Data#

Electronic Configuration Files#

While the examples folder contains many example electronic configuration files useful for testing and learning what EXCEED-DM can do, they are not suitable for publication quality results. The datasets are simply too small; they do no adequately represent the collection of electronic states in the target. The publication quality electronic configuration files are too big to host on the Github repository, typically being \(\mathcal{O}(\text{GB})\) in size. There are two ways around this:

  1. Create your own electronic configuration file to the specifications given in File Specifications - Electronic Configuration File. This is the best option if you are studying a novel target.

  2. Use a publicly available electronic configuration file. The files for Si and Ge are hosted on Zenodo, with links given below. It is highly recommeded that you make your electronic configuration files public so that results can be easily reproduced.

Note

Remember to cite the associated Zenodo repository if you use these publically available electronic configuration files.

Si#

  • Link: https://zenodo.org/record/7246141#.Y1g31raSnZc

    • 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 \(\mathbf{k}\) point (\(\mathbf{k} = 0\)), 10 bands). States are the electrons in the \(1s \rightarrow 2p\) orbitals, for both Si in the unit cell. The sum over lattice vectors, \(\mathbf{r}\) extends to cells \(\pm 1\) away from the center, i.e., includes 27 cells in total. Each state is sampled on a \(128 \times 128 \times 128\) uniform grid in the unit cell. STO basis coefficients, e.g., \(C_{j, l, n, \kappa}\) 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 \(\mathbf{k}\) 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 \(\mathbf{k}\) points. Since the main features of these states are at high momentum, this is prioritized.

        • PW basis

          • 4000 states (\(10 \times 10 \times 10 \, \mathbf{k}\) points, 4 bands). Computed with DFT (VASP), see Ref. [1] for more details. Uniform sampling in the 1BZ. Each state was expanded to an \(E_\text{cut} = \text{keV}\) and then all-electron reconstructed with pawpyseed to \(E_\text{cut} = 2 \, \text{keV}\). Lowest energy state at \(-11.814 \, \text{eV}\).

      • 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 (\(10 \times 10 \times 10 \, \mathbf{k}\) points, 60 bands). Computed with DFT (VASP), see Ref. [1] for more details. Uniform sampling in the 1BZ. Each state was expanded to an \(E_\text{cut} = \text{keV}\) and then all-electron reconstructed with pawpyseed to \(E_\text{cut} = 2 \, \text{keV}\). Lowest energy state at \(1.11 \, \text{eV}\). All bands which have an \(E_{i \mathbf{k}} < 60 \, \text{eV}\), for any \(\mathbf{k}\), are included.

        • single PW basis

          • 40000 states (\(10 \times 10 \times 400\) grid in \((\theta, \phi, p)\) space). Uniformly sampled on the sphere in \((\theta, \phi)\), logarithmically sampled in \(E = p^2/2m_e\) between \(E_\text{min} = 60 \, \text{eV}\) and \(E_\text{max} = 400 \, \text{eV}\).

  • Link: https://zenodo.org/record/7246141#.Y1g31raSnZc

    • 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 (\(10 \times 10 \times 10 \, \mathbf{k}\) points, 10 bands). States are the electrons in the \(1s \rightarrow 2p\) orbitals, for both Si in the unit cell. \(\mathbf{k}\) grid is uniformly sampled over the 1BZ. The sum over lattice vectors, \(\mathbf{r}\) extends to cells \(\pm 1\) away from the center, i.e., includes 27 cells in total. Each state is sampled on a \(128 \times 128 \times 128\) uniform grid in the unit cell. STO basis coefficients, e.g., \(C_{j, l, n, \kappa}\) 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 \(\mathbf{k}\) 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 (\(10 \times 10 \times 10 \, \mathbf{k}\) points, 4 bands). Computed with DFT (VASP), see Ref. [1] for more details. Uniform sampling in the 1BZ. Each state was expanded to an \(E_\text{cut} = \text{keV}\) and then all-electron reconstructed with pawpyseed to \(E_\text{cut} = 2 \, \text{keV}\). Lowest energy state at \(-11.814 \, \text{eV}\).

      • 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 (\(10 \times 10 \times 10 \, \mathbf{k}\) points, 60 bands). Computed with DFT (VASP), see Ref. [1] for more details. Uniform sampling in the 1BZ. Each state was expanded to an \(E_\text{cut} = \text{keV}\) and then all-electron reconstructed with pawpyseed to \(E_\text{cut} = 2 \, \text{keV}\). Lowest energy state at \(1.11 \, \text{eV}\). All bands which have an \(E_{i \mathbf{k}} < 60 \, \text{eV}\), for any \(\mathbf{k}\), are included.

        • single PW basis

          • 2152000 states (\(10 \times 10 \times 10 \, \mathbf{k}\) grid). \(\mathbf{k}\) points are sampled uniformly in the 1BZ. For each \(\mathbf{k}\), all \(\mathbf{G}\) were included such that \(60 \, \text{eV} < |\mathbf{k} + \mathbf{G}|^2/2m_e < \text{keV}\). Different \(\mathbf{G}\) correspond to different bands when the parabolic dispersion relation gets folded in to the 1BZ.

Ge#

  • Link: https://zenodo.org/record/7246141#.Y1g31raSnZc

    • 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 \(\mathbf{k}\) point (\(\mathbf{k} = 0\)), 28 bands). States are the electrons in the \(1s \rightarrow 3d\) orbitals, for both Ge in the unit cell. The sum over lattice vectors, \(\mathbf{r}\) extends to cells \(\pm 1\) away from the center, i.e., includes 27 cells in total. Each state is sampled on a \(128 \times 128 \times 128\) uniform grid in the unit cell. STO basis coefficients, e.g., \(C_{j, l, n, \kappa}\) 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 \(\mathbf{k}\) 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 \(\mathbf{k}\) points. Since the main features of these states are at high momentum, this is prioritized.

        • PW basis

          • 4000 states (\(10 \times 10 \times 10 \, \mathbf{k}\) points, 4 bands). Computed with DFT (VASP), see Ref. [1] for more details. Uniform sampling in the 1BZ. Each state was expanded to an \(E_\text{cut} = \text{keV}\) and then all-electron reconstructed with pawpyseed to \(E_\text{cut} = 2 \, \text{keV}\). Lowest energy state at \(-11.814 \, \text{eV}\).

      • 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 (\(10 \times 10 \times 10 \, \mathbf{k}\) points, 82 bands). Computed with DFT (VASP), see Ref. [1] for more details. Uniform sampling in the 1BZ. Each state was expanded to an \(E_\text{cut} = \text{keV}\) and then all-electron reconstructed with pawpyseed to \(E_\text{cut} = 2 \, \text{keV}\). Lowest energy state at \(0.67 \, \text{eV}\). All bands which have an \(E_{i \mathbf{k}} < 60 \, \text{eV}\), for any \(\mathbf{k}\), are included.

        • single PW basis

          • 40000 states (\(10 \times 10 \times 400\) grid in \((\theta, \phi, p)\) space). Uniformly sampled on the sphere in \((\theta, \phi)\), logarithmically sampled in \(E = p^2/2m_e\) between \(E_\text{min} = 60 \, \text{eV}\) and \(E_\text{max} = 400 \, \text{eV}\).

  • Link: https://zenodo.org/record/7246141#.Y1g31raSnZc

    • 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 (\(10 \times 10 \times 10 \, \mathbf{k}\) points, 28 bands). States are the electrons in the \(1s \rightarrow 3d\) orbitals, for both Ge in the unit cell. \(\mathbf{k}\) grid is uniformly sampled over the 1BZ. The sum over lattice vectors, \(\mathbf{r}\) extends to cells \(\pm 1\) away from the center, i.e., includes 27 cells in total. Each state is sampled on a \(128 \times 128 \times 128\) uniform grid in the unit cell. STO basis coefficients, e.g., \(C_{j, l, n, \kappa}\) 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 \(\mathbf{k}\) 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 (\(10 \times 10 \times 10 \, \mathbf{k}\) points, 4 bands). Computed with DFT (VASP), see Ref. [1] for more details. Uniform sampling in the 1BZ. Each state was expanded to an \(E_\text{cut} = \text{keV}\) and then all-electron reconstructed with pawpyseed to \(E_\text{cut} = 2 \, \text{keV}\). Lowest energy state at \(-11.814 \, \text{eV}\).

      • 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 (\(10 \times 10 \times 10 \, \mathbf{k}\) points, 82 bands). Computed with DFT (VASP), see Ref. [1] for more details. Uniform sampling in the 1BZ. Each state was expanded to an \(E_\text{cut} = \text{keV}\) and then all-electron reconstructed with pawpyseed to \(E_\text{cut} = 2 \, \text{keV}\). Lowest energy state at \(0.67 \, \text{eV}\). All bands which have an \(E_{i \mathbf{k}} < 60 \, \text{eV}\), for any \(\mathbf{k}\), are included.

        • single PW basis

          • 2586000 states (\(10 \times 10 \times 10 \, \mathbf{k}\) grid). \(\mathbf{k}\) points are sampled uniformly in the 1BZ. For each \(\mathbf{k}\), all \(\mathbf{G}\) were included such that \(60 \, \text{eV} < |\mathbf{k} + \mathbf{G}|^2/2m_e < \text{keV}\). Different \(\mathbf{G}\) correspond to different bands when the parabolic dispersion relation gets folded in to the 1BZ.

EXCEED-DM Results#

Below are links to datasets used for previously published results. See the refereces for more details.

EXCEED-DMv1.0.0: Extended Calculation of Electronic Excitations for Direct Detection of Dark Matter#

  • Ref: https://arxiv.org/abs/2210.14917

    • Link: https://zenodo.org/record/7250090#.Y1g4J7aSnZc

    • Description:
      Output of all the calculations performed in the v1.0.0 user manual. Specifically, for Si and Ge targets,

      • Numerically computed dielectric (to be used to screen the scattering rate calculation).

      • Binned scatter rate of DM fermion in kinetically mixed dark photon model with different screenings: no screening, an analytic model of screening, and screened with the aforementioned numerically computed dielectric.

      • Binned scatter rate of DM fermion in a model where the scattering potential depends on the electron velocity (light mediator).

      • Extended absorption rate calculation for scalar, pseudoscalar, and vector DM.

      • Annual modulation of binned scatter rate of DM fermion in kinetically mixed dark photon model.

[1] (1,2,3,4,5,6,7,8)

Sinéad M. Griffin, Katherine Inzani, Tanner Trickle, Zhengkang Zhang, and Kathryn M. Zurek. Extended calculation of dark matter-electron scattering in crystal targets. Phys. Rev. D, 104(9):095015, 5 2021. arXiv:2105.05253, doi:10.1103/PhysRevD.104.095015.