Dr. Mauro Melchiades Doria, professor Instituto de Física, Universidade Federal do Rio de Janeiro, Brazil has presented a lecture for all the students and employees of MIEM

Dr. Mauro Doria, recognized specialist in the field of new superconducting materials, has held an interesting scientific event for all MIEM employees and students - a lecture "The Origin of the Dirac Linear Spectrum and Topology "

In this talk a historical over view was presented about the developments in surface electronic states that dates back to the work of Igor Tamn (1930’s) and Vitaly Ginzburg (1960’s), to finally reach the proposal of Alex Abrikosov (1990’s) that the Dirac spectrum explains the linear magneto resistance observed in many layered materials.
Nevertheless, the currently accepted explanation for the presence of a linear Dirac spectrum, given for graphene, relies on two intertwined hexagonal lattices, but this is not applicable to most of the two-dimensional electronic systems, whose crystallographic structure is not of this kind. From the other side the bare assumption of the Dirac equation defies the absence of relativistic invariance in such two- dimensional electronic systems.
And yet the linear Dirac spectrum is found in iron-based, cuprate superconductors, topological insulators, and many other compounds. The simplest Hamiltonian associated to the linear Dirac spectrum is the Weyl equation, which is not acceptable in Condensed Matter Physics since it violates reflection symmetry. The Weyl equation with real spin can be at best a parametric equation.
A new era of surface electronic states started with the discovery of the quantum Hall effect (1980’s) and extended to the so-called topological insulators (2010 ́s) that display novel properties[1], such as spin-momentum locking, which is currently attributed to the so-called Rashba interaction.
Possible applications of topological insulators are spin filters, spintronic devices, topological qubits and thermoelectric devices. In a topological insulator the electronic state is ‘knotted’ by topology as it moves through momentum space. The point of view taken here is that a surface electronic state can only be localized in momentum but not in position space.
All such matters were discussed during the presentation and were concluded with a discussion about the zero helicity state which is a special limit of the Weyl state.