Abstract
In topological systems, a modulation in the gap onset near interfaces can lead to the appearance of massive edge states, as were first described by Volkov and Pankratov. In this work, we study graphene nanoribbons in the presence of intrinsic spin-orbit coupling smoothly modulated near the system edges. We show that this space modulation leads to the appearance of Volkov-Pankratov states, in addition to the topologically protected ones. We obtain this result by means of two complementary methods, one based on the effective low-energy Dirac equation description and the other on a fully numerical tight-binding approach, finding excellent agreement between the two. We then show how transport measurements might reveal the presence of Volkov-Pankratov states, and discuss possible graphene-like structures in which such states might be observed.
Highlights
Graphene was the first material theoretically predicted to be a quantum spin Hall (QSH) insulator
Two different approaches have mainly been followed to overcome this limitation. (a) Find ways to induce a stronger spin-orbit coupling (SOC) in graphene, for example, by depositing heavy adatoms on the graphene surface [4,5,6,7,8] or by proximity to materials with much stronger SOC than carbon such as transition metal dichalcogenides (TMDs) [9,10,11,12,13,14,15]. (b) Grow graphenelike honeycomb structures made of heavier elements in groups IV and V [16,17,18,19,20,21,22,23,24]
We have investigated the appearance of Volkov-Pankratov edge states in topological graphene nanoribbons of zigzag and armchair type
Summary
Graphene was the first material theoretically predicted to be a quantum spin Hall (QSH) insulator. Intrinsic SOC leads to band inversion at the K and K points, and due to the smooth SOC modulation at the edges, new massive edge states appear in addition to the topologically protected ones. Other studies focused on two-dimensional quantum wells within the Bernevig-Hughes-Zhang model [33] In these works the VP states appeared due to the smooth modulations in the band structure near the edges. The opening of a new conduction channel via a VP state is accompanied by the appearance of a dip in conductance These dips resemble the ones observed in quasi-one-dimensional quantum wires in the presence of an attractive impurity [35]. Some technical details are relegated to the three Appendices at the end of the paper
Sign-in/Register to view highlights & summary 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.
