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Register a new userMomentum-resolved superconducting gap in the bulk of Ba$_{1-x}$K$_{x}$Fe$_2$As$_2$ from combined ARPES and $mu$SR measurements
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Here we present a calculation of the temperature-dependent London penetration depth, $lambda(T)$, in Ba$_{1-x}$K$_{x}$Fe$_2$As$_2$ (BKFA) on the basis of the electronic band structure [1,2] and momentum-dependent superconducting gap [3] extracted from angle-resolved photoemission spectroscopy (ARPES) data. The results are compared to the direct measurements of $lambda(T)$ by muon spin rotation ($mu$SR) [4]. The value of $lambda(T=0)$, calculated with emph{no} adjustable parameters, equals 270 nm, while the directly measured one is 320 nm; the temperature dependence $lambda(T)$ is also easily reproduced. Such agreement between the two completely different approaches allows us to conclude that ARPES studies of BKFA are bulk-representative. Our review of the available experimental studies of the superconducting gap in the new iron-based superconductors in general allows us to state that all hole-doped of them bear two nearly isotropic gaps with coupling constants $2Delta/k_{rm B}T_{rm c}=2.5pm1.5$ and $7pm2$.
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The precise momentum dependence of the superconducting gap in the iron-arsenide superconductor with Tc = 32K (BKFA) was determined from angle-resolved photoemission spectroscopy (ARPES) via fitting the distribution of the quasiparticle density to a model. The model incorporates finite lifetime and experimental resolution effects, as well as accounts for peculiarities of BKFA electronic structure. We have found that the value of the superconducting gap is practically the same for the inner Gamma-barrel, X-pocket, and blade-pocket, and equals 9 meV, while the gap on the outer Gamma-barrel is estimated to be less than 4 meV, resulting in 2Delta/kT_c=6.8 for the large gap, and 2Delta/kT_c<3 for the small gap. A large (77 pm 3%) non-superconducting component in the photoemission signal is observed below T_c. Details of gap extraction from ARPES data are discussed in Appendix.
We report inelastic x-ray scattering measurements of the in-plane polarized transverse acoustic phonon mode propagating along $qparallel$[100] in various hole-doped compounds belonging to the 122 family of iron-based superconductors. The slope of the dispersion of this phonon mode is proportional to the square root of the shear modulus $C_{66}$ in the $q rightarrow 0$ limit and, hence, sensitive to the tetragonal-to-orthorhombic structural phase transition occurring in these compounds. In contrast to a recent report for Ba(Fe$_{0.94}$Co$_{0.06}$)$_2$As$_2$ [F. Weber et al., Phys. Rev. B 98, 014516 (2018)], we find qualitative agreement between values of $C_{66}$ deduced from our experiments and those derived from measurements of the Youngs modulus in Ba$_{1-x}$(K,Na)$_x$Fe$_2$As$_2$ at optimal doping. These results provide an upper limit of about 50 {AA} for the nematic correlation length for the optimally hole-doped compounds. Furthermore, we also studied compounds at lower doping levels exhibiting the orthorhombic magnetic phase, where $C_{66}$ is not accessible by volume probes, as well as the C4 tetragonal magnetic phase.investigated
The electron band around $M$ point in (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ compound -- completely lifted above the Fermi level for $x > 0.7$ and hence has no Fermi Surface (FS) -- can still form an isotropic s-wave gap ($Delta_e$) and it is the main pairing resource generating an s-wave gap ($Delta_h$) with an opposite sign on the hole pocket around $Gamma$ point. The electron band developing the SC order parameter $Delta_e$ but having no FS displays a {it shadow gap} feature which will be easily detected by various experimental probes such as angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscope (STM). Finally, the formation of the nodal gap $Delta_{nodal}$ with $A_{1g}$ symmetry on the other hole pocket with a larger FS is stabilized due to the balance of the interband pairing interactions from the main hole band gap $Delta_h=+Delta$ and the hidden electron band gap $Delta_e = -Delta$.
We investigate the iron-based superconductor Ba$_{1-x}$K$_x$Fe$_2$As$_2$ using a terahertz (THz) pump near-infrared probe scheme. In the superconducting state we observe an instantaneous signal that is assigned to a non-linear THz Kerr effect. The THz Kerr signal is profoundly affected by the coexistence with the nematic order. In the absence of nematic order the $C_4$ symmetric polarization dependence of the THz Kerr signal is consistent with a coupling to the Higgs mode. In the coexisting nematic and superconducting state the signal becomes purely nematic with a vanishing $C_4$ symmetric component, signaling the possible emergence of a new superconducting collective mode activated by nematicity.
Combined neutron and x-ray diffraction experiments demonstrate the formation of a low-temperature minority tetragonal phase in Ba$_{0.76}$K$_{0.24}$Fe$_2$As$_2$ in addition to the majority magnetic, orthorhombic phase. A coincident enhancement in the magnetic ($frac{1}{2}$ $frac{1}{2}$ 1) peaks shows that this minority phase is of the same type that was observed in Ba$_{1-x}$Na$_x$Fe$_2$As$_2$ ($0.24 leq x leq 0.28$), in which the magnetic moments reorient along the $c$-axis. This is evidence that the tetragonal magnetic phase is a universal feature of the hole-doped iron-based superconductors.
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