"This proposal addresses new scientific challenges in spintrontronics, with the focus on the miniaturization of magnetic sensors. Bismuth crystals and graphene layers show anomalously high Fermi wave length and mean free path. This allows us the observation of electron confinement effects in the length scale of nano-lithography techniques. Both systems can be grown and processed on Si-based substrates, which paves the way for the integration with the existing semiconducting technology. Quantum transport properties are to be studied twofold: by means of intense magnetic fields in nano-patterned devices, and by means of scanning tunnelling microscopy (STM) and spectroscopy (STS) at the surface level. In Bi epitaxial films and graphene flakes, Landau quantization grants access to the topology of the Fermi surface through magnetotransport measurements. The exceptional high-mobility of Bi and graphene gives rise to giant Hall and magnetoresistance effects (> 300,000 %), strongly influenced by structural parameters. Another consequence is the large spin-difussion length, which enables the transport of spin-polarized currents through large distances. Furthermore, the spin-split surface state of Bi crystals and graphene in contact with magnetic electrodes opens up the possibility of polarizing magnetically the medium and injecting spin-polarized currents. The purpose of STM studies here is to assess the influence of structural details at the atomic level on the macroscopic magnetotransport properties of Bi and graphene. STM in combination with pulsed field experiments will be used to investigate the loss of the 2-dimensional character of the electric transport as a function of the sample thickness. Both research lines are very appealing because of the enormous potential for practical device applications and the underlying Physics behind them."