Self-energy driven resonancelike inelastic neutron spectrum in the s++ -wave state in Fe-based superconductors

Abstract

To elucidate the pairing states in Fe-based superconductors, we perform careful calculation of the dynamical spin susceptibility χ S (q, ω) at very low temperatures (T > ∼ 1meV). The feedback effect on both the self-energy and χ S (q, ω) from the superconducting gap are self-consistently analyzed based on the fluctuation-exchange (FLEX) approximation. In the s±-wave state, which has sign-reversal in the gap function, χ S (q, ω) at the nesting momentum q = Q shows a resonance peak even when the system is away from the magnetic quantum-critical-point (QCP). In the s++-wave state that has no sign-reversal, χ S (q, ω) shows a large hump structure when the system is close to the magnetic QCP. This result confirms the validity of self-energy driven resonance-like peak in s++-wave state proposed in our previous semi-microscopic study: The enhancement in χ S (q, ω) due to self-energy effect exceeds the suppression due to coherence factor effect near magnetic QCP. We stress that the hump structure in the s++-wave state given by the FLEX method smoothly changes to resonancelike sharp peak structure as the system approaches magnetic QCP, which was not reported in our previous studies. The obtained ω-and T -dependences of χ S (q, ω) in the s++-wave state resemble to the resonance-like feature in inelastic neutron scattering spectra recently observed in Na(Fe,Co)As and FeSe.

Dispersion of neutron spin resonance mode in Ba0.67K0.33Fe2As2 *

“…For example, excitonic excitations under s ± -pairing play a key role for the spin resonance at the low-energy range, which requires all of them below ∆ tot with much slower spin velocity in the superconducting state. [20][21][22][23][51][52][53] Above ∆ tot , the self-energy effect under s ++ -pairing may dominate at the high-energy range as predicted by the RPA calculations [20][21][22]29,30,54,55] and also shown in K x Fe 2−y (Se 1−z S z ) 2 system. [25] However, the selfenergy effect induced redistribution of spin excitations in s ++ superconducting state would basically follow the spin excitation dispersion at normal state, [20,22,29,30,54,55] which has a very large velocity similar to the spin waves in parent compound c nor,𝑞 ≈ 450 meV• Å.…”

“…[20][21][22][23][51][52][53] Above ∆ tot , the self-energy effect under s ++ -pairing may dominate at the high-energy range as predicted by the RPA calculations [20][21][22]29,30,54,55] and also shown in K x Fe 2−y (Se 1−z S z ) 2 system. [25] However, the selfenergy effect induced redistribution of spin excitations in s ++ superconducting state would basically follow the spin excitation dispersion at normal state, [20,22,29,30,54,55] which has a very large velocity similar to the spin waves in parent compound c nor,𝑞 ≈ 450 meV• Å. [9,21,23,49] It should be noticed that the iron-based superconductors are multi-band systems with different superconducting gaps on each band, so the scattering from Γ to M points has many channels under different energy limits, [16,17] which can result in multiple spin resonance modes.…”

“…[12,28] Instead of the excitonic scenario under s ± -pairing, some of them may be alternatively explained as the self-energy effect induced redistribution of spin excitations under sign-preserved (s ++ ) pairing. [29,30] In addition to the mode energy E R at antiferromagnetic wavevector 𝑄 AF , the dispersion of the spin resonance seems to highly depend on the magnetic interactions in different compounds. [9] Weak out-of-plane dispersion of the spin resonance mode along L direction has been found in those superconducting compounds proximate to the three-dimensional (3D) stripe-type AF order [e.g., BaFe 2−x (Ni, Co, Ru) x As 2 , BaFe 2 (As 1−x P x ) 2 , NaFe 1−x Co x As, Ba 1−x Na x Fe 2 As 2 , etc.…”

Efficient fluctuation exchange approach to low-temperature spin fluctuations and superconductivity: from the Hubbard model to Na$_x$CoO$_2\cdot y$H$_2$O

“…In practice, this prohibits calculations at low temperatures as the required amount of data becomes too large to be stored or processed. One of several approaches [38][39][40] to tackle these problems is to use a compact representation of Green functions as given by (orthogonal) continuous basis functions, like Legendre polynomials [41,42], Chebyshev polynomials [43] or numerical basis functions [44].…”

Effects of spin-orbit coupling on the neutron spin resonance in iron-based superconductors

“…10-12. As one of the hallmarks of sign-changing gap functions, the existence of the neutron resonance was considered strong evidence for s +− -wave pairing with sign-reversed superconducting gaps on Fermi pockets connected by Q = (π, 0) [13][14][15][16][17] . This interpretation, however, was challenged, and other scenarios for the emergence of the neutron resonance feature were proposed 18,19 . This motivated many additional studies into the properties of the neutron spin resonance including the detailed spin anisotropy of the neutron scattering resonance 11,12 .…”