Professor: Dr. Ezequiel Siqueira

Resumo: The conduction of electrons in materials has been a matter of intense research since the devel-
opment of quantum mechanics. The advances on the understanding of how electrons flow within

materials gave rise to a revolution of our society. In fact, most of the current technology, including
computers or any electronic device, is based on electrical properties of materials like silicon. The

microelectronic technology, started in the 40’s, has changed the way the people live and communi-
cate nowadays. In the 80’s, a new revolution was put forward when the researchers start wondering

how the electrons would flow in nanoscale dimensions. Within this length scale, the dynamics of
electrons is completely ruled by quantum mechanics, in contrast to the microeletronic devices, in
which a semiclassical approach may be used to describe the physics of pn-junctions and transistors.
Since the first experiments performed in the 80’s, a vigorously increase in the research on nanoscale

systems has been observed and many effects and devices have been developed. Within the profu-
sion of devices and systems proposed, we start highlighting the early devices based on the giant

magnetoresistance effect (the Nobel Prize of 2007), the spintronics devices, hybrid systems based
on quantum dots (which mimic the discrete spectrum of atoms), Majorana fermions excitations in
exotic superconductors and the new materials like graphene (the Nobel Prize of 2010) and, most
recently, the topological insulators. In these lectures, we propose an introduction to many body
methods applied to quantum transport in order to give the student the basics tools to be able to
read the first papers on this interesting field of research.