Two- and one-dimensional quantum spin Hall states in stanene-functionalized GaTe and InTe matrices

Surface and edge electronic structures as well as chemical bonding characteristics are studied in van der Waals stanene-functionalized GaTe and InTe matrices. A topologically non-trivial character of the electronic structure is found, which results in the formation of both two- (surface) and one-dimensional (thin films) quantum spin Hall states in GaSnTe and a two-dimensional quantum spin Hall state in InSnTe. We demonstrate that these compounds are characterized by a negative band-bending effect and by the two-dimensional quantum Hall state penetrating deeply into the subsurface region. We have studied the changes in the edge electronic structure of GaSnTe thin films associated with various edge geometries and the respective dangling bonds. We also show that unsaturated coordination of the Ga atoms notably influences the electronic structure at the edge.