mat-epw-mobility

Files (16)

• SKILL.md
• README.md · examples/zrs2-monolayer/
• zrs2_monolayer.cif · examples/zrs2-monolayer/
• epw_mob.in · resources/inputs/
• epw_prtgkk.in · resources/inputs/
• epw_write.in · resources/inputs/
• nscf.in · resources/inputs/
• ph_gamma.in · resources/inputs/
• ph_single_q.in · resources/inputs/
• ph_uniform.in · resources/inputs/
• scf.in · resources/inputs/
• compare_reference.py · scripts/
• gen_kpoints.py · scripts/
• parse_epw_prtgkk.py · scripts/
• parse_prt.py · scripts/
• parse_wout.py · scripts/

SKILL.md (first lines)

# mat-epw-mobility

## Goal
To compute the intrinsic phonon-limited carrier mobility $\mu(T)$ of a 2D
semiconductor in the Self-Energy Relaxation Time Approximation (SERTA), together
with the mode-resolved electron-phonon coupling matrix elements $|g(k, q, \nu)|$,
from first principles using the Quantum ESPRESSO + EPW pipeline. The route
interpolates the electron-phonon vertex onto dense fine grids via maximally
localized Wannier functions and applies the 2D Frohlich long-range kernel needed
for polar monolayers.

## Background
Carrier mobility limited by phonon scattering requires the electron-phonon
matrix elements $g_{mn\nu}(k, q)$ on grids far denser than any tractable DFPT
calculation. EPW solves this by computing $g$ on a coarse q-grid with DFPT,
transforming to a maximally localized Wannier basis, and interpolating to fine
k/q meshes. For 2D polar materials, the long-range Frohlich part of $g$ diverges
as $1/q$ near the zone centre and must be treated with a 2D-truncated Coulomb
kernel (`lpolar`, `system_2d`), otherwise $\mu$ collapses by a factor of ~3.

Unlike the DFT+AMSET route in
[mat-dft-electronic-transport](../mat-dft-electronic-transport/SKILL.md), which
uses a momentum-relaxation-time approximation on VASP band structures, this skill
computes the full first-principles electron-phonon vertex. It is complementary to
[mat-dft-electron-phonon](../mat-dft-electron-phonon/SKILL.md) (which targets
temperature-dependent bandgap renormalization) and to
[mat-phonon](../mat-phonon/SKILL.md) (MLIP phonons).

The pipeline is a DAG. Steps 3 and 5 are optional (a standalone dielectric check
and a DFPT $|g|$ benchmark); the transport path is 1 -> 2 -> 4 -> 6 -> 7 -> 9.

```
                       1 SCF
           +-------------+--------------+
           v             v              v
      3 DFPT-Gamma   4 DFPT          2 NSCF
      (eps_inf, Z*)  uniform-q       (explicit k)
      (optional)         |               |
                         v               |
                    6 pp.py gather       |
                         |    \          |
                         |     v         v
                         |   7 Wannierize
                         |     |     |
                         v     v     v
                    9 EPW    8 EPW  (8 also <- 5 DFPT single-q
                    SERTA    prtgkk      benchmark, optional)
                    mu(T)    |g|
```

The worked example below runs the whole pipeline end-to-end on a ZrS2 monolayer
and validates EPW-interpolated $|g|$ against the DFPT reference to 0.05% on the
gauge-invariant sum.

## Instructions

> [!IMPORTANT]
> Quantum ESPRESSO (`pw.x`, `ph.x`) and EPW (`epw.x`, `pp.py`) are external
> compiled MPI binaries, exactly as VASP is in
> [mat-dft-vasp](../mat-dft-vasp/SKILL.md). This skill was validated on a source
> build of **QE 7.4.1 / EPW 5.8.1** with **ONCV SG15 PBE v1.2** pseudopotentials.
> The `venv/run cpu` commands apply only to the Python parser scripts.
> Reference input decks for every step are in
> [`resources/inputs/`](resources/inputs/).

### 1. Ground-state SCF
Compute the charge density and Kohn-Sham orbitals every later step consumes. For
2D materials, `assume_isolated = '2D'` truncates the out-of-plane Coulomb tail and
**must** be mirrored in `ph.x` and EPW. Use the deck
[`resources/inputs/scf.in`](resources/inputs/scf.in).

```bash
# Requires: Quantum ESPRESSO 7.4.1 (external MPI build)
mpirun -np <ranks> pw.x -in scf.in > scf.out
```

Confirm `convergence has been achieved`. For ZrS2 the total energy is
-136.1241 Ry and the VBM (HOMO) is -6.4435 eV.

### 2. NSCF on an explicit uniform k-grid
EPW folds Bloch orbitals on an **explicit** uniform k-grid into Wannier
functions. Use `K_POINTS crystal` with the full list, never `automatic` (any
compression desynchronises EPW's k-indexing). Generate the list and stage the
NSCF into its own `tmp/` so it does not overwrite the SCF save tree that DFPT
needs. Deck: [`resources/inputs/nscf.in`](resources/inputs/nscf.in).

```bash
${CLAUDE_SKILL_DIR}/../../venv/run cpu python ${CLAUDE_SKILL_DIR}/scripts/gen_kpoints.py 12 12 1
```

```bash
# Requires: Quantum ESPRESSO 7.4.1 (external MPI build)
mpirun -np <ranks> pw.x -in nscf.in > nscf.out
```

`nbnd` must cover the disentanglement window (30 for ZrS2 = 6 occupied + 24
empty). For ZrS2 the gap is 1.1724 eV (CBM -5.2711 eV).

### 3. (Optional) Gamma DFPT for dielectric tensor and Born charges
Compute $\varepsilon_\infty$ and Born effective charges $Z^*$ as a fast
standalone sanity check (EPW itself reads them from step 4's Gamma irrep). A
non-symmetric or non-positive-definite $\varepsilon_\infty$ signals an upstream
error. Deck: [`resources/inputs/ph_gamma.in`](resources/inputs/ph_gamma.in).

```bash
# Requires: Quantum ESPRESSO 7.4.1 (external MPI build)
mpirun -np <ranks> ph.x -in ph_gamma.in > ph_gamma.out
```

For ZrS2: $\varepsilon_\infty^{xx}$ = 2.973, $Z^*_{xx}(\mathrm{Zr})$ = +7.003.

### 4. DFPT on a coarse uniform q-grid
The dynamical matrices and self-consistent perturbation potentials (`dvscf`) EPW
interpolates from. This is the most expensive step; set `recover = .true.` so a
timeout only loses the in-progress q. `fildvscf` is **required** or EPW has no
long-range kernel data. `nq1/nq2/nq3` must match the coarse `nk*` EPW reads
later. Deck: [`resources/inputs/ph_uniform.in`](resources/inputs/ph_uniform.in).

```bash

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