@article{VigliottiCalzonaTraversoZianietal.2023,
  author    = {Vigliotti, Lucia and Calzona, Alessio and Traverso Ziani, Niccol{\`o} and Bergeret, F. Sebastian and Sassetti, Maura and Trauzettel, Bj{\"o}rn},
  title     = {Effects of the spatial extension of the edge channels on the interference pattern of a helical Josephson junction},
  series = {Nanomaterials},
  volume    = {13},
  journal   = {Nanomaterials},
  number    = {3},
  issn      = {2079-4991},
  doi       = {10.3390/nano13030569},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-304846},
  year      = {2023},
  abstract  = {Josephson junctions (JJs) in the presence of a magnetic field exhibit qualitatively different interference patterns depending on the spatial distribution of the supercurrent through the junction. In JJs based on two-dimensional topological insulators (2DTIs), the electrons/holes forming a Cooper pair (CP) can either propagate along the same edge or be split into the two edges. The former leads to a SQUID-like interference pattern, with the superconducting flux quantum ϕ\(_0\) (where ϕ\(_0\)=h/2e) as a fundamental period. If CPs' splitting is additionally included, the resultant periodicity doubles. Since the edge states are typically considered to be strongly localized, the critical current does not decay as a function of the magnetic field. The present paper goes beyond this approach and inspects a topological JJ in the tunneling regime featuring extended edge states. It is here considered the possibility that the two electrons of a CP propagate and explore the junction independently over length scales comparable to the superconducting coherence length. As a consequence of the spatial extension, a decaying pattern with different possible periods is obtained. In particular, it is shown that, if crossed Andreev reflections (CARs) are dominant and the edge states overlap, the resulting interference pattern features oscillations whose periodicity approaches 2ϕ\(_0\).},
  language  = {en}
}
@article{BudichTrauzettel2013,
  author    = {Budich, Jan Carl and Trauzettel, Bj{\"o}rn},
  title     = {Z(2) Green's function topology of Majorana wires},
  series = {New Journal of Physics},
  volume    = {15},
  journal   = {New Journal of Physics},
  number    = {065006},
  doi       = {10.1088/1367-2630/15/6/065006},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-129751},
  year      = {2013},
  abstract  = {We represent the Z2 topological invariant characterizing a one-dimensional topological superconductor using a Wess-Zumino-Witten dimensional extension. The invariant is formulated in terms of the single-particle Green's function which allows us to classify interacting systems. Employing a recently proposed generalized Berry curvature method, the topological invariant is represented independent of the extra dimension requiring only the single-particle Green's function at zero frequency of the interacting system. Furthermore, a modified twisted boundary conditions approach is used to rigorously define the topological invariant for disordered interacting systems.},
  language  = {en}
}