University of Twente Student Theses


Usadel equation for a four terminal junction

Kokkeler, T.H. (2021) Usadel equation for a four terminal junction.

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Abstract:In this thesis, a model of the a four terminal SNS junction is investigated. The model predicts outcomes of experiments on spectral supercurrent, total supercurrent, differential conductance and local density of states in junctions with two conventional or unconventional superconductor terminals and two normal metal terminals. The two normal metal terminals are used to change the occupation of electron levels in the junction. The differences between the results for s-wave and p-wave superconducting electrodes is investigated. These differences can be used for experimental verification of the existence of p-wave superconductors, which are predicted to host Majorana fermions. The model used is based on the non-equilibrium Green's function theory. This theory is applied to the four terminal junction in the quasiclassical dirty limit. The model uses Tanaka Nazarov boundary conditions for the superconducting electrodes. The resulting equations in the so-called theta-parametrisation will be derived. The setup allows for variation to include topological insulators. This is important, both from a theoretical viewpoint and from the viewpoint of applications. For theoretical fundamentals it is important because it has never been proved that p-wave superconductivity exists, for applications it is of interest because in unconventional superconductivity Majorana fermions might exist, which are important for quantum computing.
Item Type:Essay (Master)
Faculty:TNW: Science and Technology
Subject:31 mathematics, 33 physics
Programme:Applied Physics MSc (60436)
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