Ultrasound evidence for multicomponent superconducting order parameter in Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ with electron quadrupling phase

Abstract

Experiments have pointed to the formation of the electron quadrupling condensate in Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ at $x\sim 0.8$. The state spontaneously breaks time-reversal symmetry and is sandwiched between two critical points, separating it from the broken time-reversal symmetry (BTRS) superconducting state at $T_{\mathrm{c}}^{U(1)}$ and normal-metal state at $T_{\mathrm{c}}^{Z2}$. We report a theory of the acoustic effects spectroscopy of systems with an electron quadrupling phase based on ultrasound-velocity measurements. We show that the experimental results are consistent with BTRS superconductivity at $x\sim 0.8$, fulfilling the necessary condition for the formation of electron quadrupling in Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$. We provide the theoretical basis and the experimental strategy to study the order parameter symmetry of emerging quadrupling condensates in superconductors.

v3: version accepted by journal. 18 pages, 8 figures