DOI: 10.5281/zenodo.7246141
title: EXCEED-DMv1.0.0: Si and Ge Electronic Configurations

description: 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). - <strong>File:</strong> <strong>Si/scatter/Si_scatter_elec_config.hdf5</strong><br> - <strong>Description:</strong> <br> - Electronic states assumed to be spin-degenerate, i.e., one-component wave functions. Used for binned scattering rate and dielectric calculations.<br> - <strong>Initial States: </strong><br> - Modelled with a combination of <strong>STO basis</strong> states and <strong>PW basis</strong> states. <strong>STO basis</strong> is used for the low energy, "core" states, while <strong>PW basis</strong> is used for the valence states.<br> - <strong>STO basis</strong><br> - 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 &lt;https://linkinghub.elsevier.com/retrieve/pii/S0092640X8371003X&gt;`_. Energy of each state is taken from the Materials Project database, material ID mp-149.<br> - 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.<br> - <strong>PW basis</strong><br> - 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}`. <br> - <strong>Final States:</strong><br> - 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".<br> - <strong>PW basis</strong><br> - 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}} &lt; 60 \, \text{eV}`, for any :math:`\mathbf{k}`, are included.<br> - <strong>single PW basis</strong><br> - 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}`. <br> - <strong>File: Si/abs/Si_abs_elec_config.hdf5</strong><br> - <strong>Description: </strong><br> - Electronic states assumed to be spin-degenerate, i.e., one-component wave functions. Used for absorption rate calculations.<br> - <strong>Initial States: </strong><br> - Modelled with a combination of <strong>STO basis</strong> states and <strong>PW basis</strong> states. <strong>STO basis</strong> is used for the low energy, "core" states, while <strong>PW basis</strong> is used for the valence states.<br> - <strong>STO basis</strong><br> - 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 &lt;https://linkinghub.elsevier.com/retrieve/pii/S0092640X8371003X&gt;`_. Energy of each state is taken from the Materials Project database, material ID mp-149.<br> - 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.<br> - <strong>PW basis</strong><br> - 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}`. <br> - <strong>Final States:</strong><br> - Modelled with a combination of <strong>PW basis</strong> and<strong> single PW basis</strong> states. <strong>PW basis</strong> is used for the lower energy "conduction" bands, <strong>single PW basis</strong> is used for higher energy states being approximated as "free".<br> - <strong>PW basis</strong><br> - 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}} &lt; 60 \, \text{eV}`, for any :math:`\mathbf{k}`, are included.<br> - <strong>single PW basis</strong><br> - 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} &lt; |\mathbf{k} + \mathbf{G}|^2/2m_e &lt; \text{keV}`. Different :math:`\mathbf{G}` correspond to different bands when the parabolic dispersion relation gets folded in to the 1BZ. <br> - <strong>File: Ge/scatter/Ge_scatter_elec_config.hdf5</strong><br> - <strong>Description: </strong><br> - Electronic states assumed to be spin-degenerate, i.e., one-component wave functions. Used for binned scattering rate and dielectric calculations.<br> - <strong>Initial States: </strong><br> - Modelled with a combination of <strong>STO basis</strong> states and <strong>PW basis</strong> states. <strong>STO basis</strong> is used for the low energy, "core" states, while <strong>PW basis</strong> is used for the valence states.<br> - <strong>STO basis</strong><br> - 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 &lt;https://linkinghub.elsevier.com/retrieve/pii/S0092640X8371003X&gt;`_. Energy of each state is taken from the Materials Project database, material ID mp-32.<br> - 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.<br> - <strong>PW basis</strong><br> - 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}`. <br> - <strong>Final States:</strong><br> - Modelled with a combination of <strong>PW basis</strong> and<strong> single PW basis</strong> states. <strong>PW basis</strong> is used for the lower energy "conduction" bands, <strong>single PW basis</strong> is used for higher energy states being approximated as "free".<br> - <strong>PW basis</strong><br> - 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}} &lt; 60 \, \text{eV}`, for any :math:`\mathbf{k}`, are included.<br> - <strong>single PW basis</strong><br> - 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}`. <br> - <strong>File: Ge/abs/Ge_abs_elec_config.hdf5</strong><br> - <strong>Description: </strong><br> - Electronic states assumed to be spin-degenerate, i.e., one-component wave functions. Used for absorption rate calculations.<br> - <strong>Initial States: </strong> - Modelled with a combination of <strong>STO basis</strong> states and <strong>PW basis</strong> states. <strong>STO basis</strong> is used for the low energy, "core" states, while <strong>PW basis</strong> is used for the valence states.<br> - <strong>STO basis</strong><br> - 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 &lt;https://linkinghub.elsevier.com/retrieve/pii/S0092640X8371003X&gt;`_. Energy of each state is taken from the Materials Project database, material ID mp-32.<br> - 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.<br> - <strong>PW basis</strong><br> - 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}`. - <strong>Final States:</strong> - Modelled with a combination of <strong>PW basis</strong> and<strong> single PW basis</strong> states. <strong>PW basis</strong> is used for the lower energy "conduction" bands, <strong>single PW basis</strong> is used for higher energy states being approximated as "free".<br> - <strong>PW basis</strong><br> - 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}} &lt; 60 \, \text{eV}`, for any :math:`\mathbf{k}`, are included.<br> - <strong>single PW basis</strong><br> - 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} &lt; |\mathbf{k} + \mathbf{G}|^2/2m_e &lt; \text{keV}`. Different :math:`\mathbf{G}` correspond to different bands when the parabolic dispersion relation gets folded in to the 1BZ.