EXCEED-DMv1.0.0: Si and Ge Electronic Configurations

This dataset contains the electronic configuration files for Si and Ge targets for use with EXCEED-DMv1.0.0. These electronic configuration files were used to compute the DM-electron interaction rates in the EXCEED-DM user manual: [2210.14917] EXCEED-DM: Extended Calculation of Electronic Excitations for Direct Detection of Dark Matter (arxiv.org). A description of the data in the files is given on the documentation website: https://tanner-trickle.github.io/EXCEED-DM/. We repeat it below for convenience (note that :math:, :cite: environments are rendered in the documentation).

- File: Si/scatter/Si_scatter_elec_config.hdf5
- Description: 
    - Electronic states assumed to be spin-degenerate, i.e., one-component wave functions. Used for binned scattering rate and dielectric calculations.
    - Initial States: 
        - Modelled with a combination of STO basis states and PW basis states. STO basis is used for the low energy, "core" states, while PW basis is used for the valence states.
        - STO basis
            - 10 states (1 :math:`\mathbf{k}` point (:math:`\mathbf{k} = 0`), 10 bands). States are the electrons in the :math:`1s \rightarrow 2p` orbitals, for both Si in the unit cell. The sum over lattice vectors, :math:`\mathbf{r}` extends to cells :math:`\pm 1` away from the center, i.e., includes 27 cells in total. Each state is sampled on a :math:`128 \times 128 \times 128` uniform grid in the unit cell. STO basis coefficients, e.g., :math:`C_{j, l, n, \kappa}` are taken from the tabulated values `here `_. Energy of each state is taken from the Materials Project database, material ID mp-149.
            - Notes: The reason for the small number of :math:`\mathbf{k}` points is due to runtime considerations, one has to choose between a larger sampling grid, i.e., sample the high momentum contributions in the unit cell, or more :math:`\mathbf{k}` points. Since the main features of these states are at high momentum, this is prioritized.
        - PW basis
            - 4000 states (:math:`10 \times 10 \times 10 \, \mathbf{k}` points, 4 bands). Computed with DFT (VASP), see Ref. :cite:`Griffin:2021znd` for more details. Uniform sampling in the 1BZ. Each state was expanded to an :math:`E_\text{cut} = \text{keV}` and then all-electron reconstructed with :code:`pawpyseed` to :math:`E_\text{cut} = 2 \, \text{keV}`. Lowest energy state at :math:`-11.814 \, \text{eV}`.

    - Final States:
        - Modelled with a combination of **PW basis** and **single PW basis** states. **PW basis** is used for the lower energy "conduction" bands, **single PW basis** is used for higher energy states being approximated as "free".
        - PW basis
            - 60000 states (:math:`10 \times 10 \times 10 \, \mathbf{k}` points, 60 bands). Computed with DFT (VASP), see Ref. :cite:`Griffin:2021znd` for more details. Uniform sampling in the 1BZ. Each state was expanded to an :math:`E_\text{cut} = \text{keV}` and then all-electron reconstructed with :code:`pawpyseed` to :math:`E_\text{cut} = 2 \, \text{keV}`. Lowest energy state at :math:`1.11 \, \text{eV}`. All bands which have an :math:`E_{i \mathbf{k}} < 60 \, \text{eV}`, for any :math:`\mathbf{k}`, are included.
        - single PW basis
                - 40000 states (:math:`10 \times 10 \times 400` grid in :math:`(\theta, \phi, p)` space). Uniformly sampled on the sphere in :math:`(\theta, \phi)`, logarithmically sampled in :math:`E = p^2/2m_e` between :math:`E_\text{min} = 60 \, \text{eV}` and :math:`E_\text{max} = 400 \, \text{eV}`.

- File: Si/abs/Si_abs_elec_config.hdf5
- Description: 
        - Electronic states assumed to be spin-degenerate, i.e., one-component wave functions. Used for absorption rate calculations.
        - Initial States: 
            - Modelled with a combination of STO basis states and PW basis states. STO basis is used for the low energy, "core" states, while PW basis is used for the valence states.
            - STO basis
                - 10000 states (:math:`10 \times 10 \times 10 \, \mathbf{k}` points, 10 bands). States are the electrons in the :math:`1s \rightarrow 2p` orbitals, for both Si in the unit cell. :math:`\mathbf{k}` grid is uniformly sampled over the 1BZ. The sum over lattice vectors, :math:`\mathbf{r}` extends to cells :math:`\pm 1` away from the center, i.e., includes 27 cells in total. Each state is sampled on a :math:`128 \times 128 \times 128` uniform grid in the unit cell. STO basis coefficients, e.g., :math:`C_{j, l, n, \kappa}` are taken from the tabulated values `here `_. Energy of each state is taken from the Materials Project database, material ID mp-149.
                - Notes: A larger number of :math:`\mathbf{k}` vectors can, and must be, used here is because transitions must be vertical. This limits the number of transitions, relative to a scattering rate calculation.
            - PW basis
                - 4000 states (:math:`10 \times 10 \times 10 \, \mathbf{k}` points, 4 bands). Computed with DFT (VASP), see Ref. :cite:`Griffin:2021znd` for more details. Uniform sampling in the 1BZ. Each state was expanded to an :math:`E_\text{cut} = \text{keV}` and then all-electron reconstructed with :code:`pawpyseed` to :math:`E_\text{cut} = 2 \, \text{keV}`. Lowest energy state at :math:`-11.814 \, \text{eV}`.

        - Final States:
            - Modelled with a combination of PW basis and single PW basis states. PW basis is used for the lower energy "conduction" bands, single PW basis is used for higher energy states being approximated as "free".
            - PW basis
                - 60000 states (:math:`10 \times 10 \times 10 \, \mathbf{k}` points, 60 bands). Computed with DFT (VASP), see Ref. :cite:`Griffin:2021znd` for more details. Uniform sampling in the 1BZ. Each state was expanded to an :math:`E_\text{cut} = \text{keV}` and then all-electron reconstructed with :code:`pawpyseed` to :math:`E_\text{cut} = 2 \, \text{keV}`. Lowest energy state at :math:`1.11 \, \text{eV}`. All bands which have an :math:`E_{i \mathbf{k}} < 60 \, \text{eV}`, for any :math:`\mathbf{k}`, are included.
            - single PW basis
                - 2152000 states (:math:`10 \times 10 \times 10 \, \mathbf{k}` grid). :math:`\mathbf{k}` points are sampled uniformly in the 1BZ. For each :math:`\mathbf{k}`, all :math:`\mathbf{G}` were included such that :math:`60 \, \text{eV} < |\mathbf{k} + \mathbf{G}|^2/2m_e < \text{keV}`. Different :math:`\mathbf{G}` correspond to different bands when the parabolic dispersion relation gets folded in to the 1BZ.

- File: Ge/scatter/Ge_scatter_elec_config.hdf5
- Description: 
        - Electronic states assumed to be spin-degenerate, i.e., one-component wave functions. Used for binned scattering rate and dielectric calculations.
        - Initial States: 
            - Modelled with a combination of STO basis states and PW basis states. STO basis is used for the low energy, "core" states, while PW basis is used for the valence states.
            - STO basis
                - 28 states (1 :math:`\mathbf{k}` point (:math:`\mathbf{k} = 0`), 28 bands). States are the electrons in the :math:`1s \rightarrow 3d` orbitals, for both Ge in the unit cell. The sum over lattice vectors, :math:`\mathbf{r}` extends to cells :math:`\pm 1` away from the center, i.e., includes 27 cells in total. Each state is sampled on a :math:`128 \times 128 \times 128` uniform grid in the unit cell. STO basis coefficients, e.g., :math:`C_{j, l, n, \kappa}` are taken from the tabulated values `here `_. Energy of each state is taken from the Materials Project database, material ID mp-32.
                - Notes: The reason for the small number of :math:`\mathbf{k}` points is due to runtime considerations, one has to choose between a larger sampling grid, i.e., sample the high momentum contributions in the unit cell, or more :math:`\mathbf{k}` points. Since the main features of these states are at high momentum, this is prioritized.
            - PW basis
                - 4000 states (:math:`10 \times 10 \times 10 \, \mathbf{k}` points, 4 bands). Computed with DFT (VASP), see Ref. :cite:`Griffin:2021znd` for more details. Uniform sampling in the 1BZ. Each state was expanded to an :math:`E_\text{cut} = \text{keV}` and then all-electron reconstructed with :code:`pawpyseed` to :math:`E_\text{cut} = 2 \, \text{keV}`. Lowest energy state at :math:`-11.814 \, \text{eV}`.

        - Final States:
            - Modelled with a combination of PW basis and single PW basis states. PW basis is used for the lower energy "conduction" bands, single PW basis is used for higher energy states being approximated as "free".
            - PW basis
                - 82000 states (:math:`10 \times 10 \times 10 \, \mathbf{k}` points, 82 bands). Computed with DFT (VASP), see Ref. :cite:`Griffin:2021znd` for more details. Uniform sampling in the 1BZ. Each state was expanded to an :math:`E_\text{cut} = \text{keV}` and then all-electron reconstructed with :code:`pawpyseed` to :math:`E_\text{cut} = 2 \, \text{keV}`. Lowest energy state at :math:`0.67 \, \text{eV}`. All bands which have an :math:`E_{i \mathbf{k}} < 60 \, \text{eV}`, for any :math:`\mathbf{k}`, are included.
            - single PW basis
                - 40000 states (:math:`10 \times 10 \times 400` grid in :math:`(\theta, \phi, p)` space). Uniformly sampled on the sphere in :math:`(\theta, \phi)`, logarithmically sampled in :math:`E = p^2/2m_e` between :math:`E_\text{min} = 60 \, \text{eV}` and :math:`E_\text{max} = 400 \, \text{eV}`.

- File: Ge/abs/Ge_abs_elec_config.hdf5
- Description: 
        - Electronic states assumed to be spin-degenerate, i.e., one-component wave functions. Used for absorption rate calculations.
        - Initial States: 

            - Modelled with a combination of STO basis states and PW basis states. STO basis is used for the low energy, "core" states, while PW basis is used for the valence states.
            - STO basis
                - 28000 states (:math:`10 \times 10 \times 10 \, \mathbf{k}` points, 28 bands). States are the electrons in the :math:`1s \rightarrow 3d` orbitals, for both Ge in the unit cell. :math:`\mathbf{k}` grid is uniformly sampled over the 1BZ. The sum over lattice vectors, :math:`\mathbf{r}` extends to cells :math:`\pm 1` away from the center, i.e., includes 27 cells in total. Each state is sampled on a :math:`128 \times 128 \times 128` uniform grid in the unit cell. STO basis coefficients, e.g., :math:`C_{j, l, n, \kappa}` are taken from the tabulated values `here `_. Energy of each state is taken from the Materials Project database, material ID mp-32.
                - Notes: A larger number of :math:`\mathbf{k}` vectors can, and must be, used here is because transitions must be vertical. This limits the number of transitions, relative to a scattering rate calculation.
            - PW basis
                - 4000 states (:math:`10 \times 10 \times 10 \, \mathbf{k}` points, 4 bands). Computed with DFT (VASP), see Ref. :cite:`Griffin:2021znd` for more details. Uniform sampling in the 1BZ. Each state was expanded to an :math:`E_\text{cut} = \text{keV}` and then all-electron reconstructed with :code:`pawpyseed` to :math:`E_\text{cut} = 2 \, \text{keV}`. Lowest energy state at :math:`-11.814 \, \text{eV}`.

        - Final States:

            - Modelled with a combination of PW basis and single PW basis states. PW basis is used for the lower energy "conduction" bands, single PW basis is used for higher energy states being approximated as "free".
            - PW basis
                - 82000 states (:math:`10 \times 10 \times 10 \, \mathbf{k}` points, 82 bands). Computed with DFT (VASP), see Ref. :cite:`Griffin:2021znd` for more details. Uniform sampling in the 1BZ. Each state was expanded to an :math:`E_\text{cut} = \text{keV}` and then all-electron reconstructed with :code:`pawpyseed` to :math:`E_\text{cut} = 2 \, \text{keV}`. Lowest energy state at :math:`0.67 \, \text{eV}`. All bands which have an :math:`E_{i \mathbf{k}} < 60 \, \text{eV}`, for any :math:`\mathbf{k}`, are included.
            - single PW basis
                - 2586000 states (:math:`10 \times 10 \times 10 \, \mathbf{k}` grid). :math:`\mathbf{k}` points are sampled uniformly in the 1BZ. For each :math:`\mathbf{k}`, all :math:`\mathbf{G}` were included such that :math:`60 \, \text{eV} < |\mathbf{k} + \mathbf{G}|^2/2m_e < \text{keV}`. Different :math:`\mathbf{G}` correspond to different bands when the parabolic dispersion relation gets folded in to the 1BZ.