Sunday, 25 August 2013
Topological Insulators- The New Physics
However, at the boundary of the interface, the electron's circular motion can rebound off the edge, creating so called 'skipping orbits'. At the quantum scale, such skipping orbits create electronic states that spread across the boundary in a one-way manner with energies that are not discrete; this state can conduct owing to the lack of an energy gap. In addition, the flow in one-direction creates perfect electric transport (electrons have no other option but to move forward because there are no backward-motion modes). Dispationless transport emerges because the electrons don't scatter and hence no energy or work is lost (it also explains the discrete transport). But topological insulators happen without a magnetic field, unlike the quantum hall effect; the job of the magnetic field is taken over by spin-orbit coupling (interplay between orbital motion of electrons via space and the electron's spin). Relativistic electrons arise in atoms with high atomic numbers and thus produce strong spin-orbit forces; so any particle will experience a strong spin-momentum reliant force that plays the part of the magnetic field (when spin changes, its direction changes). Such a comparison between a spin-reliant magnetic field and spin-orbit coupling allows us to introduce the most basic 2-D topological insulator; the quantum Hall spin state. This happens when both the spin-up and spin-down electrons experience equal but opposite 'magnetic fields'.
Just as in a regular insulator, there exists an energy gap but there are edge states where the spin-up and spin-down electrons propagate in opposition to another. Time-reversal invariance exchanges both the direction of spin and propagation; hence swapping the two oppositely-propagating modes. But the 3-D topological insulator can't be explained by a spin-dependant magnetic field. The surface state of 3-D topological insulators promotes the movement of electrons in any direction, but the direction of electronic motion decides the spin direction. The relation between momentum and energy has a Dirac cone structure like in graphene.