Continuum Model of Localized States at a Domain Wall

  • János K. Asbóth
  • László Oroszlány
  • András Pályi
Part of the Lecture Notes in Physics book series (LNP, volume 919)


So far, we have discussed edge states in lattice models, in which the states live on discrete lattice sites, and the Hamiltonian governing the physics is a matrix. Here we argue that in certain cases, the interesting edge states arising in lattice models, discussed in earlier chapters of the book, can also be described by continuum models, in which the states live in continuous space, and the Hamiltonian is a differential operator. The method applied to derive the continuum models is known as the envelope-function approximation. We obtain continuum Hamiltonians for three basic lattice models: the one-dimensional monatomic chain, the one-dimensional SSH model, and the two-dimensional QWZ model. In the cases of the SSH and QWZ models, we use the resulting effective Schrödinger equations to analytically characterize the localized states appearing at boundaries between regions with different topological invariants.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • János K. Asbóth
    • 1
  • László Oroszlány
    • 2
  • András Pályi
    • 3
    • 4
  1. 1.Wigner Research Centre for PhysicsHungarian Academy of SciencesBudapestHungary
  2. 2.Department of Physics of Complex SystemsEötvös Loránd UniversityBudapestHungary
  3. 3.Department of Materials PhysicsEötvös Loránd UniversityBudapestHungary
  4. 4.Department of PhysicsBudapest University of Technology and EconomicsBudapestHungary

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