Probing electron quadrupling order through ultrasound

Recent experiments have pointed to the formation of a new state of matter, the electron quadrupling condensate in Ba₁₋ₓKₓFe₂As₂ . The state spontaneously breaks time-reversal symmetry and is sandwiched between two critical points, separating it from the superconducting and normal metal states. The adjacent two critical points make acoustic effects a promising tool to study such states because of their sensitivity to symmetry-breaking transitions. We report a theory of the acoustic effects of systems with an electron quadrupling phase and new ultrasound velocity measurements of Ba₁₋ₓKₓFe₂As₂ single crystals. The presented theory for the electron quadrupling state gives the same type of singularities that are observed in experiment.