All materials on the earth are divided into two types of conductors, metals and insulators (equivalently semiconductors). Free electrons in the metals, which are
travelling through the crystal lattice, carry electrical current. These itinerant electrons are quantum mechanically described as plane waves that coherently develop over a sample body.
When we study the magnetic response of the materials, we find that some of them strongly respond to an external magnetic field like a magnet. If you could look microscopically inside the magnet, then you would observe that spin and angular momentum of the electrons are responsible for the strong magnetism. These electrons are well localized at the atom site, and hence can be counted as 1, 2, 3 … , like particles.
The f electrons of rare earth and actinide elements are known to be localized at the atom site. Interestingly, they can move in a circumstance from one atom to the neighboring atom, albeit a small probability, by means of tunneling effect that is characteristic of quantum mechanical objects. As a result, these f electrons finally get the duality of particle-like localized nature and wave-like itinerant nature. In some materials called heavy fermions (or heavy electrons), the electrons with the dual nature carry a heavy mass due to the repulsive Coulomb interaction between the electrons with the negative charge, which can amount to 1000m0 (where m0 is a rest mass of electron).
In our laboratory, we study novel materials showing interesting phenomena that are hardly explained by the exiting theories. One example of such the materials is a
superconducting magnet. As mentioned above, the heavy mass arises from the repulsive interaction. On the contrary, it is known that the superconductivity needs some attractive interaction between
the electrons. Furthermore, it has been believed that the internal magnetic field inside the magnet would destroy Cooper pairs carrying supercurrent with zero resistivity. These considerations
may imply that there would be no material that exhibit magnetism and superconductivity simultaneously. Interestingly, there exists such a superconducting magnet. It is now understood that in a
case, the coexistence of magnetism and superconductivity is possible due to the dual nature of the heavy fermions. Readers who are interested in this subject may visit our scientific paper: N. K.
Sato et al., Nature 410 (2001) 340.
Another example of the novel materials is a semiconductor that shows a phase transition from a black semiconductor phase to a golden metal phase at a high pressure. This black to golden transition itself attracts our attention, but more exotic phenomenon may be hidden in the black phase: we speculate that pairs of electrons and holes (called excitons) may condensate at low temperatures like the Bose condensation of the Cooper pairs in superconductors. Experimentally observing the novel exciton-condensation remains a formidable challenge.
As another example of the novel materials, we take a quasicrystal, an intermetallic alloy that possesses aperiodic structures with diffraction symmetries forbidden to the conventional crystals. It is believed that their electronic states are critical, neither extended nor localized. Besides of extensive efforts, such the critical state is not experimentally established yet. However, our recent experiment may reveal this state unique to the quasicrystal. For details, we refer to our scientific paper: K. Deguchi et al., Nature Mat. 11 (2012) 1013.