Topological Materials

Topology is a field of Mathematics which nowadays often appears in Condensed Matter Physics research articles. And it has come to stay. As an example, the Nobel Prize in Physics 2016 was awarded to David J. Thouless, F. Duncan M. Haldane and J. Michael Kosterlitz "for theoretical discoveries of topological phase transitions and topological phases of matter".

In a nutshell, Topology deals with the properties of bodies that are preserved upon continuous deformations, which are represented by topological invariants. The concept of continuous deformation is often intuitively illustrated with the following (worn-out, but powerful) everyday life analogue: a mug and a donut are topologically equivalent because they have only one hole (or, more technically, they have the same genus g=1). Nevertheless, they are topologically distinct from a sphere or a pretzel, which have 0 and 3 holes, respectively. Another layman example of the issues that Topology deals with is the Hairy Ball  Theorem (that's its real name). Owing to this theorem, you cannot  comb the hairs of a coconut without creating a cowlick, and you can prove there is always at least one cyclone or anticyclone on the Earth's surface.

Topological insulators (TIs) are a new quantum phase of matter which is characterised by a topological invariant, as opposed to Ginzburg-Landau phases of matter which are characterised by an order parameter. Their most prominent feature is that, while being bulk insulators, a state will localise at the boundary when confronted with a trivial (or non-topological) material, such as vacuum or an ordinary insulator. These boundary states show spin-momentum locking, which means that electrons conducting in a particular direction will have a fixed spin value. Because of this, TIs have attracted a great deal of attention from the spintronics community, whose aim is to employ the spin degree freedom as an information channel, in the same way the electric charge is employed in conventional electronics.

Among three-dimensional (3D) topological insulators, the Bi2Se3 family of compounds (Bi2Te3, Sb2Te3, Sb2Se3, and Bi2Se3 itself) has played an important role in early studies of topological insulators. They are the first stoichiometric compounds which were predicted (and soon thereafter experimentally confirmed) to be 3D TIs. Along my PhD studies, I studied different low dimensional effects in 2D and 3D topological insulators from a theoretical point of view. In this section you can find a summary of the most relevant results I have obtained with my supervisor and collaborators, such as the effect of stacking defects, magnetic capping or strain. We also proposed and calculated the electronic and transport properties of a topological insulator based AC spin source and a topological pn junction.