s+is superconductivity with incipient bands: Doping dependence and STM signatures

Abstract

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.

Properties of dirty two-band superconductors with repulsive interband interaction: Normal modes, length scales, vortices, and magnetic response

“…This should be experimentally measureable in muon-spin-rotation experiments. Note finally that qualitatively similar features should also be expected in other realizations of s + is states [10][11][12][13][14]43].…”

Influence of multiband sign-changing superconductivity on vortex cores and vortex pinning in stoichiometric high- Tc CaKFe4As4

“…It would be interesting to search for doping induced modifications in the superconducting order parameter sign between the electron and hole bands. If the hole band can be brought closer to the Fermi level, predictions range from intraband s± superconductivity to time-reversal symmetry breaking s + is superconductivity, with superconducting order parameter phase differences among bands that are not multiples of π, due to the competition between Coulomb repulsion and spin fluctuations [20,42,43]. Furthermore, the presence of hedgehog spin vortex crystal in Ni doped CaKFe 4 As 4 , which could be related to the absence of glide plane [13,42,44,45], adds an interesting ingredient likely favoring unconventional superconducting properties.…”

Field-induced coexistence of s++ and s± superconducting states in dirty multiband superconductors

“…The competition between those terms is responsible for the existence of the impurity-induced s + is state [10]. The s-wave states that spontaneously break the time-reversal symmetry have been a subject of much interest in recent years; see, e.g., [9][10][11][12][13][14][15][16][17]. In this work, we focus on the physics of the direct s ± to the s ++ impurity-induced crossover in an external magnetic field (denoted by the solid black line on Fig.…”