What is it?
Issues and Comments
EliashMEM is a
program to extract the Eliashberg function directly from the
photoemission data. Basically, it takes input from the high resolution
photoemission measurement, and unfolds the Eliashberg function for the
electron-phonon (or other bosonic modes) coupling by fitting to the
quasi-particle dispersion. The Maximum Entropy Method (MEM) is employed
to overcome the numerical instability for a direct inversion.
This work is a collaborative effort involving researchers from a number
of institutions: Junren Shi
(Oak Ridge National Lab), S.-J. Tang (University of Tennessee),
Biao Wu (University of
Texas at Austin and ORNL),
Sprunger (Louisiana State University),
W. L. Yang,
V. Brouet (Stanford University and Advanced Light Source of LNBL),
J. Zhou (Stanford University),
Hussain (Advanced Light Source),
and E. W.
Plummer (University of Tennessee and ORNL).
The details of the technique can be found in
Phys. Rev. Lett. 92, 186401 (2004).
provide an overview to the technique.
The related paper:
Multiple Fine Structures in Electron Self-Energy of La2-xSrxCuO4,''
X. J. Zhou, Junren Shi, T. Yoshida, T. Cuk, W.L. Yang, V. Brouet,
J. Nakamura, N. Mannella, S. Komiya, Y. Ando, F. Zhou, W. X. Ti, J. W.
Xiong, Z. X. Zhao, T. Sasagawa, T. Kakeshita, H. Eisaki, S. Uchida, A.
Fujimori, Zhenyu Zhang, E. W. Plummer, R. B. Laughlin, Z. Hussain, and
Z.-X. Shen, submitted to Phys. Rev. Lett.
The source can
be downloaded here.
To compile, it needs a
compiler as well as two numerical libraries:
To install, first unpack the package:
tar xvzf MEM.tgz
to accommodate the settings of your system, and type
The executable is called
directory includes a sample data set (dispersion.txt),
which happens to be the data presented in the
and the corresponding configuration file (CONF3.INI).
To analysis the data, run the command in the
The program reads input from a couple of
input files and generate results to a number of output files.
program reads two input files. First is the dispersion data file from
the experimental measurement. It is in simple text format with two
columns: first column is the initial state energy in the unit of eV; the
second column is the momentum in arbitrary unit. Note that the program
only utilizes the data with energy below the Fermi energy.
The second input file is CONF3.INI. It contains various parameters
controlling the behavior of the program (the essential parameters are
denoted by red row numbers):
Data File Name
The filename of
the input dispersion data
Model File Name
The program may
be supplied with a constraint function. The file is in simple text
format with first column being the photon energy (£s) in meV and
second column being the constraint function m(£s). The total number
of rows should be NA. If it is set to "NONE", the program uses the
simple constraint function described in the
The prefix for
the output files. For instance, setting the field to "Be1010", the
output files will be "Be1010_SPT.dat", "Be1010_DAT.dat" ...
number of rows of the input dispersion data file
number of interpolation points for the output Eliashberg function.
If the constraint function is provided, it should be the total
number of rows of that file.
The high energy
tail of the dispersion data is usually too noisy. This parameter
supplies a cutoff energy (in eV) and only the data points below this
energy are utilized in the MEM fitting.
used. Always set it to zero.
particle dispersion is modeled as: £`0(k)=A1(k-kF)+A2(k-kF)2.
This is the first parameter.
parameter for the bare particle dispersion.
The position of
the Fermi energy (in eV).
The position of
the Fermi wave vector, in arbitrary unit.
the error bars of the real part of self-energy data (£mi)
the error bars for the real part of self energy data (determined
from the dispersion) are calculated by ERRB0+ERRB1*(E-EF);
the error bars are determined automatically from the data noise
and each data point may have different error bar;
same as ERRB0<0 except the resulting error bars are averaged and
all data points are assigned with the same averaged error bar.
parameter for the error bar determination
multiplier a with no
this comprehensive review by M. Jarrell for the details of the
iteration number for the MEM fitting. 1000 is usually sufficient.
In rare cases when the fitting is not converging, set it to a larger
number. (A non-converging MEM fitting will give rise a Eliashberg
with lot of artifacts).
the setting of Method parameter:
maximum value of the multiplier a
from which the iteration starts -- set it to a large number
- the value
of the multiplier a
when using the Bryan's method (Method=3): step length for the
iteration of a.
when using the historic method (Method=1): the target £q2
for the constraint function (See Eq. 6 of
parameter for the constraint function: £sm. It also set
the maximum photon frequency above which the Eliashberg function
parameter for the constraint function: m0
for calculating the average <£s£]>
the £s-axis to a NBin bins and the program calculates <£s£]>
for each bin.
It is followed by NBin+1 numbers that specify start and end points
of each bin.
- ND: the
number of data points utilized in the MEM fitting
the average error bar of the real part of self-energy
- CHI^2: the
mean deviation of the final fitting: £q2
- ALPHA: final
value of a.
- LAMBDA: the
mass enhancement factor calculated
error bar of the determined mass enhancement factor
- OMEGALOG: the
average phonon frequency that appears in Eliashberg's Tc formula.
All output files
start with [Output Prefix] that is supplied in CONF3.INI file:
Prefix].LOG: includes various information for the fitting.
Prefix]_SPT.dat: the Eliashberg function: column 1: £s (meV); 2:
Eliashberg function; 3: constraint function
Prefix]_DAT.dat: Self energy data and fitting. column 1: initial state
energy (meV); 2: real part of self energy data (meV); 3: error bars (meV);
4: fitting to the real part of self-energy (meV); 5: calculated
imaginary part of self-energy (meV).
Dispersion data and fitting: column 1: initial state energy data (eV);
2: momentum data; 3: fitting to the momentum data; 4: calculated
imaginary part of self-energy (eV); 5: calculated photoemission peak
Unfortunately, the program is not fully automated. It still needs
inputs of human being to get proper settings of parameters. The most
important parameters are A0 and A1, which determine the bare particle
dispersion through £`0(k)=A1(k-kF)+A2(k-kF)2.
Fortunately, it is not too difficult to get a reasonable set of values
for them by following the proper working procedure. It is hopeful the
procedure will be automated in the future.
The working environment should include a easy-to use plotting software,
e.g. gnuplot for Linux or
Unix-like systems, so that the fitting quality can be constantly
contact me (firstname.lastname@example.org) for questions, comments and
program is released in hopes that it will be useful for other
researchers. We can not be responsible for any consequence incurred by
this program, neither will we claim credit for the results obtained from
It is distributed under the terms of the
GNU General Public