Interplay between boundary conditions and Wilson's mass in Dirac-like Hamiltonians
| Autor: | R. G. F. Dornelas, Daniel Varjas, Renan Maciel, Gerson J. Ferreira, Augusto L. Araújo |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Physics
Condensed Matter - Mesoscale and Nanoscale Physics Graphene FOS: Physical sciences 02 engineering and technology Fermion 021001 nanoscience & nanotechnology 01 natural sciences law.invention symbols.namesake Theoretical physics Zigzag law Topological insulator Lattice (order) Mesoscale and Nanoscale Physics (cond-mat.mes-hall) 0103 physical sciences symbols Boundary value problem 010306 general physics 0210 nano-technology Hamiltonian (quantum mechanics) Graphene nanoribbons |
| Zdroj: | Physical Review B, 100(20) |
| ISSN: | 2469-9950 |
| Popis: | Dirac-like Hamiltonians, linear in momentum $k$, describe the low-energy physics of a large set of novel materials, including graphene, topological insulators, and Weyl fermions. We show here that the inclusion of a minimal $k^2$ Wilson's mass correction improves the models and allows for systematic derivations of appropriate boundary conditions for the envelope functions on finite systems. Considering only Wilson's masses allowed by symmetry, we show that the $k^2$ corrections are equivalent to Berry-Mondragon's discontinuous boundary conditions. This allows for simple numerical implementations of regularized Dirac models on a lattice, while properly accounting for the desired boundary condition. We apply our results on graphene nanoribbons (zigzag and armchair), and on a PbSe monolayer (topological crystalline insulator). For graphene, we find generalized Brey-Fertig boundary conditions, which correctly describe the small gap seen on \textit{ab initio} data for the metallic armchair nanoribbon. On PbSe, we show how our approach can be used to find spin-orbital-coupled boundary conditions. Overall, our discussions are set on a generic model that can be easily generalized for any Dirac-like Hamiltonian. 14 pages, 6 figures |
| Databáze: | OpenAIRE |
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