Silicon Walkthrough (QE + LetzElPhC)

This tutorial provides a step-by-step walkthrough of the example located in examples/qe/silicon. We will compute the electron-phonon matrix elements for bulk Silicon.

Prerequisites

• Quantum Espresso (pw.x, ph.x)
• Yambo (p2y, yambo)
• LetzElPhC (lelphc)
• The Si.upf pseudopotential (included in the example directory).

Directory Structure

The example directory is organized as follows:

examples/qe/silicon/
├── Si.upf          # Pseudopotential
├── run.sh          # All-in-one script
├── scf/            # Step 1: SCF
├── ph/             # Step 2: Phonons
├── nscf/           # Step 3: NSCF & Yambo Setup
└── elph/           # Step 4: LetzElPhC Calculation

You can run the entire workflow using ./run.sh, but we will go through each step manually to understand the process.

---

Step 1: SCF Calculation

First, we perform a self-consistent field (SCF) calculation to obtain the ground state density.

Input: scf/scf.in

&CONTROL
  prefix = 'si'
  calculation = 'scf'
  ...
/
&SYSTEM
  ibrav = 0, nat = 2, ntyp = 1
  ecutwfc = 40.0
  ...
/
...
K_POINTS automatic
    4  4  4  0  0  0

Command:

cd scf
pw.x < scf.in > scf.out
cd ..

---

Step 2: Phonon Calculation

Next, we calculate the phonons and the deformation potentials (\(\delta V_{SCF}\)) on a uniform q-grid.

Input: ph/ph.in

&inputph 
  nq1 = 2, nq2 = 2, nq3 = 2,   ! 2x2x2 q-grid
  fildyn = 'si.dyn', 
  tr2_ph = 1e-12, 
  prefix = 'si', 
  fildvscf = 'dvscf',          ! Important: Save potential changes
  ldisp = .true., 
  reduce_io = .true.
/ 

Important Notes: * We use a 2x2x2 q-grid. * fildvscf is specified to save the potential variation files.

Command:

cd ph
cp -r ../scf/si.* .  # Copy SCF data
ph.x < ph.in > ph.out
cd ..

---

Step 3: NSCF Calculation & Yambo Setup

We need the electronic wavefunctions on a k-grid that is commensurate with our phonon q-grid.

Input: nscf/nscf.in

&CONTROL
  calculation = 'nscf'
  prefix = 'si'
  ...
/
&SYSTEM
  ...
  nbnd = 10                  ! Number of bands
  force_symmorphic = .true.  ! Crucial for Yambo compatibility
/
...
K_POINTS automatic
    4  4  4  0  0  0         ! 4x4x4 k-grid (commensurate with 2x2x2 q-grid)

Command:

cd nscf
cp -r ../scf/si.* .  # Copy SCF data
pw.x < nscf.in > nscf.out

Initialize Yambo Database

Once the NSCF run is complete, we enter the save directory and initialize the Yambo database.

cd si.save
p2y        # Convert QE data to Yambo format
yambo      # Initialize Yambo SAVE directory
cd ../..

---

Step 4: LetzElPhC Preprocessing

Before running the main calculation, we run the preprocessor in the phonon directory to organize the phonon data into a ph_save directory.

Command:

cd ph
lelphc -pp --code=qe -F ph.in
cd ..

This creates ph/ph_save.

---

Step 5: LetzElPhC Calculation

Finally, we compute the electron-phonon matrix elements.

Input: elph/elph.in

nkpool          = 1 
nqpool          = 1

start_bnd       = 2
end_bnd         = 6

save_dir        = ../nscf/si.save/SAVE   # Path to Yambo SAVE
ph_save_dir     = ../ph/ph_save          # Path to ph_save

kernel          = dfpt                   # Use full DFPT screening
convention      = standard               # <k+q|dV|k>

Command:

cd elph
lelphc -F elph.in

Output

The code will generate: * Standard output with progress information. * ndb.elph: The database containing the electron-phonon matrix elements (in LetzElPhC format). * If running with Yambopy or converting later, this can be transformed into Yambo's ndb.elph_gkkp databases.