Add projectability-disentangled Wannier functions

.gitignore

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 *~
 *.x.dSYM
 .vscode
+*.mod

.markdownlint.yaml

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+# MD046/code-block-style : https://github.com/DavidAnson/markdownlint/blob/v0.33.0/doc/md046.md
+# for code blocks in list https://github.com/DavidAnson/markdownlint/issues/327
+MD046:
+  style: fenced

docs/docs/tutorials/tutorial_34.md

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+# 34: Graphene — Projectability-disentangled Wannier functions
+
+## Outline
+
+Obtain MLWFs for graphene using projectability disentanglement.
+For more details on the methodology, see Ref.[@Qiao2023-pdwf].
+
+## Input files
+<!-- markdownlint-disable code-block-style -->
+
+- Directory: [`tutorial/tutorial34/`](https://github.com/wannier-developers/wannier90/tree/develop/tutorials/tutorial34)
+
+- `graphene.scf` The `pw.x` input file for ground state calculation
+
+    ??? quote "graphene.scf"
+
+        ```fortran linenums="1" title="Input file"
+        --8<-- "tutorials/tutorial34/graphene.scf"
+        ```
+
+- `graphene.bands` The `pw.x` input file for band structure calculation
+
+    ??? quote "graphene.bands"
+
+        ```fortran linenums="1" title="Input file"
+        --8<-- "tutorials/tutorial34/graphene.bands::48"
+        ...
+        ...
+        ```
+
+- `graphene.bandsx` The `bands.x` input file for extracting band structure
+    eigenvalues
+
+    ??? quote "graphene.bandsx"
+
+        ```fortran linenums="1" title="Input file"
+        --8<-- "tutorials/tutorial34/graphene.bandsx"
+        ```
+
+- `graphene.projwfc` The `projwfc.x` input file for projectability calculation
+
+    ??? quote "graphene.projwfc"
+
+        ```fortran linenums="1" title="Input file"
+        --8<-- "tutorials/tutorial34/graphene.projwfc"
+        ```
+
+- `graphene.plotband` The `plotband.x` input file for plotting
+    band structure
+
+    ??? quote "graphene.plotband"
+
+        ```fortran linenums="1" title="Input file"
+        --8<-- "tutorials/tutorial34/graphene.plotband"
+        ```
+
+- `graphene.nscf` The `pw.x` input file to obtain Bloch states on a
+    uniform grid
+
+    ??? quote "graphene.nscf"
+
+        ```fortran linenums="1" title="Input file"
+        --8<-- "tutorials/tutorial34/graphene.nscf::48"
+        ...
+        ...
+        ```
+
+- `graphene.pw2wan` Input file for `pw2wannier90.x`
+
+    ??? quote "graphene.pw2wan"
+
+        ```fortran linenums="1" title="Input file"
+        --8<-- "tutorials/tutorial34/graphene.pw2wan"
+        ```
+
+- `graphene.win` The `wannier90.x` input file
+
+    ??? quote "graphene.win"
+
+        ```fortran linenums="1" title="Input file"
+        --8<-- "tutorials/tutorial34/graphene.win::55"
+        ...
+        ...
+        ```
+
+- `graphene_bandsdiff.gnu` The gnuplot script to compare DFT and Wannier bands
+
+    ??? quote "graphene_bandsdiff.gnu"
+
+        ```gnuplot linenums="1" title="Gnuplot script"
+        --8<-- "tutorials/tutorial34/graphene_bandsdiff.gnu"
+        ```
+
+## Steps
+
+1. Run `pw.x` to obtain the ground state of graphene
+
+    ```bash title="Terminal"
+    pw.x < graphene.scf > scf.out
+    ```
+
+2. Run `pw.x` to obtain the band structure of graphene
+
+    ```bash title="Terminal"
+    pw.x < graphene.bands > bands.out
+    ```
+
+3. Run `projwfc.x` to obtain the band structure projectability of graphene
+
+    ```bash title="Terminal"
+    projwfc.x < graphene.projwfc > projwfc.out
+    ```
+
+4. Run `bands.x` to obtain a `graphene.bands.dat` file containing the
+    band structure of graphene
+
+    ```bash title="Terminal"
+    bands.x < graphene.bandsx > bandsx.out
+    ```
+
+5. Run `plotband.x` to plot the band structure with projectability for
+    graphene
+
+    !!! note
+
+        Run `plotband.x` interactively to see the meaning of each line in the
+        input file.
+
+    1. First rename file so that it can be recognized by `plotband.x`
+
+        ```bash title="Terminal"
+        mv graphene.bands.dat.proj.projwfc_up graphene.bands.dat.proj
+        ```
+
+    2. Run `plotband.x`
+
+        ```bash title="Terminal"
+        plotband.x < graphene.plotband > plotband.out
+        ```
+
+    3. Generate a `graphene.projbands.gnu_projected.ps` file
+
+        ```bash title="Terminal"
+        gnuplot graphene.projbands.gnu
+        ```
+
+    4. Generate a `graphene.projbands.gnu_projected.pdf` file, see the following
+        Fig. [Projected bands](#fig:graphene_projbands)
+
+        ```bash title="Terminal"
+        ps2pdf graphene.projbands.gnu_projected.ps
+        ```
+
+        <figure markdown="span" id="fig:graphene_projbands">
+        ![Projected bands](./graphene_projbands.webp){width="500"}
+        <figcaption markdown="span">Band structure of graphene with projectability.
+        </figcaption>
+        </figure>
+
+6. Run `pw.x` to obtain the Bloch states on a uniform k-point grid
+
+    ```bash title="Terminal"
+    pw.x < graphene.nscf > nscf.out
+    ```
+
+7. Run `pw.x` to generate a list of the required overlaps (written into the
+    `graphene.nnkp` file).
+
+    !!! note
+
+        See `win` input file, no need to specify initial projections,
+        they are automatically chosen from the pseudo-atomic orbitals inside
+        pseudopotentials used in the scf calculation.
+
+    ```bash title="Terminal"
+    wannier90.x -pp graphene
+    ```
+
+8. Run `pw2wannier90.x` to compute the overlap between Bloch states and
+    the projections for the starting guess (written in the
+    `graphene.mmn` and `graphene.amn` files).
+
+    ```bash title="Terminal"
+    pw2wannier90.x < graphene.pw2wan > pw2wan.out
+    ```
+
+9. Run  to compute the MLWFs.
+
+    ```bash title="Terminal"
+    wannier90.x graphene
+    ```
+
+10. Run `gnuplot` to compare DFT and Wannier-interpolated bands, this
+    will generate a PDF file `graphene_bandsdiff.pdf`, see the following
+    Fig. [Bands comparison](#fig:graphene_bandsdiff).
+
+    ```bash title="Terminal"
+    ./graphene_bandsdiff.gnu
+    ```
+
+    Notice that high-projectability states in the conduction region are
+    properly reproduced. Try commenting out the
+    `dis_froz_proj, dis_proj_max/min` lines in the `win` input file, and
+    use the energy disentanglement `dis_froz_max/min`, and compare the
+    band interpolations.
+
+    <figure markdown="span" id="fig:graphene_bandsdiff">
+    ![Bands diff](./graphene_bandsdiff.webp){width="500"}
+    <figcaption markdown="span">Comparison of DFT and Wannier bands.
+    </figcaption>
+    </figure>
+
+11. (Optional) Clean up all output files
+
+    ```bash title="Terminal"
+    make clean
+    ```