TY - JOUR
T1 - Symmetry-Based Model Hamiltonians for Topological Analysis of 2D Materials with Square Lattice
AU - van Niekerk, Chani Stella
AU - Warmbier, Robert
N1 - Publisher Copyright:
© 2023 The Authors. physica status solidi (b) basic solid state physics published by Wiley-VCH GmbH.
PY - 2023/9
Y1 - 2023/9
N2 - Classes of symmetry-based model Hamiltonians can be constructed with specific point group restrictions. These models combine the flexibility of tight-binding models with the analytical simplicity of the Su–Schrieffer–Heeger model and can be scaled in either direction. The applicability of models with two, three, and four bands to topological analysis is investigated and limitations to describing topological behaviour are assessed. The models are applied to fitting density functional theory (DFT) band structures for selected 2D materials with and without spin–orbit coupling. Suitable parameters for selected materials are obtained and used to describe the topological phase of the materials. Based on these results, a single two-, three-, and four-band model is found which describes the band structure and topological properties of all the selected 2D materials. Suitable simplifications to the models are outlined to further illustrate how the analyzability can be scaled with the accuracy of the model. While generally a higher degree of symmetry helps the formation of topological phases, extremely symmetric point groups like (Formula presented.) restrict the allowed interactions to a degree that makes topological phases less easy to achieve.
AB - Classes of symmetry-based model Hamiltonians can be constructed with specific point group restrictions. These models combine the flexibility of tight-binding models with the analytical simplicity of the Su–Schrieffer–Heeger model and can be scaled in either direction. The applicability of models with two, three, and four bands to topological analysis is investigated and limitations to describing topological behaviour are assessed. The models are applied to fitting density functional theory (DFT) band structures for selected 2D materials with and without spin–orbit coupling. Suitable parameters for selected materials are obtained and used to describe the topological phase of the materials. Based on these results, a single two-, three-, and four-band model is found which describes the band structure and topological properties of all the selected 2D materials. Suitable simplifications to the models are outlined to further illustrate how the analyzability can be scaled with the accuracy of the model. While generally a higher degree of symmetry helps the formation of topological phases, extremely symmetric point groups like (Formula presented.) restrict the allowed interactions to a degree that makes topological phases less easy to achieve.
KW - 2D materials
KW - model Hamiltonian
KW - topological insulators
UR - http://www.scopus.com/inward/record.url?scp=85162895050&partnerID=8YFLogxK
U2 - 10.1002/pssb.202300018
DO - 10.1002/pssb.202300018
M3 - Article
AN - SCOPUS:85162895050
SN - 0370-1972
VL - 260
JO - Physica Status Solidi (B): Basic Research
JF - Physica Status Solidi (B): Basic Research
IS - 9
M1 - 2300018
ER -