Thermal and Electrical Insights into Topological and Non-Topological Andreev Bound States

Mukhopadhyay, Aabir (2024) Thermal and Electrical Insights into Topological and Non-Topological Andreev Bound States. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (PhD thesis of Aabir Mukhopadhyay (16IP019)) 16IP019.pdf - Submitted Version Restricted to Repository staff only Download (9MB)

Abstract

This thesis focuses on the thermal and electrical transport properties of Josephson junctions described within the mean-field theory of superconductivity. Instead of studying only the sub-gap transport phenomena, we start by considering thermal-bias induced transports dominated by above-the-gap quasiparticles. We have shown that applying a thermal bias across a Josephson junction not only causes a heat current but also gives rise to a measurable electrical current (thermo-current), particularly in the ballistic and moderate junction length regimes. Our study suggests distinct transmission probabilities for a Bogoliubov quasiparticle traversing the junction in opposite directions. This asymmetry, mediated by the dynamical phase, breaks particle-hole (ω → - ω) symmetry and gives rise to the thermo-current effect. On the other hand, thermal transport in a topological three-terminal Josephson junction exhibits distinct signatures of Majorana bound states through the poles of transmission probability in the complex energy plane. These phenomena arise from the presence of confirmed zero mode, originating from the hybridization of an odd number of Majoranas. In addition to the inherent topological nature of superconductors, the sub-gap bound states of multiterminal junctions can host additional band topology due to their periodic dependence on the Josephson phase biases. This band topology can affect the electrical transport phenomena, specifically the AC Josephson current behavior. Consequently, we explore the role of Bogoliubov-de Gennes symmetry in sub-gap bound states and show that the topology of Andreev bands depends only on the scattering matrix of the junction and is independent of the topological nature of superconductors forming the Josephson junction. Additionally, we demonstrate the possibility of designing completely flat Andreev bands that are devoid of Berry curvature, facilitated by the support of a quantum Hall state. Finally, we study the symmetry properties of the pairing potential induced in the junction due to its proximity to multiple superconductors. In particular, we study the presence of oddfrequency superconducting pairing in the Josephson junction and its possible detection via electrical transport measurements.

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