mat-edi-mobility

Files (20)

• SKILL.md
• README.md · examples/mos2-s-vacancy/
• mos2_monolayer.cif · examples/mos2-s-vacancy/
• reference_mos2_transport.dat · examples/mos2-s-vacancy/
• edi_direct.in · resources/inputs/
• edi_setup.in · resources/inputs/
• edi_transport.in · resources/inputs/
• extract_pot.in · resources/inputs/
• kf.dat · resources/inputs/
• ki.dat · resources/inputs/
• nscf_primitive.in · resources/inputs/
• scf_defect_super.in · resources/inputs/
• scf_primitive.in · resources/inputs/
• scf_pristine_super.in · resources/inputs/
• compare_edmat.py · scripts/
• compare_reference.py · scripts/
• gen_kgrid.py · scripts/
• parse_edmat.py · scripts/
• parse_inv_tau.py · scripts/
• parse_transport.py · scripts/

SKILL.md (first lines)

# mat-edi-mobility

## Goal
To compute the point-defect-limited carrier mobility $\mu(T)$ of a semiconductor
and the underlying electron-defect scattering matrix elements
$M(\mathbf{k}_i, \mathbf{k}_f) = \langle \psi_{\mathbf{k}_i} | \Delta V | \psi_{\mathbf{k}_f} \rangle$
from first principles, using the supercell difference-potential method of the
Quantum ESPRESSO + EDI pipeline. Here $\Delta V = V_{\text{defect}} - V_{\text{pristine}}$
is the Kohn-Sham perturbation potential of an isolated point defect, extracted as
the difference between the potentials of a defect-containing supercell and a
pristine supercell. The matrix elements are computed on a coarse k-grid,
transformed to a maximally localized Wannier basis $M(\mathbf{R}, \mathbf{R}')$,
and interpolated onto dense fine grids. The state-resolved scattering rate follows
from Fermi's golden rule,

$$\frac{1}{\tau_{n\mathbf{k}}} = \frac{2\pi}{\hbar}\, n_{\text{d}}\, \frac{1}{N_{\mathbf{k}}} \sum_{m,\mathbf{k}'} |M_{n\mathbf{k}, m\mathbf{k}'}|^2\, \delta(\varepsilon_{n\mathbf{k}} - \varepsilon_{m\mathbf{k}'}),$$

and the mobility from the linearized Boltzmann transport equation in the
self-energy (SERTA) and momentum (MRTA) relaxation-time approximations. The three
first-class outputs are the **direct** matrix elements $M$ on the coarse grid, the
**Wannier-interpolated** $M$ on a fine k-path, and the final mobility $\mu(T)$.

## Background
Defect-limited transport requires $M(\mathbf{k}_i, \mathbf{k}_f)$ on k-grids far
denser than any tractable supercell calculation can supply. EDI solves this the
way EPW solves the electron-phonon problem: compute $M$ directly on a coarse grid
commensurate with the supercell, rotate into a Wannier basis where
$M(\mathbf{R}, \mathbf{R}')$ decays rapidly with $|\mathbf{R}|$ and $|\mathbf{R}'|$,
and interpolate to $300\times300$ or denser at negligible cost. The scattering
rate scales linearly with the defect concentration $n_{\text{d}}$ (dilute,
incoherent-defect limit), so **the mobility scales as $1/n_{\text{d}}$ and the
concentration must always be reported alongside $\mu$**. For 2D materials the
pristine and defect supercells are computed independently, so their electrostatic
potentials carry an arbitrary offset that must be removed by vacuum-level
alignment (`pot_align = 'vacuum'`).

This skill is the defect-scattering companion to
[mat-epw-mobility](../mat-epw-mobility/SKILL.md), which computes the
*phonon*-limited mobility. At finite temperature the two channels combine by
Matthiessen's rule, $1/\mu_{\text{total}} = 1/\mu_{\text{phonon}} + 1/\mu_{\text{defect}}$.
Defect *energetics* (formation energies, charge states) that set which defects
dominate come from
[mat-defect-energy](../mat-defect-energy/SKILL.md); the AMSET route in
[mat-dft-electronic-transport](../mat-dft-electronic-transport/SKILL.md) is an
alternative phonon-limited channel.

### External binary: building Quantum ESPRESSO 7.5 + EDI
EDI is an **in-tree plugin** of Quantum ESPRESSO, not a standalone code: it links
QE's compiled static libraries and must be built against a matching QE version.

1. Obtain QE 7.5 (GitLab tag archive; no ReleasePack is required —
   `make w90` auto-fetches the pinned Wannier90 submodule even from a tarball) and
   configure it.
2. Clone EDI into the QE root and build:

   ```bash
   # Requires: Quantum ESPRESSO 7.5 + EDI (external MPI build)
   cd <QE-root>
   make pw
   make w90
   git clone https://github.com/yuanyue-liu-group/EDI edi-code
   cd edi-code && make
   ```

   This produces `src/edi.x` (MPI) and `src/extract_pot.x` (serial).
3. **gfortran patch (required for GCC builds):** `ed_coarse.f90` contains lines up
   to 158 characters, so add long-line support to `edi-code/src/makefile` after the
   `include` line:

   ```make
   F90FLAGS += -ffree-line-length-none
   FFLAGS   += -ffree-line-length-none
   ```

4. **`extract_pot.x` segfault patch (required):** `extract_pot.f90` calls
   `clean_pw(.TRUE.)` at line 77, before any `read_file`, which segfaults on a
   fresh process. Comment it out (or delete that line) and rebuild:

   ```fortran
   ! CALL clean_pw(.TRUE.)   ! upstream bug: runs before any read_file, segfaults
   ```

Pseudopotentials for the worked example are PseudoDojo NC-SR v0.5 PBE **stringent**
(`https://www.pseudo-dojo.org/pseudos/nc-sr-05_pbe_stringent_upf.tgz`); the Mo and
S UPFs are used as `Mo.upf` and `S.upf`. QE 7.5 must be built with Wannier90.

## Instructions

> [!IMPORTANT]
> Quantum ESPRESSO (`pw.x`) and EDI (`edi.x`, `extract_pot.x`) are external
> compiled MPI binaries, exactly as VASP is in
> [mat-dft-vasp](../mat-dft-vasp/SKILL.md). This skill targets a source build of
> **QE 7.5 + EDI v2.0** (repo `main` @ `41fed72`) with **PseudoDojo NC-SR v0.5 PBE stringent**
> 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/). Replace `<ranks>` with your MPI rank
> count; `mpirun -np` and `srun -n` are interchangeable. Set `pseudo_dir` in each
> deck to your UPF directory (the decks use `./pseudo/`).

The pipeline is a DAG. The two supercell SCFs (step 3) are independent of the
primitive cell and of each other and can run in parallel. Steps 5 and 6 must run
in order (6 reads the Wannier archive written by 5).

### 1. Primitive-cell SCF
Compute the ground-state charge density of the pristine primitive cell.
`assume_isolated = '2D'` truncates the out-of-plane Coulomb tail and **must** be
consistent across every calculation. Deck:
[`resources/inputs/scf_primitive.in`](resources/inputs/scf_primitive.in).

```bash
# Requires: Quantum ESPRESSO 7.5 + EDI (external MPI build)
mpirun -np <ranks> pw.x -nk <pools> < scf_primitive.in > scf_primitive.out
```

Confirm `convergence has been achieved`.

### 2. Primitive-cell NSCF on the explicit coarse grid
Produce the Bloch states EDI folds into Wannier functions. The grid **must be an
explicit `K_POINTS crystal` list** (never `automatic`) and its dimensions **must

From learningmatter-mit/AtomisticSkills, MIT.

More from learningmatter-mit/AtomisticSkills