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 analyse 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 changes from $0$ to $\pi$ through an intermediate $s+is$ state breaking time-reversal symmetry. 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 tunnelling microscopy (STM) experiments also taking incipient bands into account.

18 pages, 9 figures

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• Effective model and Magnetic Properties of the Resistive Electron Quadrupling State
• Detecting sign-changing superconducting gap in LiFeAs using quasiparticle interference
• Pseudogap and Strong Pairing Induced by Incipient and Shallow Bands in the Quasi-Two-Dimensional KCa${}_2$Fe${}_4$As${}_4$F${}_2$
• Quasi-one Dimensional Nanostructures as Sign of Nematicity in Iron Pnictides and Chalcogenides
• Time-reversal symmetry breaking from lattice dislocations in superconductors
• Derivation of a Ginzburg-Landau free energy density containing mixed gradient terms of a $p+ip$ superconductor with spin-orbit coupling
• Magnetic field behaviour in $s+is$ and $s+id$ superconductors: twisting of applied and spontaneous fields
• Change of the vortex core structure in two-band superconductors at impurity-scattering-driven $s_{\pm }/s_{++}$ crossover
• Non-adiabatic dynamics in d+id-wave fermionic superfluids
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• SNS Junctions along the BCS-BEC Crossover
• Possibility of BCS-BEC crossover in $\kappa$-type organic superconductors