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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.

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suter_a 2015-06-25 08:42:32 +02:00
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34
doc/examples/BMWlibs/data/libGapIntegrals-test.dat
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@ -12,15 +12,25 @@ ENERGY: 4200
# here the data will follow # here the data will follow
data data
# x, y, error y # x, y, error y
0.02, 12.0, 0.5 0.0318411, 7.77455, 0.2
0.1, 11.8, 0.8 0.0629929, 7.9869, 0.15
0.2, 9.9, 0.4 0.113914, 7.64209, 0.15
0.33, 7.2, 0.15 0.202492, 7.37699, 0.15
0.41, 3.8, 0.38 0.302725, 7.70893, 0.12
0.5, 2.7, 0.5 0.447456, 7.77565, 0.12
0.64, 1.0, 0.7 0.611685, 7.45768, 0.12
0.7, 0.1, 0.2 0.813613, 7.19287, 0.12
0.8, 0.0, 0.8 1.00822, 7.57813, 0.12
0.9, 0.1, 0.5 1.24793, 7.31343, 0.12
1.2, 0.0, 0.1 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

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doc/examples/BMWlibs/test-libGapIntegrals-ASCII.msr
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@ -2,18 +2,16 @@ Test superconductor data
############################################################### ###############################################################
FITPARAMETER FITPARAMETER
# Nr. Name Value Step Pos_Error Boundaries # Nr. Name Value Step Pos_Error Boundaries
1 lambdaInvSq0 11.69 0.39 none 1 lambdaInvSq0 7.983 -0.042 0.042
2 Tc 0.558 0.018 none 0 2 2 Tc 4.470 -0.015 0.016 0 5
3 Delta0 0.0673 0.0035 none 3 Delta0 1.547 -0.026 0.027
4 aG 1 0 none 4 c0 1.468 0 none
5 aG 1.33333 0 none
############################################################### ###############################################################
THEORY THEORY
asymmetry 1 asymmetry 1
userFcn libGapIntegrals TGapSWave 2 3 4 userFcn libGapIntegrals TGapDWave 2 3 4 5
###############################################################
#FUNCTIONS
############################################################### ###############################################################
RUN data/libGapIntegrals-test PIM3 PSI ASCII (name beamline institute data-file-format) RUN data/libGapIntegrals-test PIM3 PSI ASCII (name beamline institute data-file-format)
@ -26,15 +24,15 @@ packing 1
############################################################### ###############################################################
COMMANDS COMMANDS
MINIMIZE MINIMIZE
HESSE #HESSE
#MINOS MINOS
SAVE SAVE
############################################################### ###############################################################
PLOT 8 (non muSR plot) PLOT 8 (non muSR plot)
runs 1 runs 1
range 0 1.5 range 0 6
############################################################### ###############################################################
STATISTIC --- 2014-10-28 10:40:31 STATISTIC --- 2015-06-25 08:39:03
chisq = 14.3, NDF = 8, chisq/NDF = 1.790471 chisq = 58.3, NDF = 19, chisq/NDF = 3.066272

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src/external/libGapIntegrals/GapIntegrals.pdf vendored
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69
src/external/libGapIntegrals/GapIntegrals.tex vendored
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@ -12,6 +12,7 @@
\usepackage{rotating} \usepackage{rotating}
\usepackage{dcolumn} \usepackage{dcolumn}
\usepackage{geometry} \usepackage{geometry}
\usepackage{color}
\geometry{a4paper,left=20mm,right=20mm,top=20mm,bottom=20mm} \geometry{a4paper,left=20mm,right=20mm,top=20mm,bottom=20mm}
@ -72,7 +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}% \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} \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\,, 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} \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} \subsection*{Implemented gap functions and function calls from MUSRFIT}
Currently the calculation of $\tilde{I}(T)$ is implemented for various gap functions. 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}. 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} \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} \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} \begin{description}
\item [\textit{s}-wave:] $a_{\rm G}=1$ \qquad with $\Delta_0 = 1.76\, k_{\rm B} T_c$ \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 $\Delta_0 = 2.14\, k_{\rm B} T_c$ \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} \end{description}
\begin{equation}\label{eq:gapT_Manzano} \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} \end{equation}
The \gapint plug-in calculates $\tilde{I}(T)$ for the following $\Delta(\varphi)$: 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} \begin{equation}
\Delta(\varphi) = \Delta_0 \Delta(\varphi) = \Delta_0
\end{equation} \end{equation}
\musrfit theory line: \verb?userFcn libGapIntegrals TGapSWave 1 2 [3]?\\ \musrfit theory line: \verb?userFcn libGapIntegrals TGapSWave 1 2 [3 4]?\\[1.5ex]
(Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $[a_{\rm G}~(1)]$. If $a_{\rm G}$ is given, the temperature dependence 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,
according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized.) 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}:] \item[\textit{d}-wave gap \cite{Deutscher}:]
\begin{equation} \begin{equation}
\Delta(\varphi) = \Delta_0\cos\left(2\varphi\right) \Delta(\varphi) = \Delta_0\cos\left(2\varphi\right)
\end{equation} \end{equation}
\musrfit theory line: \verb?userFcn libGapIntegrals TGapDWave 1 2 [3]?\\ \musrfit theory line: \verb?userFcn libGapIntegrals TGapDWave 1 2 [3 4]?\\[1.5ex]
(Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $[a_{\rm G}~(1)]$. If $a_{\rm G}$ is given, the temperature dependence 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,
according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized.) 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}:] \item[non-monotonic \textit{d}-wave gap \cite{Matsui}:]
\begin{equation} \begin{equation}
\Delta(\varphi) = \Delta_0\left[a \cos\left(2\varphi\right) + (1-a)\cos\left(6\varphi\right)\right] \Delta(\varphi) = \Delta_0\left[a \cos\left(2\varphi\right) + (1-a)\cos\left(6\varphi\right)\right]
\end{equation} \end{equation}
\musrfit theory line: \verb?userFcn libGapIntegrals TGapNonMonDWave1 1 2 3 [4]?\\ \musrfit theory line: \verb?userFcn libGapIntegrals TGapNonMonDWave1 1 2 3 [4 5]?\\[1.5ex]
(Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $a~(1)$, $[a_{\rm G}~(1)]$. If $a_{\rm G}$ is given, the temperature dependence 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,
according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized.) 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}:] \item[non-monotonic \textit{d}-wave gap \cite{Eremin}:]
\begin{equation} \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 \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} \end{equation}
\musrfit theory line: \verb?userFcn libGapIntegrals TGapNonMonDWave2 1 2 3 [4]?\\ \musrfit theory line: \verb?userFcn libGapIntegrals TGapNonMonDWave2 1 2 3 [4 5]?\\[1.5ex]
(Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $a~(1)$, $a~(1)$, $[a_{\rm G}~(1)]$. If $a_{\rm G}$ is given, the temperature dependence Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $a~(1)$, $a~(1)$, $[c_0~(1),~a_{\rm G}~(1)]$.
according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized.) 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}:] \item[anisotropic \textit{s}-wave gap \cite{AnisotropicSWave}:]
\begin{equation} \begin{equation}
\Delta(\varphi) = \Delta_0\left[1+a\cos\left(4\varphi\right)\right]\,,\,0\leqslant a\leqslant1 \Delta(\varphi) = \Delta_0\left[1+a\cos\left(4\varphi\right)\right]\,,\,0\leqslant a\leqslant1
\end{equation} \end{equation}
\musrfit theory line: \verb?userFcn libGapIntegrals TGapAnSWave 1 2 3 [4]?\\ \musrfit theory line: \verb?userFcn libGapIntegrals TGapAnSWave 1 2 3 [4 5]?\\[1.5ex]
(Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $a~(1)$, $[a_{\rm G}~(1)]$. If $a_{\rm G}$ is given, the temperature dependence Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $a~(1)$, $[c_0~(1),~a_{\rm G}~(1)]$.
according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized.) 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} \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. \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} \begin{equation}
\frac{\lambda(0)^2}{\lambda(T)^2} = 1-\left(\frac{T}{T_{\mathrm c}}\right)^n \frac{\lambda(0)^2}{\lambda(T)^2} = 1-\left(\frac{T}{T_{\mathrm c}}\right)^n
\end{equation} \end{equation}
\musrfit theory line: \verb?userFcn libGapIntegrals TGapPowerLaw 1 2?\\ \musrfit theory line: \verb?userFcn libGapIntegrals TGapPowerLaw 1 2?\\[1.5ex]
(Parameters: $T_{\mathrm c}~(\mathrm{K})$, $n~(1)$) Parameters: $T_{\mathrm c}~(\mathrm{K})$, $n~(1)$
\item[dirty \textit{s}-wave \cite{Tinkham}:] \item[dirty \textit{s}-wave \cite{Tinkham}:]
\begin{equation} \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] \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} \end{equation}
with $\Delta(T)$ given by Eq.(\ref{eq:gapT}).\\ \musrfit theory line: \verb?userFcn libGapIntegrals TGapDirtySWave 1 2 [3 4]?\\[1.5ex]
\musrfit theory line: \verb?userFcn libGapIntegrals TGapDirtySWave 1 2 [3]?\\ Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $[c_0~(1),~a_{\rm G}~(1)]$.
(Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $[a_{\rm G}~(1)]$. If $a_{\rm G}$ is given, the temperature dependence If $c_0$ and $a_{\rm G}$ are provided, the temperature dependence according to Eq.(\ref{eq:gapT_Prozorov}) will be used,
according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized.) otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized.
\end{description} \end{description}
\noindent Currently there are two gap functions to be found in the code which are \emph{not} documented here: \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} \bibliographystyle{plain}
\begin{thebibliography}{1} \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{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{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 \bibitem{Manzano} A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205

83
src/external/libGapIntegrals/TGapIntegrals.cpp vendored
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@ -459,10 +459,12 @@ TLambdaInvNonMonDWave2::~TLambdaInvNonMonDWave2() {
*/ */
double TGapSWave::operator()(double t, const vector<double> &par) const { double TGapSWave::operator()(double t, const vector<double> &par) const {
assert((par.size() == 2) || (par.size() == 3)); // two or three parameters: Tc (K), Delta(0) (meV), [a (1)] // parameters: [0] Tc (K), [1] Delta0 (meV), [[2] c0 (1), [3] aG (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 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 // and Erratum Supercond. Sci. Technol. 21 (2008) 082003
// c0 in the original context is c0 = (pi kB Tc) / Delta0
if (t<=0.0) if (t<=0.0)
return 1.0; return 1.0;
else if (t >= par[0]) else if (t >= par[0])
@ -509,7 +511,7 @@ double TGapSWave::operator()(double t, const vector<double> &par) const {
if (par.size() == 2) { // Carrington/Manzano if (par.size() == 2) { // Carrington/Manzano
intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51)));
} else { // Prozorov/Giannetta } 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); fGapIntegral->SetParameters(intPar);
@ -536,10 +538,12 @@ double TGapSWave::operator()(double t, const vector<double> &par) const {
*/ */
double TGapDWave::operator()(double t, const vector<double> &par) const { double TGapDWave::operator()(double t, const vector<double> &par) const {
assert((par.size() == 2) || (par.size() == 3)); // two or three parameters: Tc (K), Delta(0) (meV), [a (1)] // parameters: [0] Tc (K), [1] Delta0 (meV), [[2] c0 (1), [3] aG (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 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 // and Erratum Supercond. Sci. Technol. 21 (2008) 082003
// c0 in the original context is c0 = (pi kB Tc) / Delta0
if (t<=0.0) if (t<=0.0)
return 1.0; return 1.0;
else if (t >= par[0]) else if (t >= par[0])
@ -585,7 +589,7 @@ double TGapDWave::operator()(double t, const vector<double> &par) const {
if (par.size() == 2) { // Carrington/Manzano if (par.size() == 2) { // Carrington/Manzano
intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51)));
} else { // Prozorov/Giannetta } 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(4.0*(t+intPar[1])); // upper limit of energy-integration: cutoff energy
intPar.push_back(TMath::PiOver2()); // upper limit of phi-integration intPar.push_back(TMath::PiOver2()); // upper limit of phi-integration
@ -618,9 +622,10 @@ double TGapDWave::operator()(double t, const vector<double> &par) const {
*/ */
double TGapCosSqDWave::operator()(double t, const vector<double> &par) const { double TGapCosSqDWave::operator()(double t, const vector<double> &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)] // 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)]
// 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 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 // and Erratum Supercond. Sci. Technol. 21 (2008) 082003
if (t<=0.0) if (t<=0.0)
return 1.0; return 1.0;
@ -667,14 +672,14 @@ double TGapCosSqDWave::operator()(double t, const vector<double> &par) const {
if (par.size() == 3) { // Carrington/Manzano if (par.size() == 3) { // Carrington/Manzano
intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51)));
} else { // Prozorov/Giannetta } 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(1.0*(t+intPar[1])); // upper limit of energy-integration: cutoff energy
intPar.push_back(TMath::Pi()); // upper limit of phi-integration intPar.push_back(TMath::Pi()); // upper limit of phi-integration
if (par.size() == 3) { // Carrington/Manzano if (par.size() == 3) { // Carrington/Manzano
intPar.push_back(par[2]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); intPar.push_back(par[2]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51)));
} else { // Prozorov/Giannetta } 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 // double xl[] = {0.0, 0.0}; // lower bound E, phi
@ -705,10 +710,12 @@ double TGapCosSqDWave::operator()(double t, const vector<double> &par) const {
*/ */
double TGapSinSqDWave::operator()(double t, const vector<double> &par) const { double TGapSinSqDWave::operator()(double t, const vector<double> &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)] // 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)]
// 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 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 // and Erratum Supercond. Sci. Technol. 21 (2008) 082003
// c0 in the original context is c0 = (pi kB Tc) / Delta0
if (t<=0.0) if (t<=0.0)
return 1.0; return 1.0;
else if (t >= par[0]) else if (t >= par[0])
@ -754,14 +761,14 @@ double TGapSinSqDWave::operator()(double t, const vector<double> &par) const {
if (par.size() == 3) { // Carrington/Manzano if (par.size() == 3) { // Carrington/Manzano
intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51)));
} else { // Prozorov/Giannetta } 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(1.0*(t+intPar[1])); // upper limit of energy-integration: cutoff energy
intPar.push_back(TMath::Pi()); // upper limit of phi-integration intPar.push_back(TMath::Pi()); // upper limit of phi-integration
if (par.size() == 3) { // Carrington/Manzano if (par.size() == 3) { // Carrington/Manzano
intPar.push_back(par[2]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); intPar.push_back(par[2]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51)));
} else { // Prozorov/Giannetta } 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 // double xl[] = {0.0, 0.0}; // lower bound E, phi
@ -792,10 +799,13 @@ double TGapSinSqDWave::operator()(double t, const vector<double> &par) const {
*/ */
double TGapAnSWave::operator()(double t, const vector<double> &par) const { double TGapAnSWave::operator()(double t, const vector<double> &par) const {
assert((par.size() == 3) || (par.size() == 4)); // three or four parameters: Tc (K), Delta(0) (meV), a (1), [aS_Gap (1)] // parameters: [0] Tc (K), [1] Delta0 (meV), [2] a (1), [[3] c0 (1), [4] aG (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 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 // and Erratum Supercond. Sci. Technol. 21 (2008) 082003
// c0 in the original context is c0 = (pi kB Tc) / Delta0
if (t<=0.0) if (t<=0.0)
return 1.0; return 1.0;
else if (t >= par[0]) else if (t >= par[0])
@ -841,7 +851,7 @@ double TGapAnSWave::operator()(double t, const vector<double> &par) const {
if (par.size() == 3) { // Carrington/Manzano if (par.size() == 3) { // Carrington/Manzano
intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51)));
} else { // Prozorov/Giannetta } 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(par[2]);
intPar.push_back(4.0*(t+(1.0+par[2])*intPar[1])); // upper limit of energy-integration: cutoff energy 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<double> &par) const {
*/ */
double TGapNonMonDWave1::operator()(double t, const vector<double> &par) const { double TGapNonMonDWave1::operator()(double t, const vector<double> &par) const {
assert((par.size() == 3) || (par.size() == 4)); // three or four parameters: Tc (K), Delta(0) (meV), a (1), [aD_Gap (1)] // parameters: [0] Tc (K), [1] Delta0 (meV), [2] a (1), [[3] c0 (1), [4] aG (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 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 // and Erratum Supercond. Sci. Technol. 21 (2008) 082003
// c0 in the original context is c0 = (pi kB Tc) / Delta0
if (t<=0.0) if (t<=0.0)
return 1.0; return 1.0;
else if (t >= par[0]) else if (t >= par[0])
@ -924,7 +936,7 @@ double TGapNonMonDWave1::operator()(double t, const vector<double> &par) const {
if (par.size() == 3) { // Carrington/Manzano if (par.size() == 3) { // Carrington/Manzano
intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51)));
} else { // Prozorov/Giannetta } 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(par[2]);
intPar.push_back(4.0*(t+intPar[1])); // upper limit of energy-integration: cutoff energy 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<double> &par) const {
*/ */
double TGapNonMonDWave2::operator()(double t, const vector<double> &par) const { double TGapNonMonDWave2::operator()(double t, const vector<double> &par) const {
assert((par.size() == 3) || (par.size() == 4)); // three parameters: Tc (K), Delta(0) (meV), a (1), [aD_Gap (1)] // parameters: [0] Tc (K), [1] Delta0 (meV), [2] a (1), [[3] c0 (1), [4] aG (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 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 // and Erratum Supercond. Sci. Technol. 21 (2008) 082003
// c0 in the original context is c0 = (pi kB Tc) / Delta0
if (t<=0.0) if (t<=0.0)
return 1.0; return 1.0;
else if (t >= par[0]) else if (t >= par[0])
@ -1004,7 +1018,7 @@ double TGapNonMonDWave2::operator()(double t, const vector<double> &par) const {
if (par.size() == 3) { // Carrington/Manzano if (par.size() == 3) { // Carrington/Manzano
intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51)));
} else { // Prozorov/Giannetta } 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(par[2]);
intPar.push_back(4.0*(t+intPar[1])); // upper limit of energy-integration: cutoff energy 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<double> &par) const {
*/ */
double TGapDirtySWave::operator()(double t, const vector<double> &par) const { double TGapDirtySWave::operator()(double t, const vector<double> &par) const {
assert((par.size() == 2) || (par.size() == 3)); // two or three parameters: Tc (K), Delta(0) (meV) [a (1)] // parameters: [0] Tc (K), [1] Delta0 (meV), [[2] c0 (1), [3] aG (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 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 // and Erratum Supercond. Sci. Technol. 21 (2008) 082003
if (t<=0.0) if (t<=0.0)
return 1.0; return 1.0;
@ -1069,7 +1084,7 @@ double TGapDirtySWave::operator()(double t, const vector<double> &par) const {
if (par.size() == 2) { // Carrington/Manzano if (par.size() == 2) { // Carrington/Manzano
deltaT = tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51)); deltaT = tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51));
} else { // Prozorov/Giannetta } 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 return deltaT*tanh(par[1]*deltaT/(0.172346648*t)); // Delta(T)/Delta(0)*tanh(Delta(T)/2 kB T), kB in meV/K