Derivation of Wannier orbitals and minimal-basis tight-binding Hamiltonians for twisted bilayer graphene: First-principles approach
Twisted bilayer graphene (TBLG) has emerged as an important platform for studying correlated phenomena, including unconventional superconductivity, in two-dimensional systems. The complexity of the atomic-scale structures in TBLG has made even the study of single-particle physics at low energies aro...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2019-11-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.1.033072 |
| _version_ | 1797211677498802176 |
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| author | Stephen Carr Shiang Fang Hoi Chun Po Ashvin Vishwanath Efthimios Kaxiras |
| author_facet | Stephen Carr Shiang Fang Hoi Chun Po Ashvin Vishwanath Efthimios Kaxiras |
| author_sort | Stephen Carr |
| collection | DOAJ |
| description | Twisted bilayer graphene (TBLG) has emerged as an important platform for studying correlated phenomena, including unconventional superconductivity, in two-dimensional systems. The complexity of the atomic-scale structures in TBLG has made even the study of single-particle physics at low energies around the Fermi level, quite challenging. Our goal here is to provide a convenient and physically motivated picture of single-particle physics in TBLG using reduced models with the smallest possible number of localized orbitals. The reduced models exactly reproduce the low-energy bands of ab initio tight-binding models, including the effects of atomic relaxations. Furthermore, we obtain for the first time the corresponding Wannier orbitals that incorporate all symmetries of TBLG, which are also calculated as a function of angle, a requisite first step towards incorporating electron interaction effects. We construct eight-band and five-band models for the low-energy states for twist angles between 1.3^{∘} and 0.6^{∘}. The models are created using a multistep Wannier projection technique starting with appropriate ab initio k·p continuum Hamiltonians. Our procedure can also readily capture the perturbative effects of substrates and external displacement fields while offering a significant reduction in complexity for studying electron-electron correlation phenomena in realistic situations. |
| first_indexed | 2024-04-24T10:30:17Z |
| format | Article |
| id | doaj.art-773914e9ec034a29864ce3a754e67ff7 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:30:17Z |
| publishDate | 2019-11-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-773914e9ec034a29864ce3a754e67ff72024-04-12T16:46:37ZengAmerican Physical SocietyPhysical Review Research2643-15642019-11-011303307210.1103/PhysRevResearch.1.033072Derivation of Wannier orbitals and minimal-basis tight-binding Hamiltonians for twisted bilayer graphene: First-principles approachStephen CarrShiang FangHoi Chun PoAshvin VishwanathEfthimios KaxirasTwisted bilayer graphene (TBLG) has emerged as an important platform for studying correlated phenomena, including unconventional superconductivity, in two-dimensional systems. The complexity of the atomic-scale structures in TBLG has made even the study of single-particle physics at low energies around the Fermi level, quite challenging. Our goal here is to provide a convenient and physically motivated picture of single-particle physics in TBLG using reduced models with the smallest possible number of localized orbitals. The reduced models exactly reproduce the low-energy bands of ab initio tight-binding models, including the effects of atomic relaxations. Furthermore, we obtain for the first time the corresponding Wannier orbitals that incorporate all symmetries of TBLG, which are also calculated as a function of angle, a requisite first step towards incorporating electron interaction effects. We construct eight-band and five-band models for the low-energy states for twist angles between 1.3^{∘} and 0.6^{∘}. The models are created using a multistep Wannier projection technique starting with appropriate ab initio k·p continuum Hamiltonians. Our procedure can also readily capture the perturbative effects of substrates and external displacement fields while offering a significant reduction in complexity for studying electron-electron correlation phenomena in realistic situations.http://doi.org/10.1103/PhysRevResearch.1.033072 |
| spellingShingle | Stephen Carr Shiang Fang Hoi Chun Po Ashvin Vishwanath Efthimios Kaxiras Derivation of Wannier orbitals and minimal-basis tight-binding Hamiltonians for twisted bilayer graphene: First-principles approach Physical Review Research |
| title | Derivation of Wannier orbitals and minimal-basis tight-binding Hamiltonians for twisted bilayer graphene: First-principles approach |
| title_full | Derivation of Wannier orbitals and minimal-basis tight-binding Hamiltonians for twisted bilayer graphene: First-principles approach |
| title_fullStr | Derivation of Wannier orbitals and minimal-basis tight-binding Hamiltonians for twisted bilayer graphene: First-principles approach |
| title_full_unstemmed | Derivation of Wannier orbitals and minimal-basis tight-binding Hamiltonians for twisted bilayer graphene: First-principles approach |
| title_short | Derivation of Wannier orbitals and minimal-basis tight-binding Hamiltonians for twisted bilayer graphene: First-principles approach |
| title_sort | derivation of wannier orbitals and minimal basis tight binding hamiltonians for twisted bilayer graphene first principles approach |
| url | http://doi.org/10.1103/PhysRevResearch.1.033072 |
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