The 2016 Nobel prize in physics was awarded for the development of topological concepts in condensed matte physics. A lot of this helps us discover new quantum materials, and classify their electronic states systematically. However, what can be a practical use for these concepts, especially from a device perspective? The conventional argument is enhanced mobility - after all, topological properties that limit backscattering increases their ON current. However, for most electronic switches, the challenge is the OFF current, which is exponentially sensitive to transmission, as opposed to ON current. We argue that topology, specifically how relevant degrees of freedom wind around the Fermi surface (spins, pseudospins, magnetization) determines the OFF current across tunnel barriers as well, due to added conservation rules enforced by symmetry.
Take a look at the following classes of materials, and their winding indices. Much like topology distinguishes shape differences between a donut and a bun, the rate of winding of the arrows here separates the materials into different indices or Chern numbers.
In short, quantum topology controls transport properties (lifetime, mobility, barrier transmission) across barriers, because of the constraints imposed by conservation of energy, momentum, and Chern number. Topology depends on symmetries inherent in the system. Barriers and symmetries can be gated. We posit therefore that topological properties allow us to realize unconventional <i>classical computing paradigms</i> using quantum properties.