Thermoelectric probe for neutral edge modes in the fractional quantum Hall regime

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.