Abstract
This thesis presents an investigation of different topological phases in mercury-cadmium-telluride (HgCdTe or MCT) based heterostructures. These solid state systems are indeed a perfect playground to study topological states, as their band structure can be easily varied from inverted to non-inverted, by changing internal or external parameters. If a system has an inverted band ordering, its electronic structure has a non-trivial topology. One cannot change its topological order without closing the band gap, which is inevitably accompanied with the appearance of massless particles in the bulk. A system, that has an inverted band structure and a finite gap in which the Fermi level is positioned, is called a topological insulator. These novel materials are insulators in the bulk, but host gapless metallic states with linear dispersion relation at boundaries, protected against disorder and backscattering on non-magnetic impurities. These states arise at the interfaces between materials characterized by a different topological order. A 2D topological insulator is thus characterized by a set of 1D spin-polarized channels of conductance at the edges, while a 3D topological insulator supports spin-polarized 2D Dirac fermions on its surfaces.The 2D and 3D massless fermions have already been demonstrated experimentally in HgCdTe-based heterostructures. However, the topological phase transitions during which the massless particles appear remain barely explored. The HgCdTe band structure can be tuned from inverted to non-inverted using chemical composition, pressure, temperature, or quantum confinement. These parameters therefore allow to probe the system in the vicinity of different topological phase transitions. In this thesis, the use of temperature as continuous band gap tuning parameter allows to study the appearance and the parameters of semi-relativistic 2D Dirac and 3D Kane fermions emerging at the points of phase transitions.The systems investigated were Hg_{1-x}Cd_xTe bulk systems and HgTe/CdTe quantum wells characterized by an inverted and regular band order, and strained HgTe films which can be considered as 3D topological insulators with a residual quantum confinement. All these systems exhibit topological properties, and the experimental results are interpreted according to theoretical predictions based on the Kane model. This thesis is complemented by an overview and the preliminary results obtained on a different compound -- a InAs/GaSb broken-gap quantum well, which was also identified as a topological insulator. The structures were studied by means of terahertz and mid-infrared magneto-transmission spectroscopy in a specifically designed experimental system, in which temperature could be tuned in a broad range.