) surface via angle‐resolved spectroscopy measurements. Many other proposed TCIs still await experimental confirmation.…”

Topologically Protected Edge States in Triangular Lattices

“…[4] showed how point group symmetries can induce a phase possessing gapless surface states, which are otherwise trivial in the framework of earlier topological classification systems [10]. More recent studies into the influence of crystalline symmetries has yielded a plethora of new phenomena, including higher order topological insulators [11] and surface rotation anomalies [12,13]. These demonstrations have been recently unified under more general notions of symmetries based on point and space groups, commonly referred to as symmetry indicators [14][15][16], which rely on information of the real space configuration as well as knowledge of the wavefunctions at various high symmetry point in BZ.…”