From da93db557f05b5e860f08aac47d01352ad7c51c0 Mon Sep 17 00:00:00 2001 From: Suter Andreas Date: Thu, 25 Jun 2015 08:36:26 +0200 Subject: [PATCH 1/2] small correction of the skewed Gaussian for extrem parameter values. --- src/classes/PTheory.cpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/classes/PTheory.cpp b/src/classes/PTheory.cpp index 9da9847c..08d7f176 100644 --- a/src/classes/PTheory.cpp +++ b/src/classes/PTheory.cpp @@ -2307,7 +2307,7 @@ Double_t PTheory::SkewedGauss(register Double_t t, const PDoubleVector& paramVal Double_t freq = TWO_PI*val[1]; if ((zp >= 25.0) || (zm >= 25.0)) // needed to prevent crash of 1F1 - skg = 2.0e300; + skg = 2.0e6; else if (fabs(val[2]) == fabs(val[3])) // sigma+ == sigma- -> Gaussian skg = TMath::Cos(phase+freq*tt) * gp; else From 012b2e58915cded8ec44d1c0798b5d146890c993 Mon Sep 17 00:00:00 2001 From: Suter Andreas Date: Thu, 25 Jun 2015 08:42:32 +0200 Subject: [PATCH 2/2] adopted the temperature dependence of the gap function (see Eq.(8) of the memo), which breaks the self-consistency. Makes it more flexible but requires that the user is using his brain. --- .../BMWlibs/data/libGapIntegrals-test.dat | 34 ++++--- .../BMWlibs/test-libGapIntegrals-ASCII.msr | 24 +++-- src/external/libGapIntegrals/GapIntegrals.pdf | Bin 174295 -> 175705 bytes src/external/libGapIntegrals/GapIntegrals.tex | 69 +++++++++------ .../libGapIntegrals/TGapIntegrals.cpp | 83 +++++++++++------- 5 files changed, 123 insertions(+), 87 deletions(-) diff --git a/doc/examples/BMWlibs/data/libGapIntegrals-test.dat b/doc/examples/BMWlibs/data/libGapIntegrals-test.dat index 6179895a..d9644f4b 100644 --- a/doc/examples/BMWlibs/data/libGapIntegrals-test.dat +++ b/doc/examples/BMWlibs/data/libGapIntegrals-test.dat @@ -12,15 +12,25 @@ ENERGY: 4200 # here the data will follow data # x, y, error y -0.02, 12.0, 0.5 -0.1, 11.8, 0.8 -0.2, 9.9, 0.4 -0.33, 7.2, 0.15 -0.41, 3.8, 0.38 -0.5, 2.7, 0.5 -0.64, 1.0, 0.7 -0.7, 0.1, 0.2 -0.8, 0.0, 0.8 -0.9, 0.1, 0.5 -1.2, 0.0, 0.1 - +0.0318411, 7.77455, 0.2 +0.0629929, 7.9869, 0.15 +0.113914, 7.64209, 0.15 +0.202492, 7.37699, 0.15 +0.302725, 7.70893, 0.12 +0.447456, 7.77565, 0.12 +0.611685, 7.45768, 0.12 +0.813613, 7.19287, 0.12 +1.00822, 7.57813, 0.12 +1.24793, 7.31343, 0.12 +1.50635, 7.16818, 0.12 +1.74591, 6.99634, 0.12 +1.99795, 6.90414, 0.12 +2.25061, 6.41393, 0.12 +2.4958, 6.66666, 0.12 +2.75514, 5.93766, 0.12 +3.00753, 5.61992, 0.12 +3.26056, 4.89091, 0.12 +3.49414, 4.52005, 0.08 +3.75356, 3.73799, 0.08 +3.99425, 2.84974, 0.08 +4.30518, 1.35139, 0.08 diff --git a/doc/examples/BMWlibs/test-libGapIntegrals-ASCII.msr b/doc/examples/BMWlibs/test-libGapIntegrals-ASCII.msr index c6e714ca..e819c669 100644 --- a/doc/examples/BMWlibs/test-libGapIntegrals-ASCII.msr +++ b/doc/examples/BMWlibs/test-libGapIntegrals-ASCII.msr @@ -2,18 +2,16 @@ Test superconductor data ############################################################### FITPARAMETER # Nr. Name Value Step Pos_Error Boundaries - 1 lambdaInvSq0 11.69 0.39 none - 2 Tc 0.558 0.018 none 0 2 - 3 Delta0 0.0673 0.0035 none - 4 aG 1 0 none + 1 lambdaInvSq0 7.983 -0.042 0.042 + 2 Tc 4.470 -0.015 0.016 0 5 + 3 Delta0 1.547 -0.026 0.027 + 4 c0 1.468 0 none + 5 aG 1.33333 0 none ############################################################### THEORY asymmetry 1 -userFcn libGapIntegrals TGapSWave 2 3 4 - -############################################################### -#FUNCTIONS +userFcn libGapIntegrals TGapDWave 2 3 4 5 ############################################################### RUN data/libGapIntegrals-test PIM3 PSI ASCII (name beamline institute data-file-format) @@ -26,15 +24,15 @@ packing 1 ############################################################### COMMANDS MINIMIZE -HESSE -#MINOS +#HESSE +MINOS SAVE ############################################################### PLOT 8 (non muSR plot) runs 1 -range 0 1.5 +range 0 6 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+73,7 @@ E-Mail: & \verb?andreas.suter@psi.ch? && % \section*{\musrfithead plug-in for the calculation of the temperature dependence of $\bm{1/\lambda^2}$ for various gap symmetries}% -This memo is intended to give a short summary of the background on which the \gapint plug-in for \musrfit \cite{musrfit} has been developped. The aim of this implementation is the efficient calculation of integrals of the form +This memo is intended to give a short summary of the background on which the \gapint plug-in for \musrfit \cite{musrfit} has been developed. The aim of this implementation is the efficient calculation of integrals of the form \begin{equation}\label{int} I(T) = 1 + \frac{1}{\pi}\int_0^{2\pi}\int_{\Delta(\varphi,T)}^{\infty}\left(\frac{\partial f}{\partial E}\right) \frac{E}{\sqrt{E^2-\Delta^2(\varphi,T)}}\mathrm{d}E\mathrm{d}\varphi\,, \end{equation} @@ -104,18 +105,27 @@ For the numerical integration we use algorithms of the \textsc{Cuba} library \ci \subsection*{Implemented gap functions and function calls from MUSRFIT} Currently the calculation of $\tilde{I}(T)$ is implemented for various gap functions. The temperature dependence of the gap functions is either given by Eq.(\ref{eq:gapT_Prozorov}) \cite{Prozorov}, or by Eq.(\ref{eq:gapT_Manzano}) \cite{Manzano}. + +\vspace{2mm} + +\noindent \color{red}\textbf{A few words of warning:~}\color{black} The temperature dependence of the gap function is typically derived from within the BCS framework, +and strongly links $T_c$ and $\Delta_0$ (e.g.\xspace $\Delta_0 = 1.76\, k_{\rm B} T_c$ for an s-wave superconductor). In a self-consistent +description this would mean that $\Delta_0$ of $\Delta(\varphi)$ is locked to $T_c$ as well. In the implementation provided, this limitation +is lifted, and therefore the \emph{user} should judge and question the result if the ratio $\Delta_0/(k_{\rm B}T_c)$ is strongly deviating from +BCS values! + \begin{equation}\label{eq:gapT_Prozorov} - \Delta(\varphi,T) \simeq \Delta(\varphi,0)\,\tanh\left[\frac{\pi k_{\rm B} T_{\rm c}}{\Delta_0}\sqrt{a_{\rm G} \left(\frac{T_{\rm c}}{T}-1\right)}\right] + \Delta(\varphi,T) \simeq \Delta(\varphi)\,\tanh\left[c_0\,\sqrt{a_{\rm G} \left(\frac{T_{\rm c}}{T}-1\right)}\right] \end{equation} -\noindent with $\Delta_0$ as given below, and $a_{\rm G}$ depends on the pairing state: +\noindent with $\Delta(\varphi)$ as given below, and $c_0$ and $a_{\rm G}$ depends on the pairing state: \begin{description} - \item [\textit{s}-wave:] $a_{\rm G}=1$ \qquad with $\Delta_0 = 1.76\, k_{\rm B} T_c$ - \item [\textit{d}-wave:] $a_{\rm G}=4/3$ \quad with $\Delta_0 = 2.14\, k_{\rm B} T_c$ + \item [\textit{s}-wave:] $a_{\rm G}=1$ \qquad with $c_0 = \frac{\displaystyle\pi k_{\rm B} T_{\rm c}}{\displaystyle\Delta_0} = \pi/1.76 = 1.785$ + \item [\textit{d}-wave:] $a_{\rm G}=4/3$ \quad with $c_0 = \frac{\displaystyle\pi k_{\rm B} T_{\rm c}}{\displaystyle\Delta_0} = \pi/2.14 = 1.468$ \end{description} \begin{equation}\label{eq:gapT_Manzano} -\Delta(\varphi,T) \simeq \Delta(\varphi)\tanh\left(1.82\left(1.018\left(\frac{T_{\mathrm c}}{T}-1\right)\right)^{0.51}\right)\,. +\Delta(\varphi,T) \simeq \Delta(\varphi)\tanh\left[1.82\left(1.018\left(\frac{T_{\mathrm c}}{T}-1\right)\right)^{0.51}\right]\,. \end{equation} The \gapint plug-in calculates $\tilde{I}(T)$ for the following $\Delta(\varphi)$: @@ -124,37 +134,39 @@ The \gapint plug-in calculates $\tilde{I}(T)$ for the following $\Delta(\varphi) \begin{equation} \Delta(\varphi) = \Delta_0 \end{equation} - \musrfit theory line: \verb?userFcn libGapIntegrals TGapSWave 1 2 [3]?\\ - (Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $[a_{\rm G}~(1)]$. If $a_{\rm G}$ is given, the temperature dependence - according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized.) + \musrfit theory line: \verb?userFcn libGapIntegrals TGapSWave 1 2 [3 4]?\\[1.5ex] + Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $[c_0~(1),~ a_{\rm G}~(1)]$. If $c_0$ and $a_{\rm G}$ are provided, + the temperature dependence according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized. \item[\textit{d}-wave gap \cite{Deutscher}:] \begin{equation} \Delta(\varphi) = \Delta_0\cos\left(2\varphi\right) \end{equation} - \musrfit theory line: \verb?userFcn libGapIntegrals TGapDWave 1 2 [3]?\\ - (Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $[a_{\rm G}~(1)]$. If $a_{\rm G}$ is given, the temperature dependence - according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized.) + \musrfit theory line: \verb?userFcn libGapIntegrals TGapDWave 1 2 [3 4]?\\[1.5ex] + Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $[c_0~(1),~a_{\rm G}~(1)]$. If $c_0$ and $a_{\rm G}$ are provided, + the temperature dependence according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized. \item[non-monotonic \textit{d}-wave gap \cite{Matsui}:] \begin{equation} \Delta(\varphi) = \Delta_0\left[a \cos\left(2\varphi\right) + (1-a)\cos\left(6\varphi\right)\right] \end{equation} - \musrfit theory line: \verb?userFcn libGapIntegrals TGapNonMonDWave1 1 2 3 [4]?\\ - (Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $a~(1)$, $[a_{\rm G}~(1)]$. If $a_{\rm G}$ is given, the temperature dependence - according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized.) + \musrfit theory line: \verb?userFcn libGapIntegrals TGapNonMonDWave1 1 2 3 [4 5]?\\[1.5ex] + Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $a~(1)$, $[c_0~(1),~a_{\rm G}~(1)]$. If $c_0$ and $a_{\rm G}$ are provided, + the temperature dependence according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized. \item[non-monotonic \textit{d}-wave gap \cite{Eremin}:] \begin{equation} \Delta(\varphi) = \Delta_0\left[\frac{2}{3} \sqrt{\frac{a}{3}}\cos\left(2\varphi\right) / \left( 1 + a\cos^2\left(2\varphi\right)\right)^{\frac{3}{2}}\right],\,a>1/2 \end{equation} - \musrfit theory line: \verb?userFcn libGapIntegrals TGapNonMonDWave2 1 2 3 [4]?\\ - (Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $a~(1)$, $a~(1)$, $[a_{\rm G}~(1)]$. If $a_{\rm G}$ is given, the temperature dependence - according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized.) + \musrfit theory line: \verb?userFcn libGapIntegrals TGapNonMonDWave2 1 2 3 [4 5]?\\[1.5ex] + Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $a~(1)$, $a~(1)$, $[c_0~(1),~a_{\rm G}~(1)]$. + If $c_0$ and $a_{\rm G}$ are provided, the temperature dependence according to Eq.(\ref{eq:gapT_Prozorov}) will be used, + otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized. \item[anisotropic \textit{s}-wave gap \cite{AnisotropicSWave}:] \begin{equation} \Delta(\varphi) = \Delta_0\left[1+a\cos\left(4\varphi\right)\right]\,,\,0\leqslant a\leqslant1 \end{equation} - \musrfit theory line: \verb?userFcn libGapIntegrals TGapAnSWave 1 2 3 [4]?\\ - (Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $a~(1)$, $[a_{\rm G}~(1)]$. If $a_{\rm G}$ is given, the temperature dependence - according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized.) + \musrfit theory line: \verb?userFcn libGapIntegrals TGapAnSWave 1 2 3 [4 5]?\\[1.5ex] + Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $a~(1)$, $[c_0~(1),~a_{\rm G}~(1)]$. + If $c_0$ and $a_{\rm G}$ are provided, the temperature dependence according to Eq.(\ref{eq:gapT_Prozorov}) will be used, + otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized. \end{description} \noindent It is also possible to calculate a power law temperature dependence (in the two fluid approximation $n=4$) and the dirty \textit{s}-wave expression. @@ -164,16 +176,16 @@ Obviously for this no integration is needed. \begin{equation} \frac{\lambda(0)^2}{\lambda(T)^2} = 1-\left(\frac{T}{T_{\mathrm c}}\right)^n \end{equation} - \musrfit theory line: \verb?userFcn libGapIntegrals TGapPowerLaw 1 2?\\ - (Parameters: $T_{\mathrm c}~(\mathrm{K})$, $n~(1)$) + \musrfit theory line: \verb?userFcn libGapIntegrals TGapPowerLaw 1 2?\\[1.5ex] + Parameters: $T_{\mathrm c}~(\mathrm{K})$, $n~(1)$ \item[dirty \textit{s}-wave \cite{Tinkham}:] \begin{equation} \frac{\lambda(0)^2}{\lambda(T)^2} = \frac{\Delta(T)}{\Delta_0}\,\tanh\left[\frac{\Delta(T)}{2 k_{\rm B} T}\right] \end{equation} - with $\Delta(T)$ given by Eq.(\ref{eq:gapT}).\\ - \musrfit theory line: \verb?userFcn libGapIntegrals TGapDirtySWave 1 2 [3]?\\ - (Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $[a_{\rm G}~(1)]$. If $a_{\rm G}$ is given, the temperature dependence - according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized.) + \musrfit theory line: \verb?userFcn libGapIntegrals TGapDirtySWave 1 2 [3 4]?\\[1.5ex] + Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $[c_0~(1),~a_{\rm G}~(1)]$. + If $c_0$ and $a_{\rm G}$ are provided, the temperature dependence according to Eq.(\ref{eq:gapT_Prozorov}) will be used, + otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized. \end{description} \noindent Currently there are two gap functions to be found in the code which are \emph{not} documented here: @@ -187,7 +199,8 @@ The \gapint library is free software; you can redistribute it and/or modify it u \bibliographystyle{plain} \begin{thebibliography}{1} -\bibitem{musrfit} A.~Suter, \textit{\musrfit User Manual}, https://wiki.intranet.psi.ch/MUSR/MusrFit +\bibitem{musrfit} A. Suter, and B.M. Wojek, Physics Procedia \textbf{30}, 69 (2012). + A.~Suter, \textit{\musrfit User Manual}, http://lmu.web.psi.ch/musrfit/user/MUSR/WebHome.html \bibitem{cuba} T.~Hahn, \textit{Cuba -- a library for multidimensional numerical integration}, Comput.~Phys.~Commun.~\textbf{168}~(2005)~78-95, http://www.feynarts.de/cuba/ \bibitem{Prozorov} R.~Prozorov and R.W.~Giannetta, \textit{Magnetic penetration depth in unconventional superconductors}, Supercond.\ Sci.\ Technol.\ \textbf{19}~(2006)~R41-R67, and Erratum in Supercond.\ Sci.\ Technol.\ \textbf{21}~(2008)~082003. \bibitem{Manzano} A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205 diff --git a/src/external/libGapIntegrals/TGapIntegrals.cpp b/src/external/libGapIntegrals/TGapIntegrals.cpp index 102fd02b..c2736ebc 100644 --- a/src/external/libGapIntegrals/TGapIntegrals.cpp +++ b/src/external/libGapIntegrals/TGapIntegrals.cpp @@ -459,10 +459,12 @@ TLambdaInvNonMonDWave2::~TLambdaInvNonMonDWave2() { */ double TGapSWave::operator()(double t, const vector &par) const { - assert((par.size() == 2) || (par.size() == 3)); // two or three parameters: Tc (K), Delta(0) (meV), [a (1)] - // 2 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205 - // 3 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67 + // parameters: [0] Tc (K), [1] Delta0 (meV), [[2] c0 (1), [3] aG (1)] + + assert((par.size() == 2) || (par.size() == 4)); // 2 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205 + // 4 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67 // and Erratum Supercond. Sci. Technol. 21 (2008) 082003 + // c0 in the original context is c0 = (pi kB Tc) / Delta0 if (t<=0.0) return 1.0; else if (t >= par[0]) @@ -509,7 +511,7 @@ double TGapSWave::operator()(double t, const vector &par) const { if (par.size() == 2) { // Carrington/Manzano intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); } else { // Prozorov/Giannetta - intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(par[2]*(par[0]/t-1.0)))); // tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K + intPar.push_back(par[1]*tanh(par[2]*sqrt(par[3]*(par[0]/t-1.0)))); // Delta0*tanh(c0*sqrt(aG*(Tc/T-1))) } fGapIntegral->SetParameters(intPar); @@ -536,10 +538,12 @@ double TGapSWave::operator()(double t, const vector &par) const { */ double TGapDWave::operator()(double t, const vector &par) const { - assert((par.size() == 2) || (par.size() == 3)); // two or three parameters: Tc (K), Delta(0) (meV), [a (1)] - // 2 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205 - // 3 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67 + // parameters: [0] Tc (K), [1] Delta0 (meV), [[2] c0 (1), [3] aG (1)] + + assert((par.size() == 2) || (par.size() == 4)); // 2 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205 + // 4 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67 // and Erratum Supercond. Sci. Technol. 21 (2008) 082003 + // c0 in the original context is c0 = (pi kB Tc) / Delta0 if (t<=0.0) return 1.0; else if (t >= par[0]) @@ -585,7 +589,7 @@ double TGapDWave::operator()(double t, const vector &par) const { if (par.size() == 2) { // Carrington/Manzano intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); } else { // Prozorov/Giannetta - intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(par[2]*(par[0]/t-1.0)))); // tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K + intPar.push_back(par[1]*tanh(par[2]*sqrt(par[3]*(par[0]/t-1.0)))); // Delta0*tanh(c0*sqrt(aG*(Tc/T-1))) } intPar.push_back(4.0*(t+intPar[1])); // upper limit of energy-integration: cutoff energy intPar.push_back(TMath::PiOver2()); // upper limit of phi-integration @@ -618,9 +622,10 @@ double TGapDWave::operator()(double t, const vector &par) const { */ double TGapCosSqDWave::operator()(double t, const vector &par) const { - assert((par.size() == 3) || (par.size() == 5)); // three or five parameters: Tc (K), DeltaD(0) (meV), DeltaS(0) (meV), [aD (1), aS (1)] - // 3 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205 - // 5 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67 + // parameters: [0] Tc (K), [1] Delta0_D (meV), [2] Delta0_S (meV) [[3] c0_D (1), [4] aG_D (1), [5] c0_S (1), [6] aG_S (1)] + + assert((par.size() == 3) || (par.size() == 7)); // 3 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205 + // 7 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67 // and Erratum Supercond. Sci. Technol. 21 (2008) 082003 if (t<=0.0) return 1.0; @@ -667,14 +672,14 @@ double TGapCosSqDWave::operator()(double t, const vector &par) const { if (par.size() == 3) { // Carrington/Manzano intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); } else { // Prozorov/Giannetta - intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(par[3]*(par[0]/t-1.0)))); // DeltaD(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K + intPar.push_back(par[1]*tanh(par[3]*sqrt(par[4]*(par[0]/t-1.0)))); // Delta0_D*tanh(c0_D*sqrt(aG_D*(Tc/T-1))) } intPar.push_back(1.0*(t+intPar[1])); // upper limit of energy-integration: cutoff energy intPar.push_back(TMath::Pi()); // upper limit of phi-integration if (par.size() == 3) { // Carrington/Manzano intPar.push_back(par[2]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); } else { // Prozorov/Giannetta - intPar.push_back(par[2]*tanh(0.2707214816*par[0]/par[2]*sqrt(par[4]*(par[0]/t-1.0)))); // DeltaS(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K + intPar.push_back(par[2]*tanh(par[5]*sqrt(par[6]*(par[0]/t-1.0)))); // Delta0_S*tanh(c0_S*sqrt(aG_S*(Tc/T-1))) } // double xl[] = {0.0, 0.0}; // lower bound E, phi @@ -705,10 +710,12 @@ double TGapCosSqDWave::operator()(double t, const vector &par) const { */ double TGapSinSqDWave::operator()(double t, const vector &par) const { - assert((par.size() == 3) || (par.size() == 5)); // three or five parameters: Tc (K), DeltaD(0) (meV), DeltaS(0) (meV), [aD (1), aS (1)] - // 3 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205 - // 5 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67 + // parameters: [0] Tc (K), [1] Delta0_D (meV), [2] Delta0_S (meV) [[3] c0_D (1), [4] aG_D (1), [5] c0_S (1), [6] aG_S (1)] + + assert((par.size() == 3) || (par.size() == 7)); // 3 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205 + // 7 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67 // and Erratum Supercond. Sci. Technol. 21 (2008) 082003 + // c0 in the original context is c0 = (pi kB Tc) / Delta0 if (t<=0.0) return 1.0; else if (t >= par[0]) @@ -754,14 +761,14 @@ double TGapSinSqDWave::operator()(double t, const vector &par) const { if (par.size() == 3) { // Carrington/Manzano intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); } else { // Prozorov/Giannetta - intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(par[3]*(par[0]/t-1.0)))); // DeltaD(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K + intPar.push_back(par[1]*tanh(par[3]*sqrt(par[4]*(par[0]/t-1.0)))); // Delta0_D*tanh(c0_D*sqrt(aG_D*(Tc/T-1))) } intPar.push_back(1.0*(t+intPar[1])); // upper limit of energy-integration: cutoff energy intPar.push_back(TMath::Pi()); // upper limit of phi-integration if (par.size() == 3) { // Carrington/Manzano intPar.push_back(par[2]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); } else { // Prozorov/Giannetta - intPar.push_back(par[2]*tanh(0.2707214816*par[0]/par[2]*sqrt(par[4]*(par[0]/t-1.0)))); // DeltaS(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K + intPar.push_back(par[2]*tanh(par[5]*sqrt(par[6]*(par[0]/t-1.0)))); // Delta0_S*tanh(c0_S*sqrt(aG_S*(Tc/T-1))) } // double xl[] = {0.0, 0.0}; // lower bound E, phi @@ -792,10 +799,13 @@ double TGapSinSqDWave::operator()(double t, const vector &par) const { */ double TGapAnSWave::operator()(double t, const vector &par) const { - assert((par.size() == 3) || (par.size() == 4)); // three or four parameters: Tc (K), Delta(0) (meV), a (1), [aS_Gap (1)] - // 3 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205 - // 4 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67 + // parameters: [0] Tc (K), [1] Delta0 (meV), [2] a (1), [[3] c0 (1), [4] aG (1)] + + assert((par.size() == 3) || (par.size() == 5)); // 3 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205 + // 5 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67 // and Erratum Supercond. Sci. Technol. 21 (2008) 082003 + // c0 in the original context is c0 = (pi kB Tc) / Delta0 + if (t<=0.0) return 1.0; else if (t >= par[0]) @@ -841,7 +851,7 @@ double TGapAnSWave::operator()(double t, const vector &par) const { if (par.size() == 3) { // Carrington/Manzano intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); } else { // Prozorov/Giannetta - intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(par[3]*(par[0]/t-1.0)))); // DeltaS(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K + intPar.push_back(par[1]*tanh(par[3]*sqrt(par[4]*(par[0]/t-1.0)))); // Delta0*tanh(c0*sqrt(aG*(Tc/T-1))) } intPar.push_back(par[2]); intPar.push_back(4.0*(t+(1.0+par[2])*intPar[1])); // upper limit of energy-integration: cutoff energy @@ -875,10 +885,12 @@ double TGapAnSWave::operator()(double t, const vector &par) const { */ double TGapNonMonDWave1::operator()(double t, const vector &par) const { - assert((par.size() == 3) || (par.size() == 4)); // three or four parameters: Tc (K), Delta(0) (meV), a (1), [aD_Gap (1)] - // 3 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205 - // 4 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67 + // parameters: [0] Tc (K), [1] Delta0 (meV), [2] a (1), [[3] c0 (1), [4] aG (1)] + + assert((par.size() == 3) || (par.size() == 5)); // 3 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205 + // 5 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67 // and Erratum Supercond. Sci. Technol. 21 (2008) 082003 + // c0 in the original context is c0 = (pi kB Tc) / Delta0 if (t<=0.0) return 1.0; else if (t >= par[0]) @@ -924,7 +936,7 @@ double TGapNonMonDWave1::operator()(double t, const vector &par) const { if (par.size() == 3) { // Carrington/Manzano intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); } else { // Prozorov/Giannetta - intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(par[3]*(par[0]/t-1.0)))); // DeltaD(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K + intPar.push_back(par[1]*tanh(par[3]*sqrt(par[4]*(par[0]/t-1.0)))); // Delta0*tanh(c0*sqrt(aG*(Tc/T-1))) } intPar.push_back(par[2]); intPar.push_back(4.0*(t+intPar[1])); // upper limit of energy-integration: cutoff energy @@ -955,10 +967,12 @@ double TGapNonMonDWave1::operator()(double t, const vector &par) const { */ double TGapNonMonDWave2::operator()(double t, const vector &par) const { - assert((par.size() == 3) || (par.size() == 4)); // three parameters: Tc (K), Delta(0) (meV), a (1), [aD_Gap (1)] - // 3 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205 - // 4 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67 + // parameters: [0] Tc (K), [1] Delta0 (meV), [2] a (1), [[3] c0 (1), [4] aG (1)] + + assert((par.size() == 3) || (par.size() == 5)); // 3 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205 + // 5 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67 // and Erratum Supercond. Sci. Technol. 21 (2008) 082003 + // c0 in the original context is c0 = (pi kB Tc) / Delta0 if (t<=0.0) return 1.0; else if (t >= par[0]) @@ -1004,7 +1018,7 @@ double TGapNonMonDWave2::operator()(double t, const vector &par) const { if (par.size() == 3) { // Carrington/Manzano intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); } else { // Prozorov/Giannetta - intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(par[3]*(par[0]/t-1.0)))); // DeltaD(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K + intPar.push_back(par[1]*tanh(par[3]*sqrt(par[4]*(par[0]/t-1.0)))); // Delta0*tanh(c0*sqrt(aG*(Tc/T-1))) } intPar.push_back(par[2]); intPar.push_back(4.0*(t+intPar[1])); // upper limit of energy-integration: cutoff energy @@ -1056,9 +1070,10 @@ double TGapPowerLaw::operator()(double t, const vector &par) const { */ double TGapDirtySWave::operator()(double t, const vector &par) const { - assert((par.size() == 2) || (par.size() == 3)); // two or three parameters: Tc (K), Delta(0) (meV) [a (1)] - // 2 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205 - // 3 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67 + // parameters: [0] Tc (K), [1] Delta0 (meV), [[2] c0 (1), [3] aG (1)] + + assert((par.size() == 2) || (par.size() == 4)); // 2 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205 + // 4 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67 // and Erratum Supercond. Sci. Technol. 21 (2008) 082003 if (t<=0.0) return 1.0; @@ -1069,7 +1084,7 @@ double TGapDirtySWave::operator()(double t, const vector &par) const { if (par.size() == 2) { // Carrington/Manzano deltaT = tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51)); } else { // Prozorov/Giannetta - deltaT = tanh(0.2707214816*par[0]/par[1]*sqrt(par[2]*(par[0]/t-1.0))); // tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K + deltaT = tanh(par[2]*sqrt(par[3]*(par[0]/t-1.0))); // tanh(c0*sqrt(aG*(Tc/T-1))) } return deltaT*tanh(par[1]*deltaT/(0.172346648*t)); // Delta(T)/Delta(0)*tanh(Delta(T)/2 kB T), kB in meV/K