318 research outputs found
Majoranas with and without a 'character': hybridization, braiding and Majorana number
In this paper we demonstrate under what conditions a pseudo-spin degree of
freedom or character can be ascribed to the Majorana bound states (MBS) which
can be created at the end of one dimensional non-interacting systems,
corresponding to D, DIII and BDI in the usual classification scheme. We have
found that such a character is directly related to the class of the topological
superconductor and its description by a , rather than a
, invariant which corresponds to the BDI class. We have also
found that the DIII case with mirror symmetry, which supports multiple MBS, is
in fact equivalent to the BDI class with an additional time-reversal symmetry.
In all cases where a character can be given to the Majorana states we show how
to construct the appropriate operator explicitly in various examples. We also
examine the consequences of the Majorana character by considering possible
hybridization of MBS brought into proximity and find that two MBS with the same
character do not hybridize. Finally, we show that having this character or not
has no consequence on the braiding properties of MBS.Comment: 10 pages, 1 figur
Majorana bound states in open quasi-1D and 2D systems with transverse Rashba coupling
We study the formation of Majorana states in quasi-1D and 2D square lattices
with open boundary conditions, with general anisotropic Rashba coupling, in the
presence of an applied Zeeman field and in the proximity of a superconductor.
For systems in which the length of the system is very large (quasi-1D) we
calculate analytically the exact topological invariant, and we find a rich
phase diagram which is strongly dependent on the width of the system. We
compare our results with previous results based on a few-band approximation. We
also investigate numerically open 2D systems of finite length in both
directions. We use the recently introduced generalized Majorana polarization,
which can locally evaluate the Majorana character of a given state. We find
that the formation of Majoranas depends strongly on the geometry of the system
and if the length and the width are comparable no Majorana states can form,
however, one can show the formation of "quasi-Majorana" states that have a
local Majorana character, but no global Majorana symmetry.Comment: 12 pages, 13 figure
Flat Majorana bands in 2-d lattices with inhomogeneous magnetic fields: topology and stability
In this paper we show that for a range of configurations of inhomogeneous
magnetic fields it is possible to create flat bands of Majorana states
localized on the edges of 2-d lattices. Majorana bound states have been
predicted to exist in both one dimensional and two dimensional systems with
Rashba spin-orbit coupling, magnetic fields, and placed in proximity to a
superconductor. For the proposed systems we present the bulk topological phase
diagrams, and we study the conditions for weak topology which predicts the
formation of bands of Majorana states. The Majorana bands are demonstrated to
be relatively stable with respect to a variety of different perturbations on
both square and hexagonal lattices.Comment: 13 pages, 17 figure
Transport Properties of an Interacting Quantum Dot with a Non-Uniform Magnetization
We study the influence of the non-homogeneity of a magnetization field on the
behaviour of interacting electrons in a quantum dot. In particular we
investigate the magnetotransport properties when the dot is weakly coupled to
two ferromagnetic leads. We take into account the interactions in the quantum
dot non-perturbatively. For a magnetization which varies slowly on the scale of
the Fermi wave length, the non-homogeneity effect is described by a gauge
potential that can be treated perturbatively.Comment: 6 pages, to be published in EP
Non-Collinear Ferromagnetic Luttinger Liquids
The presence of electron-electron interactions in one dimension profoundly
changes the properties of a system. The separation of charge and spin degrees
of freedom is just one example. We consider what happens when a system
consisting of a ferromagnetic region of non-collinearity, i.e. a domain wall,
is coupled to interacting electrons in one-dimension (more specifically a
Luttinger liquid). The ferromagnetism breaks spin charge separation and the
presence of the domain wall introduces a spin dependent scatterer into the
problem. The absence of spin charge separation and the effects of the electron
correlations results in very different behaviour for the excitations in the
system and for spin-transfer-torque effects in this model.Comment: 6 pages, submitted to Journal of Physics: Conference Series for JEMS
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