The Master's theses presents the quantization of the transconductance in a 4-terminal Josephson junction in presence of the Rashba interaction. The Bogoliubov-de Gennes formalism for a conventional superconductor is introduced. Superconductor's eigenstates and energies are derived step by step. Solution to the scattering problem between a normal and a superconducting material is written and the Andreev reflection and Andreev bound states are discussed. Then, the Josephson current, the relation between the Chern number and the transconductance and the correspondence between superconducting phases and the crystal momentum in the solid state physics are presented. Topological classification in systems with an additional symmetry or with anomalous parameters is explained. A 4-terminal Josephson junction is analyzed in absence and in presence of the Rashba interaction added in the central scattering region. Energy bands of Andreev bound states and their Berry curvatures are numerically calculated from where the Chern number and the quantised transconductance are obtained and emphasized upon. It turns out that the Rashba interaction may convert topologically trivial systems into topologically nontrivial ones. Also, the obtained symmetries of Chern numbers in the considered parameter space, ie. a superconducting phase and a Rashba phase, differ from the symmetries in a 5-terminal Josephson junction since the Chern number is an even function of the Rashba phase.
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