Abstract
One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary correspondence has been well-tested for strong topological invariants, and forms the basis for all proposed technological applications of topology. Here, we report that a group of weak topological invariants, which depend only on the symmetries of the atomic lattice, also induces a particular type of bulk-boundary correspondence. It predicts the presence or absence of states localised at the interface between two inversion-symmetric band insulators with trivial values for their strong invariants, based on the space group representation of the bands on either side of the junction. We show that this corresponds with symmetry-based classifications of topological materials. The interface modes are protected by the combination of band topology and symmetry of the interface, and may be used for topological transport and signal manipulation in heterojunction-based devices.
Highlights
We have shown that crystalline topological insulators may harbour topologically protected edge states, even in the atomic limit
These edge states are not associated with any Berry curvature or intrinsic symmetry, but rather rely on the symmetries of the atomic lattice itself
We have shown that these states arise naturally at the interface between two-dimensional atomic insulators with inversion symmetry and real-valued Wannier states, which may be realised in heterojunction architectures
Summary
Topological insulators are materials characterised by a bulk topological invariant, which predicts the existence of protected boundary modes localized at the materials’ edges [1,2,3]. There is no general proof for the correspondence between bulk topology and the presence of boundary modes [11], it is commonly accepted that topological insulators with a non-zero value for the so-called strong topological invariant host boundary states that are protected against backscattering [3] This is true both for systems with broken time-reversal symmetry whose strong invariant arises from the Chern numbers of its bands [2, 12,13,14], and for time-reversal symmetric systems, where the strong invariant is of the Z2, or Fu-Kane-Mele (FKM), type [15,16,17]. We outline the general procedure for identifying topological interface states, and argue that such states generically arise in junctions of inversion symmetric materials
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
