Trilayer Graphene

Trilayer Graphene is really interesting. It has some conduction bands like single layer (two almost linear) and some like bilayer, viz., four parabolic bands. The breaking of mirror reflection symmetry leaves just two bands in the vicinity of zero energy increasing minimum conductivity. One has to wonder about the puddling of excitons at concurrant one third filling of all three layers. Will the excitons form a Bose Einstein condensate when you apply comparable currents in opposite direction between the inner and outer layers assuming the Zeeman energy, temperature, density imbalance, layer spacing and applied magnetic field are reasonable? If so, it seems like this might be very useful in energy storage and making sensors. The more layers the flatter it gets!

Phase Transitions in Graphene

Dreaming about graphene is a beautiful thing. The leptons become light and dark excitons. Suspending graphene makes the top and bottom surfaces indistinguishable. You can even invert its handedness. Time reversal symmetry makes single layer graphene almost perfect. But bilayer is great, too. A magnetic field can be applied to change the phase of the excitons in a bilayer, half-filled system to that of a Bose Einstein condensate. When current flows in opposite directions in the two layers, the resistance goes to zero. An oddly quantized vortex binding one zero mode per valley is present, though slightly split due to a mixing of the valleys in the graphene layers. You can also have a phase transition from this coherent excitonic phase to a pair of single-layer fractional Quantum Hall States as a function of layer spacing. There is always something new to read about graphene as one drifts off to sleep.