Any superconducting state breaks spontaneously U(1) gauge symmetry at the superconducting transition temperature (T_c). In some cases, a superconducting state breaks additional symmetries such as rotational lattice symmetry or time-reversal symmetry (Z₂). Usually, multiple symmetries are broken at T* ≤ T_c. However, it was predicted theoretically that fluctuations might push T_c below T*, giving room for a new quantum state of matter, which is different by symmetry from superconducting and normal states [1]. Here, we study the multiband Ba_1-xK_xFe₂As₂ system experimentally. We found that at high K doping levels topological changes of the Fermi surface (Lifshitz transition) trigger a superconducting state that breaks time-reversal symmetry (BTRS) [2,3]. The BTRS superconducting state exists at the narrow doping range 0.7 ≤ x ≤ 0.85. More intriguing is that at x ~ 0.8, we found a BTRS state at the temperature T_c^Z2 > T_c [4]. Evidence for the Z₂ phase transition is given by additional anomalies in the specific heat and ultrasound velocity as well at T_c^Z2 we observed an enhancement of the muon spin relaxation rate and appearance of the strong spontaneous Nernst signal (Fig.1). The relation of T_c^Z2 to the superconductivity is concluded from similar magnetic field dependencies of T_c and T_c^Z2 and by a presence of superconducting fluctuations and a pseudo-gap behaviour above T_c^Z2. Based on the theoretical analysis, we proposed that T_c^Z2 is associated with a quartic order formed by a correlated state between pairs of Cooper pairs. In this talk, I will also discuss other unusual properties of this state.

Figure 1: (a) Temperature dependence of the zero-field muon spin relaxation rate (left) shown together with the static magnetic susceptibility measured in B∥ab = 0.5 mT (right) for the stack of single crystals with x = 0.78(3) [3]. (b) Temperature dependence of the spontaneous Nernst effect measured in zero magnetic field (left) shown together with the static magnetic susceptibility measured in B∥ab = 0.5 mT (right) for the sample with x = 0.77 [4]. The comparison between the μSR data and the spontaneous Nernst signal strongly suggests that the increase of the muon spin relaxation rate above T_c is not an artifact and that the origin of the spontaneous Nernst effect at T_c^Z2 is spontaneous magnetic fields.

 [1]. E. Babaev, A. Sudbø. N.W. Ashcroft Nature 431, 666–668 (2004). E Babaev Nuclear Physics B 686 (3), 397-412 for a review B.V. Svistunov, E.S. Babaev, N.V. Prokof'ev see Superfluid states of matter Crc Press (2015).
[2]. V. Grinenko, P. Materne, R. Sarkar et al., Phys. Rev. B 95, 214511 (2017).
[3]. V. Grinenko, R. Sarkar, K. Kihou, et al., Nat. Phys. 16, 789–794 (2020).
[4]. V. Grinenko, D. Weston, F. Caglieris et al., Nat. Phys. 17, 1254–1259 (2021).

Keywords: superconductivity, time reversal symmetry breaking, quartic state, pnictides