Calorimetric evidence for two phase transitions in Ba$_{\rm 1-x}$K$_{\rm x}$Fe$_{2}$As$_{2}$ with fermion pairing and quadrupling states

TL;DR

This study presents calorimetric evidence for two distinct phase transitions in Ba$_{1-x}$K$_x$Fe$_2$As$_2$, indicating the formation of a fermion quadrupling state with broken time-reversal symmetry above superconductivity.

Contribution

It provides the first calorimetric detection of a $Z_2$ phase transition related to fermion quadrupling states in this material.

Findings

Detection of two specific heat anomalies at different temperatures.

Observation of spontaneous Nernst effect indicating broken time-reversal symmetry.

Correlation of the lower temperature anomaly with the onset of superconductivity.

Abstract

Theoretically, materials that break multiple symmetries allow, under certain conditions, the formation of four-fermion condensates above the superconducting critical temperature. Such states can be stabilized by phase fluctuations. Recently a fermionic quadrupling condensate that breaks the $Z_2$ time-reversal symmetry was reported in Ba$_{\rm 1-x}$K$_{\rm x}$Fe$_{2}$As$_{2}$ [V. Grinenko et al., Nat. Phys. 17, 1254 (2021)]. Evidence for the new state of matter comes from muon-spin rotation, transport, thermoelectric, and ultrasound experiments. Observing a specific heat anomaly is a very important signature of a transition to a new state of matter. However, a fluctuation-induced specific heat singularity is usually very challenging to resolve from a background of other contributions. Here, we report on detecting two anomalies in the specific heat of Ba$_{\rm 1-x}$K$_{\rm x}$Fe$_{2}$As$_{2}$ at zero magnetic field. The anomaly at the higher temperature is accompanied by the appearance of a spontaneous Nernst effect, indicating broken time-reversal ($Z_2$) symmetry. The second anomaly at the lower temperature coincides with the transition to a zero resistance state, indicating superconductivity breaking the $U(1)$ gauge symmetry. Our data provide calorimetric evidence for the $Z_2$ phase formation above the superconducting phase transition.