  We find an unusually optimal near field heat transfer, where the maximum heat
transfer is reached at experimentally feasible gap separation. We attribute
this to the localized zero-energy electronic edge states, which also
substantially changes the near-field behaviors. We demonstrate these anomalous
behaviors in two typical carbon-based nano-structures: zigzag single-walled
carbon nanotubes and graphene nano-triangles. For the system of carbon
nanotubes, the maximal heat flux in this work surpasses all the previous
results reported so far by several orders of magnitude. The underlying
mechanisms for the peculiar effects are uncovered from a simple
Su-Schrieffer-Heeger model. Our findings also offer a novel route to active
near-field thermal switch, where the heat flux can be modulated through tuning
the presence or absence of edge states.
