Edge states and the bulk-boundary correspondence in Dirac Hamiltonians
By Roger S. K. Mong, V. Shivamoggi. 2010
211 citations recorded by the source corpus.
We present an analytic prescription for computing the edge dispersion E(k) of a tight-binding Dirac Hamiltonian terminated at an abrupt crystalline edge. Specifically, we consider translationally invariant Dirac Hamiltonians with nearest-layer interaction. We present and prove a geometric formula that relates the existence of surface states as well as their energy dispersion to properties of the bulk Hamiltonian. We further prove the bulk-boundary correspondence between the Chern number and the chiral edge modes for quantum Hall systems within the class of Hamiltonians studied in the paper. Our results can be extended to the case of continuum theories which are quadratic in the momentum, as well as other symmetry classes.
Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/951c973743f2f8cd06b00d77541789dd355c29ac
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In Atomic and Molecular Physics, and Optics
In Materials Chemistry
Citations in the corpus
- All-Si valley-Hall photonic topological insulator (2016, methodology): “Following the lesson from bulk-boundary correspondence [3], a guiding interface between two QVH-PTIs with opposite sign of the valley-Chern index will support edge states.”
- Topological photonics (2018, background): “(20), along the k⊥ direction over the first Brillouin zone (Ryu and Hatsugai, 2002; Delplace, Ullmo, and Montambaux, 2011; Mong and Shivamoggi, 2011): WðkkÞ ¼ 1 2π Z BZ dk⊥ dθðk⊥; kkÞ dk⊥ : ð68Þ The information about the specific type of edge is contained in the choice of unit cell dimer and unit…”
- Topological node-line semimetal in three-dimensional graphene networks (2014, methodology): “The topology of this effective continuum bulk hamiltonian has been analyzed [33] (See Supplemental Material for details) and found to have topologically protected (001) surface states with dispersionless zero eigen energy inside of the projected node-line circle given by k̄(2) x + k̄ 2 y = M B .”