Visualizing coexisting surface states in the weak and crystalline topological insulator Bi2TeI

Abstract

The established diversity of electronic topology classes lends the opportunity to pair them into dual topological complexes. Bulk-surface correspondence then ensures the coexistence of a combination of boundary states that cannot be realized but only at the various surfaces of such a dual topological material. We show that the layered compound Bi2TeI realizes a dual topological insulator. It exhibits band inversions at two time reversal symmetry points of the bulk band which classify it as a weak topological insulator with metallic states on its (010) 'side' surfaces. Additional mirror symmetry of the crystal structure concurrently classifies it as a topological crystalline insulator. Bi2TeI is therefore predicted to host a pair of Dirac cones protected by time reversal symmetry on its 'side' surfaces and three pairs of Dirac cones protected by mirror symmetry on its 'top' and 'bottom' (001) surfaces. We spectroscopically map the top cleaved surface of Bi2TeI, and crystallographic step edges therein. We show the existence of both two dimensional surface states which are susceptible to mirror symmetry breaking, as well as one dimensional channels that reside along the step edges. Their mutual coexistence on the step edge where both facets join is facilitated by momentum and energy segregation. Our observations of a dual topological insulator make way to additional pairing of other dual topology classes with distinct surface manifestations coexisting at their boundaries.

Dual topology in jacutingaite Pt2HgSe3

“…Further, we hope that the tight-binding models we have introduced will allow for a better theoretical understanding of WTI+TCI materials. These include the behavior of the system under various surface perturbations, for which it can become a HOTI [17], the behavior of modes localized to step edges, which have recently been reported in Bi 2 TeI [42], as well as the effect of disorder. Moreover, they may be used to understand the degree to which surface modes can influence transport properties in the presence of coexisting bulk states, similar to the studies done for 2D systems in Refs.…”

“…Having established that Pt 2 HgSe 3 and Pd 2 HgSe 3 simultaneously realize weak and topological crystalline phases, we will now introduce tight-binding models that capture the essential topological features of this class of materials, which has been found to also include Bi 2 TeI [41,42], Bi 2 TeBr [43], BiTe [44] and BiSe [17]. Specifically, we will construct systems with three-fold rotation symmetry, which are both WTI and TCI [65].…”

“…In this work, we first address this issue and show that Pt 2 HgSe 3 is both a weak topological phase and a mirror-protected topological crystalline phase. This result places Jacutingaite in the list of materials which can host surface states protected by different, unrelated crystalline symmetries [17,[41][42][43][44][45]. Second, we construct minimal tight-binding models that capture the essential topological properties of this dual topological phase in materials with three-fold rotation symmetry and compare their associated surface spectral density with those of different materials in the class.…”

Synthesis, Crystal and Topological Electronic Structures of New Bismuth Tellurohalides Bi2TeBr and Bi3TeBr

“…14,16 Chemical bonding between the [ ஶ ଶ Bi 2 ] and [ ஶ ଶ BiTeI] modules in Bi 2 TeI exceeds the van der Waals interactions in pristine BiTeI, so that a topological inversion is realized Bi 2 TeI at the Z point of the 3D BZ under normal pressure. [42][43][44] Enhanced hybridization between the states of the Bi-bilayer and the BiTeI matrix results in a dual topological insulator in the case of Bi 2 TeI and in a topological metal in the case of Bi 3 TeI 33 . A similarly developing tendency in topological properties is observed in the Bi 2 Te 3 -BiTe -Bi 4 Se 3 series.…”

Topological Quantum Materials from the Viewpoint of Chemistry

“…17 This means that the topological surface states will be absent on the surface normal to [001], while all other facets will contain even number of surface Dirac cones. Other examples of weak topological insulators are -Bi4I4 78 and Bi2TeI 79 . Interestingly, Bi2TeI, in addition to containing side surface states related to weak topological insulator, also contains surface states connected to topological crystalline insulating state which we will discuss next.…”