2D system with PHS appears to violate a fundamental fermion doubling theorem (valid also for interacting electron systems [@Wang14; @Wang14PRB]), and is ordinarily thought to only be possible at the surface of a 3D topological insulator. This apparent paradox can be resolved by noting that the action of PHS on the half-filled LL is inherently nonlocal, involving not only exchanging particles and holes, but also filling a topological LL band. Since this LL band has non-zero Chern number, it lacks a local Wannier basis and has at least one spatially extended orbital that carries the Hall conductance [@Halperin82]. The action of filling or emptying this extended orbital is an inherently non-local, and this non-local action of PHS provides an interesting, and only recently realized [@Son15; @Wang15short; @Metlitski15; @Wang15rev], exception to fermion doubling theorems, allowing certain kinds of topological-insulator surface state physics to be effectively realized in a 2D system.

In this paper, we examine thermoelectric transport signatures of the proposed Dirac-nature of CFs. While certain electrical transport signatures have been suggested [@Son15], for example examining the deviation of Hall conductance from ${e^2}/({2h})$, these proposals typically require accurately measuring small corrections to a large background signal, and it is desirable to 