2D (3D) topological insulators are novel states of matter which are characterised by topological invariants instead of symmetry breaking. These states possess an insulating gap surrounded by metallic edges (surfaces) where the momentum of electrons is locked with their spin. The underlying mechanism is the spin-orbit interaction that causes the inversion of bands of opposite parities. The Quantum Spin Hall effect (QSH) refers to the counter-propagation of electrons with opposite spin along the edges of a 2D topological insulator. One year after its prediction in (Hg,Cd)Te quantum well, transport measurements confirmed that this candidate is a topological insulator under some conditions : below a critical thickness the quantum well behaves as a trivial insulator and above the same critical thickness it is a topological insulator. In this context, we consider a junction between a doped HgTe quantum well and a s-wave singlet superconductor. In the first part of the presentation, I shall highlight that Andreev reflection can be used as a probe of the carrier dynamics in HgTe quantum well which is intermediate between linear and quadratic dispersion. In the second part, I shall show the existence of an inter-facial Spin Hall effect at junctions between the doped HgTe quantum well and the s-wave singlet superconductor. This effect is intimately related to the coexistence of propagating and evanescent modes at the interface and in absence of structure and bulk inversion asymmetry within each sub-system. |