Convenient Peierls phase choice for periodic atomistic systems under magnetic field

Abstract

Hamiltonian models based on a localized basis set are widely used in condensed matter physics, as, for example, for the calculation of electronic structures or transport properties. The presence of a weak and homogeneous magnetic field can be taken into account through Peierls phase factors on the hopping Hamiltonian elements. Here, we propose simple and convenient recipes to properly determine such Peierls phase factors for quasi-one-dimensional systems that are periodic or with periodic subcomponents (as in Hall bars, for example), and periodic two-dimensional systems. We also show some examples of applications of the formulas, and more specifically concerning the electronic structure of carbon nanotubes in magnetic fields, the integer quantum Hall effect in six-terminal bars obtained in two-dimensional electron gases, and the electronic structure of bumped graphene superlattices in the presence of a magnetic field.

arXiv comment18 pages, 6 figures

References in corpus (22)

• Maximally localized Wannier functions: Theory and applications
• Energy gaps, topological insulator state and zero-field quantum Hall effect in graphene by strain engineering
• Kwant: a software package for quantum transport
• All-graphene integrated circuits via strain engineering
• Electronic Properties of Graphene in a Strong Magnetic Field
• Graphene bubbles with controllable curvature
• Evidence of Flat Bands and Correlated States in Buckled Graphene Superlattices
• Graphene Nanobubbles as Valley Filters and Beamsplitters
• Aharonov-Bohm spectral features and coherence lengths in carbon nanotubes
• Strain Modulated Superlattices in Graphene
• Pinning of a two-dimensional membrane on top of a patterned substrate: the case of graphene
• The interplay between real and pseudo magnetic field in graphene with strain
• Hofstadter butterflies of bilayer graphene
• Gaussian deformations in graphene ribbons: flowers and confinement
• Electron density and transport in top-gated graphene nanoribbon devices: First-principles Green function algorithms for systems containing large number of atoms
• Electronic states in a graphene flake strained by a Gaussian bump
• Hofstadter butterflies of carbon nanotubes: Pseudofractality of the magnetoelectronic spectrum
• Local sublattice symmetry breaking for graphene with a centro-symmetric deformation
• Periodic Landau gauge and Quantum Hall effect in twisted bilayer graphene
• Theory of Orbital Susceptibility in the Tight-Binding Model: Corrections to the Peierls Phase
• Quenching of the quantum Hall effect in graphene with scrolled edges
• Electron transport properties of graphene nanoribbons with Gaussian deformation

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• Control of valley optical conductivity and topological phases in buckled hexagonal lattice by orientation of in-plane magnetic field
• Dots and Boxes Algorithm for Peierls Substitution: Application to Multidomain Topological Insulators
• Magnetic-field effect on excitonic condensation emergent in extended Falicov-Kimball model
• Magic-angle twisted bilayer graphene under orthogonal and in-plane magnetic fields
• Band engineering aided by topological edge state proximity effects: Inducing anti-chirality in graphene
• Inverse determination of light-matter coupling in disordered systems from transmittance spectra