Topological massive Dirac edge modes and long-range superconducting Hamiltonians

We discover novel topological effects in the one-dimensional Kitaev chain modified by long-range Hamiltonian deformations in the hopping and pairing terms. This class of models display symmetry-protected topological order measured by the Berry/Zak phase of the lower-band eigenvector and the winding number of the Hamiltonians. For exponentially decaying hopping amplitudes, the topological sector can be significantly augmented as the penetration length increases, something experimentally achievable. For power-law decaying superconducting pairings, the massless Majorana modes at the edges get paired together into a massive nonlocal Dirac fermion localized at both edges of the chain: a new topological quasiparticle that we call topological massive Dirac fermion. This topological phase has fractional topological numbers as a consequence of the long-range couplings. Possible applications to current experimental setups and topological quantum computation are also discussed.

Subband energy in two-band δ-doped semiconductors

We study electron dynamics in a two-band δ-doped semiconductor within the envelope-function approximation. Using a simple parametrization of the confining potential arising from the ionized donors in the δ -doping layer, we are able to find exact solutions of the Dirac-type equation describing the coupling of host bands. As an application we then consider Si δ -doped GaAs. In particular we find that the ground subband energy scales as a power law of the Si concentration per unit area in a wide range of doping levels. In addition, the coupling of host bands leads to a depression of the subband energy due to nonparabolicity effects.