exercise 05 :: Fermi surface, projected density of states, band structure and electron density of FCC Cu

The aim of the following exercise is demonstrate calculation of the Fermi surface, projected density of states (PDOS), band structure and electron density for Cu FCC crystal. For DFT calculations assume lattice constant of 3.597 Angstrom, for pseudopotential use Cu.pbe-dn-kjpaw_psl.1.0.0.UPF with the energy cutoff ecutoff = 45 and for the kinetic energy cutoff for charge density and potential ecutrho = 240.

TASK 01

Fermi surface calculation:

1. perform calculation = 'scf' using pw.x program. Set the ? in the following input file. Be aware of units for celldm(1) parameter.

    &control
    title = 'fcc Cu'
    calculation = 'scf'
    restart_mode = 'from_scratch',
    pseudo_dir = './',
    outdir = './tmp',
    prefix = 'cu'
    tprnfor = .true.
    tstress = .true.
    /
    &system
    ibrav = 2, celldm(1) = ?, nat = 1, ntyp = 1,
    ecutwfc = ?, ecutrho = ?, occupations = 'smearing',
    smearing = 'marzari-vanderbilt', degauss = 0.01
    /
    &electrons
    startingpot = 'file'
    conv_thr = 1.D-7
    diagonalization = 'david'
    mixing_beta = 0.7
    /
    ATOMIC_SPECIES
    Cu  63.546 Cu.pbe-dn-kjpaw_psl.1.0.0.UPF
    ATOMIC_POSITIONS
    Cu 0.0 0.0 0.0
    K_POINTS (automatic)
       10 10 10   0 0 0
   

Find Fermi energy in the output file, e.g., grep Fermi out.pw-scf.

2. perform calculation = 'nscf', i.e., non-selfconsistent calculations for

   K_POINTS (automatic)  
    30 30 30  0 0 0
   

3. Download c2x program and run it to extract the Fermi surface
   ./c2x --bxsf tmp/cu.xml copper.bxsf
   To plot the Fermi surface use
   xcrysden --bxsf copper.bxsf

TASK 02

PDOS on particular atomic orbital can be written as follows

where the Bloch wave function is projected to an atomic orbital with a specific orbital momentum. For DOS and PDOS calculation we use tetrahedron method setting occupations = 'tetrahedra' (removing smearing and degauss) and perform non-selfconsistent calculations setting calculation = 'nscf' to obtain electronic density for further post-processing.

1. For total DOS calculation use the following input for dos.x program:

   &DOS
      prefix = 'cu'
      outdir = './tmp'
      bz_sum = 'tetrahedra'
      emin = 0.0
      emax = 25.0
      deltaE = 0.1
      fildos = 'K30_tetra_de0.1.dos'
   /
   

2. For PDOS calculations we will use projwfc.x program (see documentation for input parameters ). The input file projwfc.in is as follows:

    &projwfc
        prefix = 'cu',
        outdir = './tmp'
        filproj = 'pdos.proj'
     /
   

   To run the PDOS calculations invoke: projwfc.x < projwfc.in > out.projwfc_pdos.

3. To plot the DOS and PDOS you can use the following gnuplot script:

    set term x11
    set title "Density of states of FCC Al"
    set ylabel "DOS (1/eV)"
    set xlabel "E - E_F (eV)"
    set style fill noborder
    set style fill transparent solid 0.35 noborder
   
    EF=12.8277
   
    set key right
    set grid
   
    p [-10:10] \
      'K30_tetra_de0.1.dos' u ($1-EF):2 t"total" w l lt 1 lw 2,\
      'cu.pdos_atm#1(Cu)_wfc#3(d)' u ($1-EF):2 t"d-orbital" w filledcurves lc rgb "forest-green",\
      'cu.pdos_atm#1(Cu)_wfc#2(p)' u ($1-EF):2 t"p-orbital" w l lt 3 lw 2,\
      'cu.pdos_atm#1(Cu)_wfc#1(s)' u ($1-EF):2 t"s-orbital" w l lt 2 lw 2
   

TASK 03

Band structure calculations for the FCC Cu is similar to previous exercise 04 resulting in the following plot:

TASK 04

Electron density plot can be performed using pp.x < edp.in where the input file is as follows:

 &inputpp
    prefix  = 'cu'
    outdir='./tmp/',
    filplot = 'tmp.pp'
    plot_num = 0,
 /
 &plot
   nfile=1
   filepp(1)='tmp.pp', weight(1)=1.0
   iflag=3
   output_format=3
   e1(1)=1.0, e1(2)=0.0, e1(3)=0.0
   e2(1)=0.0, e2(2)=1.0, e2(3)=0.0
   e3(1)=0.0, e3(2)=0.0, e3(3)=1.0
   x0(1)=0.0, x0(2)=0.0, x0(3)=0.0
   nx=50, ny=50, nz=50
   fileout='edp_3d.xsf'
 /

The resulting electron density plot stored in the edp_3d.xsf can be plot by XCrysDen or VESTA program:

---

Martin Gmitra :: martin.gmitra@upjs.sk
This work is licensed under a Creative Commons Attribution 4.0 International License.