From 78fa497de6437b7fe9990254512651dcb61d94bf Mon Sep 17 00:00:00 2001 From: Suter Andreas Date: Tue, 28 Oct 2014 10:43:43 +0100 Subject: [PATCH] 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. --- ChangeLog | 14 +- .../BMWlibs/test-libGapIntegrals-ASCII.msr | 21 +-- src/external/libGapIntegrals/GapIntegrals.pdf | Bin 172409 -> 174295 bytes src/external/libGapIntegrals/GapIntegrals.tex | 30 ++-- .../libGapIntegrals/TGapIntegrals.cpp | 130 ++++++++++-------- 5 files changed, 112 insertions(+), 83 deletions(-) diff --git a/ChangeLog b/ChangeLog index e4e38f6c..9f60fc6f 100644 --- a/ChangeLog +++ b/ChangeLog @@ -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 diff --git a/doc/examples/BMWlibs/test-libGapIntegrals-ASCII.msr b/doc/examples/BMWlibs/test-libGapIntegrals-ASCII.msr index e126d80d..c6e714ca 100644 --- a/doc/examples/BMWlibs/test-libGapIntegrals-ASCII.msr +++ b/doc/examples/BMWlibs/test-libGapIntegrals-ASCII.msr @@ -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 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a/src/external/libGapIntegrals/GapIntegrals.tex b/src/external/libGapIntegrals/GapIntegrals.tex index 57f8bf4d..5d9761c0 100644 --- a/src/external/libGapIntegrals/GapIntegrals.tex +++ b/src/external/libGapIntegrals/GapIntegrals.tex @@ -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: diff --git a/src/external/libGapIntegrals/TGapIntegrals.cpp b/src/external/libGapIntegrals/TGapIntegrals.cpp index 5bc09e0d..102fd02b 100644 --- a/src/external/libGapIntegrals/TGapIntegrals.cpp +++ b/src/external/libGapIntegrals/TGapIntegrals.cpp @@ -460,12 +460,9 @@ 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)] - // 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 &par) const { vector 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 &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)] - // 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 &par) const { double ds; vector 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 &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)] - - 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 &par) const { double ds; vector 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 &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)] - - 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 &par) const { double ds; vector 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 &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)] - - 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 &par) const { double ds; vector 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 &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)] - - 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 &par) const { double ds; vector 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 &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)] - - 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 &par) const { double ds; vector 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 &par) const { */ double TGapDirtySWave::operator()(double t, const vector &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 }