Thermoelectric response and entropy of fractional quantum Hall systems

Abstract

© 2020 American Physical Society. We study the thermoelectric transport properties of fractional quantum Hall systems based on an exact diagonalization calculation. Based on the relation between the thermoelectric response and thermal entropy, we demonstrate that thermoelectric Hall conductivity αxy has power-law scaling αxy Tη for gapless composite Fermi-liquid states at filling numbers ν=1/2 and 1/4 at low temperatures (T), with an exponent η∼0.5 distinctly different from Fermi liquids. The power-law scaling remains unchanged for different forms of interaction including Coulomb and short-range ones, demonstrating the robustness of non-Fermi-liquid behavior of these interacting systems at low T. In contrast, for the 1/3 fractional quantum Hall state, αxy vanishes at low T with an activation gap associated with neutral collective modes rather than charged quasiparticles. Our results establish another manifestation of the non-Fermi-liquid nature of quantum Hall fluids at a finite temperature.