Introduction: searching the periodic table for topological materials¶
How do we find a topological insulator? In the first video of today, David Vanderbilt from Rutgers University will tell us more about the material science aspects of topological insulators research.
This is an expertise that no one from the course team has, so pay close attention to it: this material stands apart from the rest.
In the rest of the lecture, we will instead discuss the experimental signatures of 3D topological insulators, similarly to what we did in the previous week for their 2D counterparts.
All the figures showing the experimental data are copyright of the Zahid Hasan lab, Princeton, 2015. They are available under CC-BY-NC-SA 4.0 International license.
Conductance of a 3D topological insulator¶
Both the quantum Hall and quantum spin Hall states have striking conductance quantization properties, thanks to the presence of perfectly transmitting one-dimensional transport channels.
The 3D topological insulators do not posses similar striking conductance properties. In a slab geometry, the surface states contribute with a finite density of propagating states. This density has a minimum at the Dirac point. The conductance increases roughly with a hyperbolic shape if the chemical potential is tuned away from the Dirac point as shown in the plot below: