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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. 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 Andeev 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 pi transform into two zero-energy states carrying two Majorana fermions.

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Pascal Simon, Université Paris Sud
Seminarraum Theoretische Physik
Contact: not specified