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BMWlibs, calculation of superconducting gap functions: allow to choose between to different parameterization of the temperature dependence of the gap. For details see the memo in the source code.

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suter_a 2014-10-28 10:43:43 +01:00
parent a4c948db7f
commit 78fa497de6
5 changed files with 112 additions and 83 deletions
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ChangeLog
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@ -23,8 +23,8 @@ NEW 2012-11-19 added a flag in the Fourier block (dc-corrected) which can
be used to subtract a potential DC-offset before the Fourier
transform is carried out.
NEW 2012-10-25 (i) add PRINT_LEVEL to the command block (0='nothing' to
3='everything'). This allows to tune the Minuit2 output. (ii) added the
possibilty to give the fit range in bins. For details see the docu.
3='everything'). This allows to tune the Minuit2 output. (ii) added the
possibilty to give the fit range in bins. For details see the docu.
NEW 2012-09-24 add header information for printing.
NEW 2012-05-31 added Noakes-Kalvius function (see A. Yaouanc and P. Dalmas de Reotiers,
"Muon Spin Rotation, Relaxation, and Resonance" Oxford, Section 6.4.1.3).
@ -60,6 +60,10 @@ FIXED 2012-09-23 fixed wrong chisq output in musrview if expected chisq is
present.
FIXED 2012-05-30 fixed RRF bug in single histo plotting.
FIXED 2012-05-18 fixed wrong forward/backward tag for ROOT-PPC (MUSR-215)
CHANGED 2014-10-28 BMWlibs, calculation of superconducting gap functions:
allow to choose between to different parameterization of the
temperature dependence of the gap. For details see the memo
in the source code.
CHANGED 2014-10-25 updated docu, since git is now available for ALL users
CHANGED 2014-02-12 since we moved to git, I cleaned up the svn prop's from
the sources.
@ -67,8 +71,8 @@ CHANGED 2013-12-20 upgrade of cuba to version 3.2. Merge in from BMW
CHANGED 2013-12-16 prettyfied the Noakes-Kalvius formulae. Furthermore added
a sub-folder with cross checks for these formulae.
CHANGED 2013-11-12 changed normalization of log max likelihood according to S.
Backer and R.D. Cousins NIM 221, 437 (1984), in order to have a
"goodness-of-fit" criteria.
Backer and R.D. Cousins NIM 221, 437 (1984), in order to have a
"goodness-of-fit" criteria.
CHANGED 2012-12-11 if multiple SAVE are present in the COMMAND block, append
MINUIT2.OUTPUT file. Added docu for PRINT_LEVEL (MUSR-244).
CHANGED 2012-11-19 replaced hard coded gyromagnetic ratio of the muon in the
@ -78,7 +82,7 @@ CHANGED 2012-11-09 when converting to WKM, take the beamline tag to decide
CHANGED 2012-08-28 prevent LF from allocating too much memory
CHANGED 2012-06-29 changed handling of the timeout for musrfit.
CHANGED 2012-05-10 prevent any2many from overwriting an input file. At the
some additional bug fixing of any2many has be carried out.
some additional bug fixing of any2many has be carried out.
CHANGED 2012-05-08 updating docu
changes since 0.10.0

21
doc/examples/BMWlibs/test-libGapIntegrals-ASCII.msr
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@ -1,15 +1,16 @@
Test libGapIntegrals (arbitrary data), ASCII data file
Test superconductor data
###############################################################
FITPARAMETER
# Nr. Name Value Step Pos_Error Boundaries
1 lambdaInvSq0 12.7664 0.40786 none
2 Tc 15 0.0203235 none 0 2
3 Delta0 26 0.00576485 none
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
###############################################################
THEORY
asymmetry 1
userFcn libGapIntegrals TGapDWave 2 3
userFcn libGapIntegrals TGapSWave 2 3 4
###############################################################
#FUNCTIONS
@ -18,8 +19,8 @@ userFcn libGapIntegrals TGapDWave 2 3
RUN data/libGapIntegrals-test PIM3 PSI ASCII (name beamline institute data-file-format)
fittype 8 (non muSR fit)
map 0 0 0 0 0 0 0 0 0 0
xy-data 1 2
fit 0.00 10.00
xy-data 1 2
fit 0 10
packing 1
###############################################################
@ -32,8 +33,8 @@ SAVE
###############################################################
PLOT 8 (non muSR plot)
runs 1
range 0.00 20
range 0 1.5
###############################################################
STATISTIC --- 2010-01-08 13:54:19
chisq = 15.4862481, NDF = 8, chisq/NDF = 1.93578101
STATISTIC --- 2014-10-28 10:40:31
chisq = 14.3, NDF = 8, chisq/NDF = 1.790471

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src/external/libGapIntegrals/GapIntegrals.pdf vendored
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30
src/external/libGapIntegrals/GapIntegrals.tex vendored
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@ -61,9 +61,9 @@
\vskip 1cm
%
\begin{tabular}{@{\hspace{-0.5cm}}ll@{\hspace{4cm}}ll}
Date: & September 19, 2009 / August 19, 2014 & & \\[3ex]
Date: & \today & & \\[3ex]
From: & B.M.~Wojek / Modified by A. Suter & \\
E-Mail: & \verb?bastian.wojek@psi.ch? / \verb?andreas.suter@psi.ch? &&
E-Mail: & \verb?andreas.suter@psi.ch? &&
\end{tabular}
%
\vskip 0.3cm
@ -102,8 +102,9 @@ For the numerical integration we use algorithms of the \textsc{Cuba} library \ci
\end{equation}
\subsection*{Implemented gap functions and function calls from MUSRFIT}
At the moment the calculation of $\tilde{I}(T)$ is implemented for various gap functions all using the approximate \textsc{BCS} temperature dependence~\cite{Prozorov}
\begin{equation}\label{eq:gapT}
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}.
\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]
\end{equation}
\noindent with $\Delta_0$ as given below, and $a_{\rm G}$ depends on the pairing state:
@ -113,8 +114,7 @@ At the moment the calculation of $\tilde{I}(T)$ is implemented for various gap f
\item [\textit{d}-wave:] $a_{\rm G}=4/3$ \quad with $\Delta_0 = 2.14\, k_{\rm B} T_c$
\end{description}
\noindent Eq.(\ref{eq:gapT}) replaces the \emph{previously} used approximation~\cite{Manzano}:
\begin{equation}
\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)\,.
\end{equation}
The \gapint plug-in calculates $\tilde{I}(T)$ for the following $\Delta(\varphi)$:
@ -125,31 +125,36 @@ The \gapint plug-in calculates $\tilde{I}(T)$ for the following $\Delta(\varphi)
\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 not given, $a_{\rm G} = 1$)
(Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $[a_{\rm G}~(1)]$. If $a_{\rm G}$ is given, the temperature dependence
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 not given, $a_{\rm G} = 4/3$)
(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.)
\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 not given, $a_{\rm G} = 4/3$)
(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.)
\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 not given, $a_{\rm G} = 4/3$)
(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.)
\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 not given, $a_{\rm G} = 1$)
(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.)
\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.
@ -167,7 +172,8 @@ Obviously for this no integration is needed.
\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 not given, $a_{\rm G} = 1$)
(Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $[a_{\rm G}~(1)]$. If $a_{\rm G}$ is given, the temperature dependence
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:

130
src/external/libGapIntegrals/TGapIntegrals.cpp vendored
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@ -460,12 +460,9 @@ TLambdaInvNonMonDWave2::~TLambdaInvNonMonDWave2() {
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)]
// see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67
// 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
// and Erratum Supercond. Sci. Technol. 21 (2008) 082003
double aa = 1.0;
if (par.size() == 3)
aa = par[2];
if (t<=0.0)
return 1.0;
else if (t >= par[0])
@ -509,7 +506,11 @@ double TGapSWave::operator()(double t, const vector<double> &par) const {
vector<double> intPar; // parameters for the integral, T & Delta(T)
intPar.push_back(0.172346648*t); // 2 kB T, kB in meV/K = 0.086173324 meV/K
intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(aa*(par[0]/t-1.0)))); // tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K
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
}
fGapIntegral->SetParameters(intPar);
ds = 1.0-1.0/intPar[0]*fGapIntegral->IntegrateFunc(0.0, 2.0*(t+intPar[1]));
@ -536,12 +537,9 @@ double TGapSWave::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)]
// see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67
// 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
// and Erratum Supercond. Sci. Technol. 21 (2008) 082003
double aa = 4.0/3.0;
if (par.size() == 3)
aa = par[2];
if (t<=0.0)
return 1.0;
else if (t >= par[0])
@ -584,7 +582,11 @@ double TGapDWave::operator()(double t, const vector<double> &par) const {
double ds;
vector<double> intPar; // parameters for the integral, T & Delta(T)
intPar.push_back(0.172346648*t); // 2 kB T, kB in meV/K = 0.086173324 meV/K
intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(aa*(par[0]/t-1.0)))); // tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K
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(4.0*(t+intPar[1])); // upper limit of energy-integration: cutoff energy
intPar.push_back(TMath::PiOver2()); // upper limit of phi-integration
@ -617,14 +619,9 @@ double TGapDWave::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)]
double aD = 4.0/3.0;
double aS = 1.0;
if (par.size() == 5) {
aD = par[3];
aS = par[4];
}
// 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
if (t<=0.0)
return 1.0;
else if (t >= par[0])
@ -667,10 +664,18 @@ double TGapCosSqDWave::operator()(double t, const vector<double> &par) const {
double ds;
vector<double> intPar; // parameters for the integral, T & Delta(T)
intPar.push_back(0.172346648*t); // 2 kB T, kB in meV/K = 0.086173324 meV/K
intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(aD*(par[0]/t-1.0)))); // DeltaD(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K
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(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(par[2]*tanh(0.2707214816*par[0]/par[2]*sqrt(aS*(par[0]/t-1.0)))); // DeltaS(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K
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
}
// double xl[] = {0.0, 0.0}; // lower bound E, phi
// double xu[] = {4.0*(t+intPar[1]), 0.5*PI}; // upper bound E, phi
@ -701,14 +706,9 @@ double TGapCosSqDWave::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)]
double aD = 4.0/3.0;
double aS = 1.0;
if (par.size() == 5) {
aD = par[3];
aS = par[4];
}
// 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
if (t<=0.0)
return 1.0;
else if (t >= par[0])
@ -751,10 +751,18 @@ double TGapSinSqDWave::operator()(double t, const vector<double> &par) const {
double ds;
vector<double> intPar; // parameters for the integral, T & Delta(T)
intPar.push_back(0.172346648*t); // 2 kB T, kB in meV/K = 0.086173324 meV/K
intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(aD*(par[0]/t-1.0)))); // DeltaD(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K
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(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(par[2]*tanh(0.2707214816*par[0]/par[2]*sqrt(aS*(par[0]/t-1.0)))); // DeltaS(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K
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
}
// double xl[] = {0.0, 0.0}; // lower bound E, phi
// double xu[] = {4.0*(t+intPar[1]), 0.5*PI}; // upper bound E, phi
@ -785,12 +793,9 @@ double TGapSinSqDWave::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)]
double aS = 1.0;
if (par.size() == 4) {
aS = par[3];
}
// 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
// and Erratum Supercond. Sci. Technol. 21 (2008) 082003
if (t<=0.0)
return 1.0;
else if (t >= par[0])
@ -833,7 +838,11 @@ double TGapAnSWave::operator()(double t, const vector<double> &par) const {
double ds;
vector<double> intPar; // parameters for the integral, T & Delta(T)
intPar.push_back(0.172346648*t); // 2 kB T, kB in meV/K = 0.086173324 meV/K
intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(aS*(par[0]/t-1.0)))); // DeltaS(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K
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[2]);
intPar.push_back(4.0*(t+(1.0+par[2])*intPar[1])); // upper limit of energy-integration: cutoff energy
intPar.push_back(TMath::PiOver2()); // upper limit of phi-integration
@ -867,12 +876,9 @@ double TGapAnSWave::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)]
double aD = 4.0/3.0;
if (par.size() == 4) {
aD = par[3];
}
// 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
// and Erratum Supercond. Sci. Technol. 21 (2008) 082003
if (t<=0.0)
return 1.0;
else if (t >= par[0])
@ -915,7 +921,11 @@ double TGapNonMonDWave1::operator()(double t, const vector<double> &par) const {
double ds;
vector<double> intPar; // parameters for the integral: 2 k_B T, Delta(T), a, E_c, phi_c
intPar.push_back(0.172346648*t); // 2 kB T, kB in meV/K = 0.086173324 meV/K
intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(aD*(par[0]/t-1.0)))); // DeltaD(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K
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[2]);
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
@ -946,12 +956,9 @@ double TGapNonMonDWave1::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)]
double aD = 4.0/3.0;
if (par.size() == 4) {
aD = par[3];
}
// 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
// and Erratum Supercond. Sci. Technol. 21 (2008) 082003
if (t<=0.0)
return 1.0;
else if (t >= par[0])
@ -994,7 +1001,11 @@ double TGapNonMonDWave2::operator()(double t, const vector<double> &par) const {
double ds;
vector<double> intPar; // parameters for the integral: 2 k_B T, Delta(T), a, E_c, phi_c
intPar.push_back(0.172346648*t); // 2 kB T, kB in meV/K = 0.086173324 meV/K
intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(aD*(par[0]/t-1.0)))); // DeltaD(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K
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[2]);
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
@ -1045,14 +1056,21 @@ double TGapPowerLaw::operator()(double t, const vector<double> &par) const {
*/
double TGapDirtySWave::operator()(double t, const vector<double> &par) const {
assert(par.size() == 2); // two parameters: Tc (K), Delta(0) (meV)
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
// and Erratum Supercond. Sci. Technol. 21 (2008) 082003
if (t<=0.0)
return 1.0;
else if (t >= par[0])
return 0.0;
double deltaT(tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51)));
double deltaT = 0.0;
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
}
return deltaT*tanh(par[1]*deltaT/(0.172346648*t)); // Delta(T)/Delta(0)*tanh(Delta(T)/2 kB T), kB in meV/K
}