Topological Transistor

At the point M(Vg)=0 the band gap Eg=2|M| vanishes — this is exactly the moment the system crosses between the topological and trivial phases. A topological transistor uses precisely this transition for switching, instead of changing dopant concentration.

On each edge, opposite spin states propagate in opposite directions (spin-momentum locking). A non-magnetic impurity cannot flip the spin, so it cannot scatter an electron from the forward-moving to the backward-moving channel — this helical conduction is protected by Kramers' theorem.

Both edges together (each carrying one helical channel) give a two-terminal conductance of G=2e²/h — this was precisely the value measured by König and colleagues (2007, HgTe/CdTe quantum well).

In a conventional transistor, S=(kT/q)ln10 is set by the thermal distribution of carriers over a barrier. In a topological transistor the switching mechanism is different — a qualitative transformation of the band structure itself, not thermal charge injection — so in principle (though not always in practice) a sharper, "non-Boltzmann" switch is possible.