463 research outputs found
Index theorem for topological heterostructure systems
We apply the Niemi-Semenoff index theorem to an s-wave superconductor
junction system attached with a magnetic insulator on the surface of a
three-dimensional topological insulator. We find that the total number of the
Majorana zero energy bound states is governed not only by the gapless helical
mode but also by the massive modes localized at the junction interface. The
result implies that the topological protection for Majorana zero modes in class
D heterostructure junctions may be broken down under a particular but realistic
condition.Comment: 8 pages, 3 figure
Spin Chains with Periodic Array of Impurities
We investigate the spin chain model composed of periodic array of two kinds
of spins and , which allows us to study the spin chains with
impurities as well as the alternating spin chains in a unified fashion. By
using the Lieb-Shultz-Mattis theorem, we first study the model rigorously, and
then by mapping it to the non-linear sigma model, we extensively investigate
low-energy properties with particular emphasis on the competition between the
massive and massless phases.Comment: 5 pages, revtex, To appear in PR
Majorana bound state of a Bogoliubov-de Gennes-Dirac Hamiltonian in arbitrary dimensions
We study a Majorana zero-energy state bound to a hedgehog-like point defect
in a topological superconductor described by a Bogoliubov-de Gennes (BdG)-Dirac
type effective Hamiltonian. We first give an explicit wave function of a
Majorana state by solving the BdG equation directly, from which an analytical
index can be obtained. Next, by calculating the corresponding topological
index, we show a precise equivalence between both indices to confirm the index
theorem. Finally, we apply this observation to reexamine the role of another
topological invariant, i.e., the Chern number associated with the Berry
curvature proposed in the study of protected zero modes along the lines of
topological classification of insulators and superconductors. We show that the
Chern number is equivalent to the topological index, implying that it indeed
reflects the number of zero-energy states. Our theoretical model belongs to the
BDI class from the viewpoint of symmetry, whereas the spatial dimension of the
system is left arbitrary throughout the paper.Comment: 12 page
Topological aspects of quantum spin Hall effect in graphene: Z topological order and spin Chern number
For generic time-reversal invariant systems with spin-orbit couplings, we
clarify a close relationship between the Z topological order and the spin
Chern number proposed by Kane and Mele and by Sheng {\it et al.}, respectively,
in the quantum spin Hall effect. It turns out that a global gauge
transformation connects different spin Chern numbers (even integers) modulo 4,
which implies that the spin Chern number and the Z topological order yield
the same classification. We present a method of computing spin Chern numbers
and demonstrate it in single and double plane of graphene.Comment: 5 pages, 3 figure
- …