Topologically protected one-dimensional electronic states in group IV two-dimensional Dirac materials

Abstract

In this report we give a brief introduction on the occurrence of topologically protected one-dimensional electronic states in group IV two-dimensional graphene-like materials. We discuss the effect of spin-orbit coupling on the electronic band structure and show that these materials are potential candidates to exhibit the quantum spin Hall effect. The quantum spin Hall effect is characterized by a gapped interior and metallic counter-propagating spin-polarized topologically protected edges states. We also elaborate on the electric-field induced formation of a hexagonal network of one-dimensional topologically protected electronic states in small-angle twisted bilayer graphene.

These are lecture notes meant for undergraduate and graduate physics students. This manuscript will not be submitted for publication. Pages: 21. Figures: 15

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