Bulk-boundary correspondence in three-dimensional topological insulators

@article{Isaev2011BulkboundaryCI,
  title={Bulk-boundary correspondence in three-dimensional topological insulators},
  author={Leonid Isaev and Young Hoon Moon and Gerardo Guzman Ortiz},
  journal={Physical Review B},
  year={2011},
  volume={84},
  pages={075444}
}
We discuss the relation between bulk topological invariants and the spectrum of surface states in three dimensional non-interacting topological insulators. By studying particular models, and considering general boundary conditions for the electron wavefunction on the crystal surface, we demonstrate that using experimental techniques that probe surface states, only strong topological and trivial insulating phases can be distinguished; the latter state being equivalent to a weak topological… Expand
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References

SHOWING 1-10 OF 20 REFERENCES
Three-Dimensional Topological Insulators
Topological insulators in three dimensions are nonmagnetic insulators that possess metallic surface states (SSs) as a consequence of the nontrivial topology of electronic wavefunctions in the bulk ofExpand
A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators
We prove a general theorem on the relation between the bulk topological quantum number and the edge states in two dimensional insulators. It is shown that whenever there is a topological order inExpand
Equivalent topological invariants of topological insulators
A time-reversal (TR) invariant topological insulator can be generally defined by the effective topological field theory with a quantized θ coefficient, which can only take values of 0 or π. ThisExpand
Topological insulators with inversion symmetry
Topological insulators are materials with a bulk excitation gap generated by the spin-orbit interaction that are different from conventional insulators. This distinction is characterized by ${Z}_{2}$Expand
Edge states and the bulk-boundary correspondence in Dirac Hamiltonians
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 translationallyExpand
Colloquium : Topological insulators
Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. These states are possible due toExpand
Interaction effects and quantum phase transitions in topological insulators
We study strong correlation effects in topological insulators via the Lanczos algorithm, which we utilize to calculate the exact many-particle ground-state wave function and its topologicalExpand
Marginality of bulk-edge correspondence for single-valley Hamiltonians
We study the correspondence between the nontrivial topological properties associated with the individual valleys of gapped bilayer graphene (BLG), as a prototypical multivalley system, and theExpand
Topological field theory of time-reversal invariant insulators
We show that the fundamental time-reversal invariant (TRI) insulator exists in $4+1$ dimensions, where the effective-field theory is described by the $(4+1)$-dimensional Chern-Simons theory and theExpand
Massive Dirac Fermion on the Surface of a Magnetically Doped Topological Insulator
TLDR
This work introduced magnetic dopants into the three-dimensional topological insulator dibismuth triselenide to break the time reversal symmetry and further position the Fermi energy inside the gaps by simultaneous magnetic and charge doping, thus achieving an insulating gapped Dirac state. Expand
...
1
2
...