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Fundamentally, what distinguishes a superconducting state from a normal state is a spontaneously broken symmetry corresponding to the long-range coherence of Cooper pairs, leading to zero resistivity and diamagnetism.
Here we report a set of thermodynamic, transport and muon spectroscopy observations on a series of hole-doped Ba$_{1−x}$K$_x$Fe$_2$As$_2$. Our specific-heat measurements indicate the formation of fermionic bound states when the temperature is lowered from the normal state. However, at the doping level $x$ ≈ 0.8, instead of the characteristic onset of diamagnetic screening and zero resistance expected below a superconducting phase transition (T$_c$), we observe the opposite effect: the generation of self-induced magnetic fields in the resistive state, measured by spontaneous Nernst effect 1 and muon spin rotation experiments [2,3] (see Fig.1). This combined evidence indicates the existence of a bosonic metal state in the temperature range T$_c$ ≤ T ≤ T$_{Z2}$ in which Cooper pairs of electrons lack coherence, but the system spontaneously breaks time-reversal symmetry (Z2). The observations are consistent with the theory of a state with fermionic quadrupling, in which long-range order exists not between Cooper pairs but only between pairs of pairs.
![(Top panel) Temperature dependence of the zero-field muon spin relaxation rate (left) and the magnetic susceptibility measured in B∥ab = 0.5 mT (right) for the stack of single crystals with x = 0.78(3) [3]. (Bottom panel) Temperature dependence of the spontaneous Nernst effect (left) and the magnetic susceptibility measured in B∥ab = 0.5 mT (right) for a sample with x = 0.77. The comparison suggests that the origin of the spontaneous Nernst effect at T$_{Z2}$ is the appearance of spontaneous magnetic fields.](https://www.dropbox.com/s/c2v8w43fggvy5pe/BKFA.jpg?dl=0)
$[$1$]$ V. Grinenko et al., Nat. Phys. 17, 1254–1259 (2021).
$[$2$]$ V. Grinenko et al., Phys. Rev. B 95, 214511 (2017).
$[$3$]$ V. Grinenko et al., Nat. Phys. 16, 789–794 (2020).
