TY  - JOUR
A1  - Budich, Jan Carl
A1  - Trauzettel, Björn
T1  - Z(2) Green's function topology of Majorana wires
JF  - New Journal of Physics
N2  - 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.
KW  - Green's function
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-129751
VL  - 15
IS  - 065006
ER  - 
TY  - JOUR
A1  - Vigliotti, Lucia
A1  - Calzona, Alessio
A1  - Traverso Ziani, Niccolò
A1  - Bergeret, F. Sebastian
A1  - Sassetti, Maura
A1  - Trauzettel, Björn
T1  - Effects of the spatial extension of the edge channels on the interference pattern of a helical Josephson junction
JF  - Nanomaterials
N2  - 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\(_0\).
KW  - edge states
KW  - Josephson junctions
KW  - topological insulators
KW  - interference pattern
KW  - 2ϕ\(_0\) periodicity
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-304846
SN  - 2079-4991
VL  - 13
IS  - 3
ER  -