Thermoelectric response and entropy of fractional quantum Hall systems

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Abstract

We study thermoelectric transport properties of fractional quantum Hall systems based on exact diagonalization calculation. Based on the relation between thermoelectric response and thermal entropy, we demonstrate that thermoelectric Hall conductivity $\alpha_{xy}$ has powerlaw scaling $\alpha_{xy} \propto T^{\eta}$ for gapless composite Fermi-liquid states at filling number $\nu=1/2$ and $1/4$ at low temperature ($T$), with exponent $\eta \sim 0.5$ distinctly different from Fermi liquids. The powerlaw scaling remains unchanged for different forms of interaction including Coulomb and short-range ones, demonstrating the robustness of non-Fermi-liquid behavior at low $T$. In contrast, for $1/3$ fractional quantum Hall state, $\alpha_{xy}$ vanishes at low $T$ with an activation gap associated with neutral collective modes rather than charged quasiparticles. Our results establish a new manifestation of the non-Fermi-liquid nature of quantum Hall fluids at finite temperature.