Quasiparticle interference in multiband superconductors with strong coupling

Abstract

We develop a theory of the quasiparticle interference (QPI) in multiband superconductors based on the strong-coupling Eliashberg approach within the Born approximation. In the framework of this theory, we study dependencies of the QPI response function in the multiband superconductors with the nodeless s-wave superconductive order parameter. We pay special attention to the difference in the quasiparticle scattering between the bands having the same and opposite signs of the order parameter. We show that at the momentum values close to the momentum transfer between two bands, the energy dependence of the quasiparticle interference response function has three singularities. Two of these correspond to the values of the gap functions and the third one depends on both the gaps and the transfer momentum. We argue that only the singularity near the smallest band gap may be used as a universal tool to distinguish between the s ++ and s ± order parameters. The robustness of the sign of the response function peak near the smaller gap value, irrespective of the change in parameters, in both the symmetry cases is a promising feature that can be harnessed experimentally.

Probing pairing symmetry in multi-band superconductors by quasiparticle interference

“…The response function is positive for all momenta in the case of s ++ symmetry and negative for all momenta for the s ± symmetry. It confirms the conclusion of the work 18 of the possibility to use the QPI response function at the energy of the small gap as an indicator of the symmetry of the superconducting order parameter. Further analysis of the momentum dependence of the QPI response function shows that the peaks in I ( ω  = Δ b , q ) correspond to certain momenta, i.e.…”

“…A small difference for other energies are not universal and may disappear with the variation of energy. It confirms the conclusion of 18 that the QPI at the smaller band gap is a universal feature and may be used as an indicator of the symmetry of the superconducting order parameter.

Figure 6The momentum dependence of the QPI response function with parameters as δμ  = 300 and ε  = 200 at certain energies, for β  = 1. Here, the panels ( a ),( b ),( c ) correspond to the s ± (left) and s ++ (right), respectively.

…”

“…for s ++ it has a maximum, and for s ± , a minimum. It makes the energy windows close to the smallest gap, an important tool for determination of the symmetry of the superconducting gap 18 . Further, the examination of the evolution of QPI function with momentum, shows that, it has non-monotonic character and demands a special consideration.…”

“…The above approximation yieldsHere, and ϕ is the angle between momentum vectors and Q . The general expression for the response function, considering a constant density of states, has the following form 18 where K ( ω ) is the coherence factor as followsHere and and are complex functions. Here, is the quasiparticle energy spectrum.…”

“…In the previous works 18,19 , it has been established that the qualitative determination of the superconducting order parameter is possible by studying the energy dependence of QPI spectra within the frequency window close to the small band gap. In the present paper, we explore the momentum dependence of the QPI-response function I ( q , ω ) to show the relation of the developed theory to experimental works, which use the momentum dependent QPI-response function at fixed energies.…”