title: Parity measurement in topological Josephson junctions.
abstract: We study the properties of a topological Josephson junction made of both edges of a two-dimensional topological insulator. We show that, due to fermion parity pumping across the bulk, the global parity of the junction has a clear signature in the periodicity and critical value of the Josephson current. In particular, we find that the periodicity with the flux changes from 4π in a junction with an even number of quasiparticles to 2π in the odd sector. In the case of long junctions, we exhibit a rigorous mathematical connection between the spectrum of Andreev bound states and the fermion parity anomaly, through bosonization. Additionally, we discuss the rather quantitative effects of Coulomb interactions on the Josephson current.
authors.affiliation: Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany.
authors.forename: François
authors.initials: F
authors.lastname: Crépin
authors.affiliation: Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany.
authors.forename: Björn
authors.initials: B
authors.lastname: Trauzettel