text: p 
  
  This is consistent with having in the NS, Σ = iΓ in accor- 
  dance with Eq 6. In the SCS, Σ(ω) is purely imaginary 
  for ω > ∆ and purely real for ω < ∆. The self-energy 
  has a square-root singularity at ω = ∆. 
  
  It is worth noting that Eq.12 is derived from the in- 
  tegration over inﬁnite band. If one uses Eq.6 for ﬁnite 
  band, Eq.12 acquires an additional frequency dependence 
  at large frequencies of the order of bandwidth (the low 
  frequency structure still remains the same as in Eq.12). 
  In principle, in a fully self-consistent analysis, one should 
  indeed evaluate the self-energy using a ﬁnite bandwidth. 
  In practice, however, the self-energy at frequencies of or- 
  der bandwidth is generally much smaller than ω and con- 
  tribute very little to optical conductivity which predom- 
  inantly comes from frequencies where the self-energy is 
  comparable or even larger than ω. Keeping this in mind, 
  below we will continue with the form of self-energy de- 
  rived form inﬁnite band. We use the same argument for 
  all four models for the self-energy. 