Suitably structured HgTe is a topological insulator in both 2- (a quantum well wider than some 6.3 nm) and 3 (an epilayer grown under tensile strain) dimensions. The material has favorable properties for quantum transport studies, i.e. a good mobility and a complete absence of bulk carriers, which allowed us to demonstrate variety of novel transport effects.

A novel development is the use of wet etching technologies to fabricate HgTe based nanostructures. This approach allows a much higher transport quality in nanodevices. We have fabricated quantum point contacts, which show remarkable spin selective transport behavior. Additionally, we have developed a gate-training technique, which pushes the scattering length for the quantum spin Hall effect well above 100 μm. A further recent development is the realization that van Hove singularities in the valence band may give rise to remarkable transport effect, such as e.g. the realization of a n=-1 quantum Hall plateau at fields as low as 20 mT.

Another regime we can study is topological superconductivity, achieved by proximity-inducing superconductivity in the topological surface states. Special emphasis will be given to recent results on the ac Josephson effect. We will present data on Shapiro step behavior that is a very strong indication for the presence of a gapless Andreev mode in our Josephson junctions, both in 2- and in 3-dimensional structure. An additional and very direct evidence for the presence of a zero mode is our observation of Josephson radiation at an energy equal to half the superconducting gap.

Controlling the strain of the HgTe layers strain opens up yet another line a research. We have recently optimized MBE growth of so-called virtual substrates ((Cd,Zn)Te superlattices as a buffer on a GaAs substrate), that allow us to vary the strain from 0.4% tensile to 1.5% compressive. While tensile strain turns 3-dimensional HgTe into a narrow gap insulator, compressive strain turns the material into a topological (Dirac/Weyl) semimetal, exhibiting clear signs of the Adler-Bell-Jackiw anomaly in its magnetoresistance. In quantum wells, compressive strain allows inverted energy gaps up to 60 meV.