Ballistic Transport Phenomena in Nanostructures of Paraelectric Lead Telluride

This is a review of our recent developments in the physics of lead telluride nanostructures. PbTe is a IV-VI narrow gap paraelectric semiconductor, characterized by the huge static dielectric constant ε >1000 at helium temperatures. We nanostructurized this material by means of e-beam lithography and wet chemical etching of modulation doped PbTe/Pb$\text{}_{1-x}$Eu$\text{}_{x}$Te quantum wells. Magnetoresistance measurements performed on the nano-structures revealed a number of magnetosize effects, confirming a ballistic motion of the carriers. The most important observation is that the conductance of narrow constrictions shows a precise zero-field quantization in 2e$\text{}^{2}$/h units, despite a significant amount of charged defects in the vicinity of the conducting channel. This unusual result is a consequence of a strong suppression of the Coulomb potential fluctuations in PbTe, an effect confirmed by numerical simulations. Furthermore, the orbital degeneracy of electron waveguide modes can be controlled by the width of PbTe/Pb$\text{}_{1-x}$Eu$\text{}_{x}$Te quantum wells, so that unusual sequences of plateau conductance can be observed. Finally, conductance measurements in a nonlinear regime allowed for an estimation of the energy spacing between the one-dimensional subbands.