I will present recent results on a one-dimensional wire with strong
Rashba and Dresselhaus spin-orbit coupling (SOC), which supports
Majorana fermions when subject to a Zeeman magnetic field and in
proximity of a superconductor. By introducing a new local quantity
dubbed as "Majorana polarization" , I will argue that it can be used as
a local order parameter to characterize the topological transition
between a trivial system and a system exhibiting Majorana bound modes.
We have found that the local "Majorana polarization" is correlated to
the transverse spin polarization, and we propose to test the presence of
Majorana fermions in a 1D system by a spin-polarized density of states
measurement [1]. Such quantity turns out to be very useful to analyze
one-dimensional topological SN and SNS long junctions obtained by
placing a topological insulating nanowire in the proximity of either one
or two superconducting finite-size leads: for a finite-size SN junction
the Andreev Bound States (ABS) spectrum exhibits a zero-energy extended
state which carries a full Majorana fermion, while the ABS of long SNS
junctions with phase difference π transform into two zero-energy
states carrying two Majorana fermions [2]. If time permits, I will also
discuss Josephson junctions between topological wires supporting
multiple Majorana fermions [3].
[1] D. Sticlet, C. Bena, P. Simon, Phys. Rev. Lett. 108, 096802 (2012).
[2] D. Chevallier, D. Sticlet, P. Simon, C. Bena, Phys. Rev. B 85,
235307 (2012).
[3] D. Sticlet, C. Bena, P. Simon,
arXiv:1211.3070