Abstract
We address the co-existence of massless and massive topological edge states at the interface between two materials with different topological phases. We modify the well known Bernevig-Hughes-Zhang model to introduce a smooth function describing the band inversion and the band bending due to electrostatic effects between the bulk of the quantum well and the vacuum. Within this minimal model we identify distinct parameter sets that can lead to the co-existence of the two types of edge states, and that determine their number and characteristics. We propose several experimental setups that could demonstrate their presence in two-dimensional topological systems, as well as ways to regulate or tune the contribution of the massive edge states to the conductance of associated electronic devices. Our results suggest that such states may also be present in novel two-dimensional Van der Waals topological materials.
Highlights
The study of edge states, or surface states for threedimensional (3D) materials, goes back to the 1930s, when Tamm and Shockley studied bound states at the surface of a periodic lattice structure [1,2]
In this work we have studied quantum wells hosting two-dimensional topological insulators within the BernevigHughes-Zhang model
We have shown the appearance of massive edge states in addition to the standard linearly dispersing mode of the quantum spin Hall effect
Summary
The study of edge states, or surface states for threedimensional (3D) materials, goes back to the 1930s, when Tamm and Shockley studied bound states at the surface of a periodic lattice structure [1,2]. Contrary to classical edge states, the conducting edge states in the IQHE result from properties of the bulk of the system, namely, its Landau levels; it turned out this was one of the first example of topological edge states [6] Are these states robust to disorder, but it is even desirable to invoke disorder for understanding why it is relatively easy to measure the conductance plateaus. We will focus on a mechanism that can induce fluctuations above 2e2/h, namely, the coexistence of additional edge states Such Shockley-type edge states can arise from electrostatic interface effects, such as band pinning or band bending, and the presence or absence of a topological edge state is not a requirement. Another possible origin of ME states at topological interfaces, discovered by Volkov and Pankratov [43], is the smooth (instead of abrupt) band inversion at the edge.
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