Dresden 2020 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 40: Topological Josephson Junctions

TT 40.1: Talk

Wednesday, March 18, 2020, 15:00–15:15, HSZ 103

Second Chern number and non-Abelian Berry phase in topological Josephson matter — •Hannes Weisbrich, Raffael L. Klees, Gianluca Rastelli, and Wolfgang Belzig — Universität Konstanz

Topology and related quantized numbers play an important role in condensed matter physics in various topics. For instance, it has been theoretically proposed that the first Chern number is related to a quantized transconductance in topological Josephson matter [1]. Higher dimensional topological phases characterized by the second Chern number can describe even more complex quantum states, e.g. the four dimensional quantum Hall effect [2]. Hereby we present a first theoretical proposal for topological Josephson matter with a non-trivial second Chern number. We show that a double quantum dot in contact with several superconducting leads can implement such exotic topological state. Moreover the lowest pair of Andreev states shows a non-Abelian Berry phase which can be used to perform arbitrary rotations within the twofold degenerate subspace by adiabatic changes of the superconducting phases. Finally, we discuss a measurement protocol for the second Chern number by means of a combination of non-Abelian Berry rotations and polarized microwave spectroscopy [3].
[1] R.-P. Riwar et al., Nat. Commun. 7, 11167 (2016).
[2] S. C. Zhang and J. Hu, Science, 294(5543), 823-828 (2001).
[3] R. L. Klees et al., arXiv:1810.11277 (2018).