101 research outputs found
Electron fractionalization in two-dimensional graphenelike structures
Electron fractionalization is intimately related to topology. In
one-dimensional systems, fractionally charged states exist at domain walls
between degenerate vacua. In two-dimensional systems, fractionalization exists
in quantum Hall fluids, where time-reversal symmetry is broken by a large
external magnetic field. Recently, there has been a tremendous effort in the
search for examples of fractionalization in two-dimensional systems with
time-reversal symmetry. In this letter, we show that fractionally charged
topological excitations exist on graphenelike structures, where quasiparticles
are described by two flavors of Dirac fermions and time-reversal symmetry is
respected. The topological zero-modes are mathematically similar to fractional
vortices in p-wave superconductors. They correspond to a twist in the phase in
the mass of the Dirac fermions, akin to cosmic strings in particle physics.Comment: 4 pages, 2 figure
Spin-directed network model for the surface states of weak three-dimensional topological insulators
A two-dimensional spin-directed network model is
constructed that describes the combined effects of dimerization and disorder
for the surface states of a weak three-dimensional
topological insulator. The network model consists of helical edge states of
two-dimensional layers of topological insulators which
are coupled by time-reversal symmetric interlayer tunneling. It is argued that,
without dimerization of interlayer couplings, the network model has no
insulating phase for any disorder strength. However, a sufficiently strong
dimerization induces a transition from a metallic phase to an insulating phase.
The critical exponent for the diverging localization length at
metal-insulator transition points is obtained by finite-size scaling analysis
of numerical data from simulations of this network model. It is shown that the
phase transition belongs to the two-dimensional symplectic universality class
of Anderson transition.Comment: 36 pages and 27 figures, plus Supplemental Materia
Ground state degeneracy of non-Abelian topological phases from coupled wires
We construct a family of two-dimensional non-Abelian topological phases from
coupled wires using a non-Abelian bosonization approach. We then demonstrate
how to determine the nature of the non-Abelian topological order (in
particular, the anyonic excitations and the topological degeneracy on the
torus) realized in the resulting gapped phases of matter. This paper focuses on
the detailed case study of a coupled-wire realization of the bosonic
Moore-Read state, but the approach we outline here can be
extended to general bosonic topological phases described by
non-Abelian Chern-Simons theories. We also discuss possible generalizations of
this approach to the construction of three-dimensional non-Abelian topological
phases.Comment: 33 pages, 3 figures. v3 replaces previous discussion of 3D case with
an outlook. Published versio
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