Thermal Hall Conductivity as a Probe of Gap Structure in Multi-band Superconductors: The Case of $\mathrm{B}{\mathrm{a}}_{1-\mathrm{x}}{\mathrm{K}}_{\mathrm{x}}\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$

Abstract

The sign and profile of the thermal Hall conductivity $\hat{I}{º}_{xy}$ gives important insights into the gap structure of multi-band superconductors. With this perspective, we have investigated $\hat{I}{º}_{xy}$ and the thermal conductivity $\hat{I}{º}_{xx}$ in $\mathrm{B}{\mathrm{a}}_{1-\mathrm{x}}{\mathrm{K}}_{\mathrm{x}}\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ which display large peak anomalies in the superconducting state. The anomalies imply that a large hole-like quasiparticle (qp) population exists below the critical temperature $T_c$. We show that the qp mean-free-path inferred from $\hat{I}{º}_{xx}$ reproduces the observed anomaly in $\hat{I}{º}_{xy}$, providing a consistent estimate of a large qp population. Further, we demonstrate that the hole-like signal is consistent with a theoretical scenario where despite potentially large gap variations on the electron pockets, the minimal homogeneous gap of the superconducting phase resides at a hole pocket. Implications for probing the gap structure in the broader class of pnictide superconductors are discussed.

5 pages, 4 figures. Orientation significantly updated from previous (0811.4668v1) reflecting new theoretical understanding of experimental results and physical implications. Introduction, discussion, and figures updated including additional figure for model calculation