software to fit optical spectra - Quantum Materials Group

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The list of the built-in special dielectric function formulas is given in Table 4-3. The selection might look strange at a first glance. The point is that it is not meant to be a comprehensive collection of functions for fitting. It is rather a set of some special formulas that RefFIT users, including myself, have ever employed in their data analysis. As was mentioned in the Introduction, the list is being continuously extended and everyone can ask me to include an extra function that he (or she) would like to have. The light frequency ω is assumed to be in cm -1 . Note, that all the formulas give a dielectric function that satisfies Kramers-Kronig relations (see section 2.2.1), unless the opposite is explicitly mentioned. Dielectric function Van der Marel’s formula for the dielectric function of a non- Fermi liquid (Ref.[11], formula (15)) 2 ω p ε = − 2α 1−2α ω( ω + iγ 1) ( ω + iγ 2 ) Formula for the c-axis dielectric function of cuprates with the body-centered tetragonal structure liquids (Ref.[11], formula (14)) 2 4 2 3 2 3 / 2 ε = ( 60i / ω) 2σ ( 1+ 2Ω )( 1− 8Ω − 8Ω ) + 16Ω ( 1+ Ω ) , 0 where Ω = ( γ 1 − iω) / γ 2 [ ] Formula for the ab-plane dielectric function of cuprates (Ref.[11], formula (3)) γ 1 ε = ( 60i / ω) σ 0 , γ − iω γ + γ − iω 1 1 The dielectric function of a weak-coupling s-wave BCS superconductor with arbitrary scattering rate (Ref. [12]). Parameter t is the reduced temperature t = T / Tc . The formulas of Ref.[12] are taken as they are, with τ = 1/ γ , except for the temperature dependence of the gap, which in this case is π ∆ ( t) = ∆ 0 cos t . 2 Note: the computational code is taken from Ref..[12]. Drude (not Lorentz!) term with arbitrary sign of the spectral weight A ε = − ω( ω + iγ ) Note: although a negative A would have a little physical meaning for the usual dielectric function, it can be used for the differential dielectric function (see section 4.7.1). Constant (frequency independent) dielectric function ε = ε1 + iε 2 Note: this function is simple but obviously NOT Kramers- 2 Wo (code) Wp G -1 ω p [cm -1 ] α -2 γ 1 [cm -1 ] γ 2 [cm -1 ] -3 σ 0 [Ω -1 cm -1 ] - -4 γ 1 [cm -1 ] γ 2 [cm -1 ] -5 σ 0 [Ω -1 cm -1 ] γ 1 [cm -1 ] Guide to RefFIT Page 60 -6 -7 ω p [cm -1 ] -8 t 0 -9 A [cm -2 ] -10 - ε 1 ε 2 γ 2 [cm -1 ] γ [cm -1 ] ∆ [cm -1 ] γ [cm -1 ]
Kronig friendly, so be careful! “Gapped” Drude function: 4πσ 1( ω) ε ε1 + i + Aδ ( ω) ω 4πσ 1( ω) ε = ε1 + i , if fSW = 0. ω = , if fSW = 1 Here σ 1 ( ω ) = Γ ( ω ) σ 1 D ( ω ) is the “gapped” conductivity, ∞ σ ′ ′ 1( ω ) dω ε1 ( ω) = 1+ 8∫ is the KK transform of σ 2 2 1 , ω′ − ω 0 1 ⎛ ⎛ ⎞ ⎜ ω − 2∆ ⎞ Γ( ω) = ξ + − ⎟ ⎜ + ⎜ ⎟ 0 ( 1 ξ 0 ) 1 tanh 2 ⎟ , ⎝ ⎝ 2δ ∆ ⎠⎠ is the smoothed step function, 2 ω pγ σ 1D ( ω) = is the Drude conductivity. 2 2 4π ( γ + ω ) Here A is the spectral weight added at zero frequency to compensate the loss of spectral weight due to the gap (if fSW = 1). In other words, A is adjusted in order to keep the total 2 spectral weight as if it there were no gap (e.g., ω / 8 ). Note: This formula has no microscopic justification. It is just a handy way to introduce the conductivity gap of a controllable shape to the Drude dielectric while keeping the KK relations. The shape depends on the gap value ∆ , the gap spread δ ∆ and the filling factor ξ (0 for the full gap, 1 for no gap). A similar 0 dielectric (but without the KK transformation) was used in Ref.[13]. Lorentz term with arbitrary sign of the spectral weight A ε = − 2 2 ω0 − ω − iγω Note: although a negative value of A would have little physical meaning for the usual dielectric function, it can be used for the differential dielectric function (see section 4.7.1). The difference between two Lorentzians with the same spectral weight and linewidth, but different frequencies A A ε = − 2 2 2 2 ω1 − ω − iγω ω2 − ω − iγω Note: this term allows to model the shift of the oscillator frequency in the differential dielectric function (see section -20 ω p [cm -1 ] -21 ∆ [cm -1 ] γ [cm -1 ] δ ∆ [cm -1 ] Guide to RefFIT Page 61 p -22 ξ 0 -25 A [cm -2 ] -26 -27 ω 0 [cm -1 ] ω 1 [cm -1 ] -28 A [cm -2 ] fSW γ [cm -1 ] - ω 2 [cm -1 ] γ [cm -1 ]
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Last updated: 20.04.2004 Guide to R
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Page 25 and 26: 3. Tutorial This chapter shows how
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Page 29 and 30: Figure 3-7 Click the button and in
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Page 35 and 36: Figure 3-18 The “Graph properties
Page 37 and 38: Figure 3-20 Loading the reflectivit
Page 39 and 40: Figure 3-22 The general RefFIT view
Page 41 and 42: Figure 3-25 The general RefFIT view
Page 43 and 44: MainWindow(XPos = 0, YPos = 0, Widt
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software to fit optical spectra - Quantum Materials Group

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