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Register a new userGap Anisotropy in Multiband Superconductors Based on Multiple Scattering Theory
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We implement the Bogoliubov-de Gennes (BdG) equation in a screened Korringa-Kohn-Rostoker (KKR) method for solving, self-consistently, the superconducting state for 3d crystals. This method combines the full complexity of the underlying electronic structure and Fermi surface geometry with a simple phenomenological parametrisation for the superconductivity. We apply this theoretical framework to the known s-wave superconductors Nb, Pb, and MgB$_2$. In these materials multiple distinct peaks at the gap in the density of states were observed, showing significant gap anisotropy which is in good agreement with experiment. Qualitatively, the results can be explained in terms of the k-dependent Fermi velocities on the Fermi surface sheets exploiting concepts from BCS theory.
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Recent angle-resolved spectroscopy in BiS$_2$-based superconductors has indicated that the superconducting gap amplitude possesses remarkable anisotropy and/or a sign change on a small Fermi pocket around $X$ point. It implies a possibility of an unconventional pairing state. Here we study the gap anisotropy in superconductivity mediated by inherent charge/quadrupole fluctuations in an extended Hubbard model, which includes inter-site interaction between Bi and S atoms. The first-principles downfolded band structure is composed of Bi $6p_x/p_y$ and S $3p_x/p_y$ orbitals on a BiS$_2$ single layer. Evaluating the linearized gap equation, we find that the ferroic charge/quadrupole fluctuation driven by the inter-site interaction leads to a fully-gapped $d_{x^2-y^2}$-wave pairing state, in which the gap amplitude has sizable anisotropy on the Fermi surface.
We implement the Bogoliubov-de Gennes (BdG) equation in real-space using the screened Korringa-Kohn-Rostoker (KKR) method. This allows us to solve, self-consistently, the superconducting state for 3d crystals including substitutional impurities with a full normal-state DFT band structure. We apply the theoretical framework to bulk Nb with impurities. Without impurities, Nb has an anisotropic gap structure with two distinct peaks around the Fermi level. In the presence of non-magnetic impurities those peaks are broadened due to the scattering between the two bulk superconducting gaps, however the peaks remain separated. As a second example of self-consistent real-space solutions of the BdG equations we examine superconducting clusters embedded within a non-superconducting bulk metallic host. This allows us to estimate the coherence length of the superconductor and we show that, within our framework, the coherence length of the superconductor is related to the inverse of the gap size, just as in bulk BCS theory.
The free energy, non-gradient terms of the Ginzburg-Landau expansion, and the jump of the specific heat of a multiband anisotropic-gap clean BCS superconductor are derived in the framework of a separable-kernel approximation. Results for a two-band superconductor, d-wave superconductor, and some recent models for MgB_2 are derived as special cases.
Disorder - impurities and defects violating an ideal order - is always present in solids. It can result in interesting and sometimes unexpected effects in multiband superconductors. Especially if the superconductivity is unconventional thus having other than the usual s-wave symmetry. This paper uses the examples of iron-based pnictides and chalcogenides to examine how both nonmagnetic and magnetic impurities affect superconducting states with $s_pm$ and $s_{++}$ order parameters. We show that disorder causes the transitions between $s_pm$ and $s_{++}$ states and examine observable effects these transitions can produce.
We investigate pairing mechanism in multiband superconductors. To put our feet on firm ground, unbiased renormalization group analysis is carried out for iron-based superconductors. It is quite remarkable that, after integrating out quantum fluctuations, the renormalization-group flows agree exceedingly well with a mean-field Hamiltonian where interband pair hopping plays an essential role. Through interband pair hopping, electrons can overcome the repulsive interaction between them and form resonating Cooper pairs between different bands. Unlike the conventional superconductors, the pairing mechanism in multiband superconductors is resonating pair hopping between different bands, just like the resonating chemical bonds in benzene. The effective mean-field Hamiltonian spots a small parameter dictating the critical temperature and also explains how interband pair hopping always enahnces spin fluctuations at the nesting momentum connecting the Fermi surfaces. In short, no attractive glue is needed and resonating interband pair hopping is the key to Cooper pair formation in unconventional superconductors. Implications to cuprates and related issues are also discussed at the end.
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