Convenient Peierls phase choice for periodic atomistic systems under magnetic field

Cresti, Alessandro

doi:10.1103/physrevb.103.045402

Cited by 9 publications

(8 citation statements)

References 51 publications

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“…For a TB Hamiltonian, (2) translates into the Peierls phase approximation [60]. In two-dimensional periodic systems [61], the flux of the magnetic field through the unit cell can only be a multiple of the quantum flux Φ 0 = h/e ≈ 4.136 × 10 3 T nm 2 . As a consequence, the orthogonal component of the magnetic field must be multiple of a value that depends on the cell surface, contrarily to the in-plane component of the magnetic field, whose flux is null.…”

Section: Methodsmentioning

confidence: 99%

Magic-angle twisted bilayer graphene under orthogonal and in-plane magnetic fields

Bigeard,

Cresti

2024

J. Phys.: Condens. Matter

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We investigate the eﬀect of a magnetic ﬁeld on the band structure of bilayer graphene with a magic twist angle of 1.08°. The coupling of a tight-binding model and the Peierls phase allows the calculation of the energy bands of periodic two-dimensional systems. For an orthogonal magnetic ﬁeld, the Landau levels are dispersive, particularly for magnetic lengths comparable to or larger than the twisted bilayer cell size. A high in-plane magnetic ﬁeld modiﬁes the low-energy bands and gap, which we demonstrate to be a direct consequence of the minimal coupling.

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Section: Methodsmentioning

confidence: 99%

Magic-angle twisted bilayer graphene under orthogonal and in-plane magnetic fields

Bigeard,

Cresti

2024

J. Phys.: Condens. Matter

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“…The DOS calculations have been carried out through direct diagonalization when allowed by the system sizes and by using the Lanczos method when we need to calculate very large systems with millions of atoms (21) where RP refers to a random phase being used to approximate the trace of large matrices [24] and η is the broadening factor that allows to control the energy resolution. We finally note that for the magnetic field calculations, we use a Peierls phase substitution in the hopping terms as discussed in [25].…”

Section: Tb Calculationsmentioning

confidence: 99%

Electronic structure of lattice relaxed alternating twist tNG-multilayer graphene: from few layers to bulk AT-graphite

et al. 2022

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Alternating twist multilayer graphene systems are at the heart of recent research efforts on flat band superconductivity and therefore precise descriptions of their atomic and electronic structures are desirable. We present the electronic structure of AA′AA′. . . stacked alternating twist N-layer (tNG) graphene for N = 3, 4, 5, 6, 8, 10, 20 layers and bulk alternating twist (AT) graphite systems where the atomic structure is relaxed using a molecular dynamics simulation code. The low energy bands depend sensitively on the relative sliding between the layers but the highly symmetric AA′AA′. . . stacking is energetically preferred among all interlayer sliding geometries for progressively added layers up to N = 6, justifying why experimental devices consistently show results compatible with this geometry. It is found that lattice relaxations enhance electron-hole asymmetry, and leads to small reductions of the magic angle values with respect to analytical or continuum model calculations with ﬁxed tunneling strengths that we quantify from few layers to bulk AT-graphite. The twist angle error tolerance near the magic angles obtained by maximizing the density of states of the nearly flat bands expand progressively from 0.05◦ for t2G to up to 0.2◦ for AT-graphite, hence allowing a greater twist angle flexibility in multilayers. We further comment on the role of perpendicular electric and magnetic fields in modifying the electronic structure of the system and how the decoupling of t$N$G multilayers bands allows mapping onto those of periodic AT-graphite's at different k z values.

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“…The presence of an external magnetic field B can be accounted by the Peierls substitution [44,45], that is, by the transformation…”

Section: A Model Hamiltonianmentioning

confidence: 99%

High-energy Landau levels in graphene beyond nearest-neighbor hopping processes: Corrections to the effective Dirac Hamiltonian

Vidarte

Lewenkopf²

2022

Phys. Rev. B

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We study the Landau level spectrum of bulk graphene monolayers beyond the Dirac Hamiltonian with linear dispersion. We consider an effective Wannier-like tight-binding model obtained from ab initio calculations, that includes long-range electronic hopping integral terms. We employ the Haydock-Heine-Kelly recursive method to numerically compute the Landau level spectrum of bulk graphene in the quantum Hall regime and demonstrate that this method is both accurate and computationally much faster than the standard numerical approaches used for this kind of study. The Landau level energies are also obtained analytically for an effective Hamiltonian that accounts for up to third nearest neighbor hopping processes. We find an excellent agreement between both approaches. We also study the effect of disorder on the electronic spectrum. Our analysis helps to elucidate the discrepancy between theory and experiment for the high-energy Landau levels energies.

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Convenient Peierls phase choice for periodic atomistic systems under magnetic field

Cited by 9 publications

References 51 publications

Magic-angle twisted bilayer graphene under orthogonal and in-plane magnetic fields

Magic-angle twisted bilayer graphene under orthogonal and in-plane magnetic fields

Electronic structure of lattice relaxed alternating twist tNG-multilayer graphene: from few layers to bulk AT-graphite

High-energy Landau levels in graphene beyond nearest-neighbor hopping processes: Corrections to the effective Dirac Hamiltonian

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