Discovery of a weak topological insulating state and van Hove singularity in triclinic RhBi2

Abstract

Time reversal symmetric (TRS) invariant topological insulators (TIs) fullfil a paradigmatic role in the field of topological materials, standing at the origin of its development. Apart from TRS protected strong TIs, it was realized early on that more confounding weak topological insulators (WTI) exist. WTIs depend on translational symmetry and exhibit topological surface states only in certain directions making it significantly more difficult to match the experimental success of strong TIs. We here report on the discovery of a WTI state in RhBi2 that belongs to the optimal space group P$$\bar{1}$$ 1 ¯ , which is the only space group where symmetry indicated eigenvalues enumerate all possible invariants due to absence of additional constraining crystalline symmetries. Our ARPES, DFT calculations, and effective model reveal topological surface states with saddle points that are located in the vicinity of a Dirac point resulting in a van Hove singularity (VHS) along the (100) direction close to the Fermi energy (EF). Due to the combination of exotic features, this material offers great potential as a material platform for novel quantum effects.

Experimental Realization of Two-Dimensional Weak Topological Insulators

“…Since then, the study of topological insulators (TIs) has become one of the most burgeoning research fields in condensed matter physics. − Another milestone in TI research is the realization of quantum spin Hall insulators [two-dimensional (2D) TIs]. − Subsequently, the 2D TIs were generalized to three-dimensional (3D) cases. − Strong and weak 3D TIs both host metallic surface states but have odd and even numbers of Dirac points, respectively. Strong 3D TIs have been observed in Bi 1– x Sb x and Bi 2 Se 3 . , However, the discovery of weak topological insulators (WTIs) occurred more than one decade later − because weak topological surface states appear only on particular surfaces. They are sensitive to disorder and usually are undetectable in real 3D crystals. − Quantum spin Hall insulators, with helical edge modes spreading over all boundaries, are regarded as strong TIs in 2D systems.…”

Exploring strong and weak topological states on isostructural substitutions in TlBiSe$$_2$$

“…The topology of TRS invariant insulators is characterized by the Z index, , which can either be 0 or 1, depicting a topologically trivial or non-trivial phase, respectively. However, it has been recently reported that even when = 0, the system can show non-trivial characteristics 21 . Based on whether the material hosts odd or even number of Dirac cones in the electronic structure of its surface, TIs are further classified as Strong Topological Insulator (STI) having Z invariant, = 1 or Weak Topological Insulator (WTI) with Z invariant, = 0 22 , 23 .…”

Exploring strong and weak topological states on isostructural substitutions in TlBiSe2

“…The topology of TRS invariant insulators is characterized by the Z 2 index, ν 0 , which can either be 0 or 1, depicting a topologically trivial or non-trivial phase, respectively. However, it has been recently reported that even when ν 0 = 0, the system can show non-trivial characteristics 16 . Based on whether the material hosts odd or even number of Dirac cones in the electronic structure of its surface, TIs are further classified as Strong Topological Insulator (STI) having Z 2 invariant, ν 0 = 1 or Weak Topological Insulator (WTI) with Z 2 invariant, ν 0 = 0 17,18 .…”