Teo, Jeffrey C.Y.

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  • Publication
    Majorana Fermoins and Non-Abelian Statistics in Three Dimensions
    (2010-01-25) Teo, Jeffrey C.Y.; Kane, Charles L
    We show that three dimensional superconductors, described within a Bogoliubov–de Gennes framework, can have zero energy bound states associated with pointlike topological defects. The Majorana fermions associated with these modes have non-Abelian exchange statistics, despite the fact that the braid group is trivial in three dimensions. This can occur because the defects are associated with an orientation that can undergo topologically nontrivial rotations. A feature of three dimensional systems is that there are ‘‘braidless’’ operations in which it is possible to manipulate the ground state associated with a set of defects without moving or measuring them. To illustrate these effects, we analyze specific architectures involving topological insulators and superconductors.
  • Publication
    Topological Defects and Gapless Modes in Insulators and Superconductors
    (2010-09-22) Teo, Jeffrey C.Y.; Kane, Charles L.
    We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians.We consider Hamiltonians H(k,r) that vary slowly with adiabatic parameters r surrounding the defect and belong to any of the ten symmetry classes defined by time-reversal symmetry and particle-hole symmetry. The topological classes for such defects are identified and explicit formulas for the topological invariants are presented. We introduce a generalization of the bulk-boundary correspondence that relates the topological classes to defect Hamiltonians to the presence of protected gapless modes at the defect. Many examples of line and point defects in three-dimensional systems will be discussed. These can host one dimensional chiral Dirac fermions, helical Dirac fermions, chiral Majorana fermions, and helical Majorana fermions, as well as zero-dimensional chiral and Majorana zero modes. This approach can also be used to classify temporal pumping cycles, such as the Thouless charge pump, as well as a fermion parity pump, which is related to the Ising non-Abelian statistics of defects that support Majorana zero modes.