Angle-resolved photoemission spectroscopy (ARPES) is a direct experimental technique to observe a distribution of the electrons (more precisely, the density of single-particle electronic excitations) in a reciprocal space. The technique is a refinement of ordinary photoemission spectroscopy, studying emission of electrons from a sample achieved usually by illumination with soft X-rays. ARPES provides information about a location of energy bands at different values of k-points relative to the Fermi level.

Steps to get the ARPES with the AMULET package

There are several steps to obtain the ARPES:

  • As a start point one needs to have two Hamiltonian files: one of them is an ordinary file to perform self-consistent calculations, other file is the Hamiltonian along high-symmetry directions of the Brillouin zone (BZ) for ARPES.
  • Perform the DFT+DMFT calculations to get a self-energy.
  • Make an analytical continuation of the self-energy to a real energy using the Pade approximation algorithm (described in other tutorial).
  • Perform the ARPES calculation by using the high-symmetry Hamiltonian and the self-energy on the real energy.

DFT+DMFT calculations of ARPES

To make DFT+DMFT calculations one needs a standard initial set of files: hamilt.amamulet.ini and impurity 1.ini. The Hamiltonian file should be prepared on the uniform k-mesh. The examples of the AMULET input files are presented below for a Phosphoren system.

The amulet.ini file is:

Beta = 20
Iwmax = 750
L = 200
rhtm = ESPRESSO ! Sets an order of real harmonics as in Quantum Espresso niter = 7 ntotal = 12

And the impurity 1.ini file may looks like:

name = P
nlm = 3
n_imp = 4
himppos = 1 4 7 10 U = 8.0 J = 0.0 DC_type = SFLL
solver = ct-qmc-w nqmc = 25000 nlegendre = 35

Then one needs to carry out the DFT+DMFT calculation until self-consistency will be reached. As a result of the this calculation the orbital resolved self-energies on the imaginary Matsubara axis will be stored in Sigma 1 1,1.dat, Sigma 1 2,2.dat, Sigma 1 3,3.dat files. The next step is to make an analytical continuation of the self-energies to the real energy axis, which is a subject of other tutorial and it is not considered here. As an output of the analytical continuation you will have the self-energies on the real energy and they should be converted to the AMULET format. For this purpose one needs to use the bash script which will produce sigma_re_1 file.

Now we are ready for the ARPES calculation. For this purpose one needs to do two things.

First, to modify slightly the amulet.ini file by adding a value of the chemical potential, m, from the last DMFT iteration.

mu = 1.46

Second, you should use the Hamiltonian file along the high-symmetry directions. You can do above steps by creating a new directory ARPES and copying there all *.ini, sigma_re_1 and "symmetric" files.

Now you can run the akw program, which will produce Akw_total.dat, Akw_1_N,N.dat and arpes.gpi. To obtaine the conventional ARPES image the arpes.gpi file should be modified to tune a color palette, energy axis range and coordinates of the high-symmetry point ticks. The example of the modified files is presented below:

set terminal postscript color enhanced
set output ''
set pm3d map
set nokey
set palette model RGB
set zeroaxis
set palette defined (0 0.098 0.098 0.439, 1 0 0.75 1, \ 2 0 1 0, 3 1 1 0, 4 0.557 0.42 0.137, 5 1 1 1) set xtics( "{/Symbol G}" 0.0, \ "Z" 1.2,\ "T" 1.7,\ "Y" 2.4,\ "G" 2.9,\ "X" 4.5,\ "S" 5.0,\ "R" 6.2 ) set grid xtics set xrange [0:6.61] set yrange [-5.0:5.0]
set cbrange [0:5]
splot 'Akw_total.dat' u 1:2:3

The execution of the gnuplot arpes.gpi command will give the figure below.

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