Bilayer graphene in periodic and quasiperiodic magnetic superlattices

Abstract

Starting from the effective Hamiltonian arising from the tight binding model, we study the behaviour of low-lying excitations for bilayer graphene placed in periodic external magnetic fields by using irreducible second order supersymmetry transformations. The coupled system of equations describing these excitations is reduced to a pair of periodic Schrödinger Hamiltonians intertwined by a second order differential operator. The direct implementation of more general second-order supersymmetry transformations allows to create nonsingular Schrödinger potentials with periodicity defects and bound states embedded in the forbidden bands, which turn out to be associated to quasiperiodic magnetic superlattices. Applications in quantum metamaterials stem from the ability to engineer and control such bound states which could lead to a fast development of the subject in the near future.

References in corpus (40)

• Electric Field Effect in Atomically Thin Carbon Films
• Graphene: Status and Prospects
• Twistronics: Manipulating the Electronic Properties of Two-dimensional Layered Structures through their Twist Angle
• Energy Spectrum and Quantum Hall Effect in Twisted Bilayer Graphene
• New generation of moiré superlattices in doubly aligned hBN/graphene/hBN heterostructures
• Electron quantum metamaterials in van der Waals heterostructures
• Self-Isospectral Periodic Potentials and Supersymmetric Quantum Mechanics
• Electronic transport through bilayer graphene flakes
• Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles
• Strain-induced band gaps in bilayer graphene
• Dirac electron in graphene under supersymmetry generated magnetic fields
• Nonlocal supersymmetric deformations of periodic potentials
• Hofstadter's Butterfly in Quantum Geometry
• Supersymmetry in quantum optics and in spin-orbit coupled systems
• The Phenomenon of Darboux Displacements
• Dirac electron in graphene with magnetic fields arising from first-order intertwining operators
• Duality and Self-Duality (Energy Reflection Symmetry) of Quasi-Exactly Solvable Periodic Potentials
• Optical Supersymmetry in the Time Domain
• Lamé polynomials, hyperelliptic reductions and Lamé band structure
• Periodic Potentials and Supersymmetry
• Construction of zero energy states in graphene through the supersymmetry formalism
• Chiral asymmetry in propagation of soliton defects in crystalline backgrounds
• Dirac Hamiltonian in a supersymmetric framework
• Electron in bilayer graphene with magnetic fields leading to shape invariant potentials
• Soliton defects in one-gap periodic system and exotic supersymmetry
• Exactly solvable associated Lame potentials and supersymmetric transformations
• Bilayer graphene in magnetic fields generated by supersymmetry
• New supersymmetric partners for the associated Lame potentials
• Supersymmetric Dirac-Hamiltonians in $(1+1)$ dimensions revisited
• Quantum Hall Superconductivity from Moir{é} Landau Levels
• Confluent Second-Order Supersymmetric Quantum Mechanics and Spectral Design
• Dual-gated hBN/bilayer-graphene superlattices and the transitions between the insulating phases at the charge neutrality point
• Generalized harmonic confinement of massless Dirac fermions in (2+ 1) dimensions
• Hierarchy of QM SUSYs on a Bounded Domain
• Complex Supersymmetry in Graphene
• Ritus functions for graphene-like systems with magnetic fields generated by first-order intertwining operators
• Dirac equation in curved spacetime: the role of local Fermi velocity
• A New Class of Solvable Two-dimensional Scalar Potentials for Graphene
• Supersymmetric Quantum Potentials Analogs of Classical Electrostatic Fields
• Solvable Two-dimensional Dirac Equation with Matrix Potential: Graphene in External Electromagnetic Field