2020/11/30 by P. C. Klipstein
Materials Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Degenerate energy levels #Graphene research and applications #Hamiltonian (control theory) #Mathematics #Physics #Quantum many-body systems #Quantum mechanics #Topological Materials and Phenomena #Topological insulator #Topology (electrical circuits) #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.104.195407
published as Physical Review B 104, 195407 (2021) · 18 pages, 14 figures, 4 tables
arxiv created 2020/12/16 · openalex publication_date 2021/11/08 · arxiv updated 2021/11/17 · openalex created_date 2021/11/22 · openalex updated_date 2025/11/06
In 2D topological insulators (TIs) based on semiconductor quantum wells such as HgTe/CdTe, hard wall spin-polarized edge states are calculated from an 8\ifmmode×\else\texttimes\fi8 linear-k multiband (LKMB) Hamiltonian based directly on k\ifmmode⋅\else\textperiodcentered\fip theory, and from a 4\ifmmode×\else\texttimes\fi4 BHZ Hamiltonian derived from it by the elimination of remote states using perturbation theory. Both approaches lead to similar results with standard boundary conditions obtained by integrating the eigenstate equation across an interface (SBCs). In contrast, open boundary conditions (OBCs) yield unphysical results and do not work for the LKMB Hamiltonian. Their failure is traced to a spurious solution introduced by the elimination process. In the BHZ treatment, SBCs are shown to be consistent with perturbation theory on both sides of the boundary, and a wall hybridization parameter is estimated for a vacuum using a basis of empty crystal free electron states. A Dirac point is not expected for a vacuum, but can exist when a thin passivation layer is used whose midgap energy is nearly degenerate with that of the TI. In the absence of interface band mixing (IBM), the Dirac point is then very close to midgap and virtually independent of the TI band asymmetry. IBM introduces a significant energy shift, which decreases monotonically with edge state wave vector. Using SBCs, the paradoxical extension of the BHZ edge states across the topological phase transition is also resolved.