The origin of spontaneous electronic nematic ordering provides important information for understanding iron-based superconductors. Here, we analyze a scenario where the dxy orbital strongly contributes to nematic ordering in FeSe. We show that the addition of dxy nematicity to a pure dxz/dyz order provides a natural explanation for the unusual Fermi surface and correctly reproduces the strongly anisotropic momentum dependence of the superconducting gap. We predict a Lifshitz transition of an electron pocket mediated by temperature and sulfur doping, whose signatures we discuss by analysing available experimental data. We present the variation of momentum dependence of the superconducting gap upon suppression of nematicity. Our quantitatively accurate model yields the transition from tetragonal to nematic FeSe and the FeSe1−xSx series, and puts strong constraints on possible nematic mechanisms.
Motivated by the recent observations of small Fermi energies and comparatively large superconducting gaps, present also on bands not crossing the Fermi energy (incipient bands) in iron-based superconductors, we analyze the doping evolution of superconductivity in a four-band model across the Lifshitz transition including BCS-BEC crossover effects on the shallow bands. Similar to the BCS case, we find that with hole doping the phase difference between superconducting order parameters of the hole bands change from 0 to π through an intermediate s + is state, breaking time-reversal symmetry (TRS). The transition, however, occurs in the region where electron bands are incipient and chemical potential renormalization in the superconducting state leads to a significant broadening of the s + is region. We further present the qualitative features of the s + is state that can be observed in scanning tunneling microscopy (STM) experiments, also taking incipient bands into account.
Motivated by recent experimental reports of significant spin-orbit coupling (SOC) and a signchanging order-parameter in the Li 1−x Fe x (OHFe) 1−y Zn y Se superconductor with only electron pockets present, we study the possible Cooper-pairing symmetries and their quasiparticle interference (QPI) signatures. We find that each of the resulting states-s-wave, d-wave and helical p-wave-can have a fully gapped density of states consistent with angle-resolved photoemission spectroscopy experiments and, due to SOC, are a mixture of spin singlet and triplet components leading to intraand inter-band features in the QPI signal. Analyzing predicted QPI patterns we find that only the spintriplet dominated even parity A 1g (s-wave) and B 2g (d-wave) pairing states are consistent with the experimental data. Additionally, we show that these states can indeed be realized in a microscopic model with atomic-like interactions and study their possible signatures in spin-resolved STM experiments.2 2 --state to acquire gap nodes, although in principle the nodal area may be very small, proportional to the hybridization ('quasinodes'). On the other hand, ARPES experiments in most of the electron-intercalated materials indicated a nodeless superconducting (sc) state [15,16]. Several proposals for the gap structure have been put forward, including a conventional s ++ -waveThe 2×2 block in equation (11) corresponds to A 1g s-wave pairing. We write J J 13 11 a ¢ = ¢ and find two eigenvalues E J U J J J U U 2 3 16 2 A 11 ¢ = , J J 13 11 ¢ = ¢˜, U 0.1 ¢ = and J 4.6 = . (c) Superconducting gap projected on the inner (blue) and outer (red) Fermi-surface as function of the Fermi angle, zero temperature and at three different values of λ SOC .
Complete theoretical understanding of the most complex superconductors requires a detailed knowledge of the symmetry of the superconducting energy-gap $${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ Δ k α , for all momenta k on the Fermi surface of every band α. While there are a variety of techniques for determining $$|{\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha |$$ ∣ Δ k α ∣ , no general method existed to measure the signed values of $${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ Δ k α . Recently, however, a technique based on phase-resolved visualization of superconducting quasiparticle interference (QPI) patterns, centered on a single non-magnetic impurity atom, was introduced. In principle, energy-resolved and phase-resolved Fourier analysis of these images identifies wavevectors connecting all k-space regions where $${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ Δ k α has the same or opposite sign. But use of a single isolated impurity atom, from whose precise location the spatial phase of the scattering interference pattern must be measured, is technically difficult. Here we introduce a generalization of this approach for use with multiple impurity atoms, and demonstrate its validity by comparing the $${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ Δ k α it generates to the $${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ Δ k α determined from single-atom scattering in FeSe where s± energy-gap symmetry is established. Finally, to exemplify utility, we use the multi-atom technique on LiFeAs and find scattering interference between the hole-like and electron-like pockets as predicted for $${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ Δ k α of opposite sign.
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