  The \nu=5/2 anti-Pfaffian state and the \nu=2/3 state are believed to have an
edge composed of counter-propagating charge and neutral modes. This situation
allows the generation of a pure thermal bias between two composite edge states
across a quantum point contact (QPC) as was experimentally established in
Nature 466, 585 (2010). We show that replacing the QPC by a quantum dot
provides a natural way for detecting the neutral modes via the finite current
generated by the thermoelectric response of the dot. We also show that the
degeneracies of the dot spectrum, dictated by the conformal field theories
(CFTs) describing these states, induce asymmetries in the thermoelectric
current peaks. This in turn provides a direct fingerprint of the corresponding
CFT.
