---
title: EXCEED-DM Direct Detection Framework
url: https://www.emergentmind.com/topics/exceed-dm
type: topic
---

# EXCEED-DM Direct Detection Framework

Searching arXiv for EXCEED-DM and closely related direct-detection tools.
Search query: EXCEED-DM direct detection dark matter electronic excitations
EXCEED-DM is an ab-initio–driven framework for computing dark-matter–electron scattering and absorption rates in realistic materials for direct detection of sub-GeV dark matter. Introduced as “EXtended Calculation of Electronic Excitations for Direct detection of Dark Matter,” it is both a formalism and a Fortran/MPI code that ingests electronic wave functions and band energies from external electronic-structure calculations, precomputes a set of primitive transition matrix elements, and uses them to evaluate scattering rates, absorption rates, dielectric response, and modulation signals in crystalline targets such as Si and Ge [2210.14917]. Its central motivation is that, in the light-DM regime, the relevant observables are electronic excitations in a medium rather than nuclear recoils, so reliable predictions require realistic material-specific electronic structure, in-medium screening, and halo kinematics to be treated in a unified way [2210.14917].

## 1. Definition and scientific context

EXCEED-DM was developed for direct detection experiments “utilizing electronic excitations,” which are described as “spearheading the search for light, sub-GeV, dark matter” [2210.14917]. In this mass range, conventional nuclear-recoil searches lose sensitivity because recoil energies fall below threshold, whereas electronic excitations in materials remain accessible due to band gaps of order eV in semiconductors and insulators, or meV in lower-gap systems [2210.14917]. The framework therefore targets the calculation of rates for dark-matter–induced transitions between electronic states in a solid.

The framework is explicitly designed to be general with respect to both the target material and the dark-matter interaction model. It is not tied to a single electronic-structure package; rather, it acts as a front-end that reads precomputed electronic states and evaluates dark-matter observables from them [2210.14917]. The paper characterizes EXCEED-DM as supporting inputs from “a variety of ab initio electronic structure calculations” and as computing dark-matter–electron interaction rates for “any DM-electron interaction rate in this regime” provided the interaction can be expressed in terms of the implemented operator basis [2210.14917].

A common misconception is that EXCEED-DM refers generically to any “EXCEED” program or to the unrelated “Exceed-Shannon” finite-time information-theory literature. In the dark-matter context, EXCEED-DM specifically denotes the direct-detection framework introduced in “EXCEED-DM: Extended Calculation of Electronic Excitations for Direct Detection of Dark Matter” [2210.14917]. A distinct communication-theory usage of “EXCEED” appears in “Finite-Time Capacity: Making Exceed-Shannon Possible?” and is unrelated in subject matter, formalism, and application [2111.00444].

## 2. Formal structure and transition-operator basis

The formalism begins from electronic eigenstates of a target Hamiltonian,
$$
\hat{H}_0 |I\rangle = E_I |I\rangle \,,
$$
with crystalline states written as Bloch states $|i,\mathbf{k}\rangle$ [2210.14917]. The central objects are transition matrix elements
$$
\mathcal{T}_{IF}(\hat{\mathcal{O}}) \equiv \langle F | \mathcal{O} | I \rangle \,,
$$
and EXCEED-DM precomputes a specific set of primitive matrix elements that can be recombined into a broad class of scattering and absorption observables [2210.14917].

The implemented primitive operators are:
$$
\begin{aligned}
\mathcal{T}_1(\mathbf{q}) &\equiv \langle F | e^{i\mathbf{q}\cdot\mathbf{x}} | I \rangle \,,\\
\mathcal{T}_{\mathbf{v}}(\mathbf{q}) &\equiv \langle F | e^{i\mathbf{q}\cdot\mathbf{x}}\, \mathbf{v} | I \rangle \,,\\
\mathcal{T}_{v^2}(\mathbf{q}) &\equiv \langle F | e^{i\mathbf{q}\cdot\mathbf{x}}\, v^2 | I \rangle \,,\\
\mathcal{T}_{\bm{\sigma}}(\mathbf{q}) &\equiv \langle F | e^{i\mathbf{q}\cdot\mathbf{x}}\, \bm{\sigma} | I \rangle \,,\\
\mathcal{T}_{\mathbf{v}\cdot\bm{\sigma}}(\mathbf{q}) &\equiv \langle F | e^{i\mathbf{q}\cdot\mathbf{x}}\, (\mathbf{v}\cdot\bm{\sigma}) | I \rangle \,,\\
\mathcal{T}_{\mathbf{v}\times\bm{\sigma}}(\mathbf{q}) &\equiv \langle F | e^{i\mathbf{q}\cdot\mathbf{x}}\, (\mathbf{v}\times\bm{\sigma}) | I \rangle \,.
\end{aligned}
$$
In the $\mathbf{q}\to 0$ limit, the exponential is dropped; those vertical matrix elements are used in absorption and optical-response calculations [2210.14917].

This operator-layer construction is one of the defining features of EXCEED-DM. It separates the material calculation from the dark-matter model: once the relevant $\mathcal{T}$ objects are known for a chosen electronic basis, new interaction models can be implemented by specifying the corresponding bilinear combination $\mathscr{F}_{IF}(\mathcal{T})$ in the rate formula [2210.14917]. This suggests an effective modularity in which electronic structure, mediator physics, and astrophysical inputs remain conceptually distinct even though they enter the final rate multiplicatively.

For Bloch-to-Bloch transitions, the formalism enforces lattice momentum conservation through reciprocal lattice vectors $\mathbf{G}$, with the scalar matrix element written as
$$
\mathcal{T}^1_{i,f,\mathbf{k},\mathbf{k}'}(\mathbf{q} = \mathbf{k}' - \mathbf{k} + \mathbf{G}) =
\frac{1}{\Omega} \sum_s \int_{\rm UC} d^3\mathbf{x}\, e^{i\mathbf{G}\cdot\mathbf{x}}\, u_{f,\mathbf{k}',s}^*(\mathbf{x})\,u_{i,\mathbf{k},s}(\mathbf{x}) \,,
$$
where $\Omega$ is the unit-cell volume [2210.14917]. Similar expressions hold for the velocity- and spin-dependent operators.

## 3. Scattering, absorption, and dielectric response

For dark-matter–electron scattering, EXCEED-DM uses the rate representation
$$
R = \frac{\pi \bar{\sigma}_e}{V\,\mu_{\chi e}^2\,m_\chi} \frac{\rho_\chi}{\rho_T}
\sum_{I F} \int \frac{d^3\mathbf{q}}{(2\pi)^3}\,
f_{\rm scr}^2(\mathbf{q},\omega)\,\mathcal{F}_\text{med}^2(q)\,
g(\mathbf{q}, E_F - E_I)\,\mathscr{F}_{IF}(\mathcal{T}) \,,
$$
where $\bar{\sigma}_e$ is a reference cross section, $f_{\rm scr}$ is the screening factor, $\mathcal{F}_\text{med}(q)$ is the mediator form factor, $g(\mathbf{q},\omega)$ is the halo-kinematic function, and $\mathscr{F}_{IF}$ is the model-dependent scattering form factor [2210.14917]. The mediator form factor is written as
$$
\mathcal{F}_\text{med}(q) = \left(\frac{\alpha m_e}{q}\right)^\beta,
$$
with $\beta = 0$ for a heavy mediator and $\beta = 2$ for a light mediator [2210.14917].

The halo dependence enters through
$$
g(\mathbf{q},\omega) = 2\pi\!\int d^3\mathbf{v}\, f_\chi(\mathbf{v})\,
\delta\!\left(\omega - \mathbf{q}\cdot\mathbf{v} + \frac{q^2}{2m_\chi}\right),
$$
which EXCEED-DM evaluates analytically for the Standard Halo Model [2210.14917]. Time dependence for annual or daily modulation is implemented by varying the Earth-velocity vector $\mathbf{v}_e(t)$ [2210.14917].

The code includes several built-in scattering structures. For spin-independent scattering,
$$
\mathscr{F}_{IF} = |\mathcal{T}_1|^2,
$$
and for spin-dependent scattering,
$$
\mathscr{F}_{IF} = \frac{1}{3}|\mathcal{T}_{\bm{\sigma}}|^2.
$$
For a velocity-dependent vector–axial operator, EXCEED-DM implements
$$
\mathscr{F}_{IF}
= \frac{1}{\alpha^2 m_e^2} \bigg( 4 m_e^2 |\mathcal{T}_\mathbf{v}|^2
+ 2 m_e\,\mathcal{T}_1 (\mathbf{q}\cdot \mathcal{T}_\mathbf{v}^*)
+ 2 m_e\,\mathcal{T}_1^* (\mathbf{q}\cdot \mathcal{T}_\mathbf{v})
+ q^2 |\mathcal{T}_1|^2 \bigg) \,,
$$
demonstrating explicit support for interactions that depend on the electron velocity operator rather than only on density-like couplings [2210.14917].

For bosonic dark-matter absorption, the rate is expressed through the in-medium self-energy of the absorbed mode,
$$
R = -\frac{\rho_\phi}{\rho_T m_\phi^2} \frac{1}{n} \sum_{\lambda=1}^n
\mathrm{Im}\!\left[\Pi_{\hat{\phi}\hat{\phi}}^\lambda(\bar{\Pi}_{\mathcal{O}_1,\mathcal{O}_2})\right],
$$
with the self-energies rewritten in terms of $\mathbf{q}\to 0$ transition matrix elements [2210.14917]. The paper gives explicit structures for scalar, pseudoscalar, and vector dark matter, including, for example,
$$
\Pi_{\hat{\phi}\hat{\phi}}^\eta = \frac{g_e^2}{4}\,\bar{\Pi}_{v^2,v^2}
$$
for scalar absorption, and
$$
\Pi_{\hat{\phi}\hat{\phi}}^\eta =
g_e^2\, \frac{ m_\phi^2 \left[\bar{\Pi}'_{\mathbf{v},\mathbf{v}}\right]^\eta}
{ m_\phi^2 - e^2 \left[\bar{\Pi}'_{\mathbf{v},\mathbf{v}}\right]^\eta}
$$
for vector absorption [2210.14917].

A further key capability is the internal calculation of the dielectric function in an RPA/Lindhard-type approximation:
$$
\varepsilon(\mathbf{q},\omega) = 1 - \frac{e^2}{q^2 V} \sum_{IF}
G(\omega, E_F - E_I,\delta) |\mathcal{T}_1|^2.
$$
Because crystal momentum conservation yields support only at discrete $\mathbf{q}$, EXCEED-DM evaluates an averaged dielectric function over momentum bins [2210.14917]. For models that couple to the electron vector current like the photon, screening is implemented through
$$
f_{\rm scr}(\mathbf{q},\omega) = \frac{1}{\varepsilon(q,\omega)}
$$
in an isotropic approximation [2210.14917].

## 4. Electronic-structure inputs and computational workflow

EXCEED-DM is notable for its independence from any single electronic-structure code. It accepts wave functions in three supported bases stored in an HDF5 “electronic configuration” format [2210.14917]. These are plane-wave Bloch states, Slater-type-orbital Bloch states, and single plane waves used to approximate high-energy free-electron final states [2210.14917].

The three basis types can be summarized as follows:

| Basis | Label | Intended use |
|---|---|---|
| Plane-wave Bloch states | `bloch_PW_basis` | Valence and conduction bands |
| Slater-type-orbital Bloch states | `bloch_STO_basis` | Core and semicore states |
| Single plane waves | `bloch_single_PW` | High-energy “free” final states |

For plane-wave Bloch states, the periodic factor is expanded as
$$
u_{i,\mathbf{k},s}(\mathbf{x}) = \sum_{\mathbf{G}}
e^{i\mathbf{G}\cdot\mathbf{x}}\, \widetilde{u}_{i,\mathbf{k},s,\mathbf{G}} \,.
$$
The STO representation is built from localized atomic Slater orbitals, while the single-plane-wave representation is used to approximate continuum-like states and may include Fermi factors to partially correct Coulomb distortions [2210.14917].

This basis heterogeneity is one of the principal extensions highlighted by the authors. It allows EXCEED-DM to combine all-electron reconstructed valence and conduction bands, deep core levels, and high-energy continuum-like states in a single rate calculation [2210.14917]. A plausible implication is that the framework is particularly well suited to studies in which the relevant kinematics span very different energy and momentum scales, since no single compact basis is optimal across the entire problem.

Operationally, the code is organized around three main calculation types: `binned_scatter_rate`, `absorption_rate`, and `dielectric` [2210.14917]. The workflow is to read the electronic configuration, compute the required transition matrix elements, perform the momentum and halo integrals, sum over initial and final states with their sampling weights, and write the results to HDF5 output [2210.14917]. Parallelization is handled through MPI, and the implementation is described as suitable for HPC clusters with relatively modest per-core memory usage [2210.14917].

The input structure contains groups for control settings, electronic configuration, material properties, the dark-matter model, the astrophysical model, numerical settings, and screening [2210.14917]. Example electronic configurations for Si and Ge, including core, valence, conduction, and free states, are stated to be publicly available from the author [2210.14917].

## 5. Demonstrated applications

The paper showcases four explicit applications in Si and Ge, each intended to illustrate a different sector of the EXCEED-DM formalism [2210.14917].

First, the framework is used to compute dark-photon–mediated scattering with numerical dielectric screening. In this case, the paper compares three screening prescriptions: no screening, an analytic dielectric model, and a numerical dielectric function computed internally from the same electronic configuration used in the scattering calculation [2210.14917]. The resulting $\varepsilon(q,\omega)$ agrees qualitatively with the analytic model, with differences of order $\mathcal{O}(10\%)$ in the low-$q$, low-$\omega$ region, and using numerical rather than analytic screening shifts rates and cross-section limits by only $\sim 10\%$ [2210.14917]. The significance of this calculation is that the same underlying electronic structure is used consistently for both screening and scattering, avoiding mismatched approximations.

Second, EXCEED-DM is applied to a velocity-dependent vector–axial interaction,
$$
\mathcal{L} \supset g_\chi V_\mu \bar{\chi}\gamma^\mu\chi + g_e V_\mu \bar{e}\gamma^\mu\gamma^5 e,
$$
which after the nonrelativistic reduction yields a scattering form factor depending on $\mathcal{T}_{\mathbf{v}}$ as well as $\mathcal{T}_1$ [2210.14917]. This example demonstrates that the framework is not restricted to density couplings or simple SI/SD cases. The paper presents projected 95% CL sensitivities to the corresponding reference cross section $\bar{\sigma}_e^{\mathrm{VA}}$ for Si and Ge with kg-year exposure and electron thresholds $Q\ge 1,2,3$ [2210.14917].

Third, the code extends previous absorption calculations for scalar, pseudoscalar, and vector dark matter up to $m_\phi \sim 1$ keV by combining deep core states, valence and conduction states, and high-energy free final states [2210.14917]. The results are shown as 95% CL sensitivities on the model couplings for Si and Ge across $m_\phi \sim 1\,{\rm eV} - 1\,{\rm keV}$ and are compared with constraints inferred from optical data, stellar-cooling bounds, XENON10/100, XENON1T, SuperCDMS, and DFSZ and KSVZ axion model bands in the pseudoscalar case [2210.14917]. For $m_\phi \lesssim 60$ eV, the new results agree with earlier EXCEED-DM absorption calculations up to differences from smearing prescriptions; above that scale, the calculation extends coverage by including states far from the Fermi level [2210.14917].

Fourth, EXCEED-DM is used to compute annual modulation of dark-photon scattering in Si and Ge, again including numerical dielectric screening [2210.14917]. The modulation fraction is defined as
$$
f_{\rm mod} = \frac{R_+ - R_-}{R_0},
$$
with $R_+$, $R_-$, and $R_0$ evaluated at Earth speeds $v_e^0 \pm 15\,\text{km/s}$ and $v_e^0=250\,\text{km/s}$ [2210.14917]. The paper reports modulation fractions of order $10\%$ across a wide range of deposited energies and at higher thresholds, with larger effects at low dark-matter masses due to kinematic turn-on behavior [2210.14917].

## 6. Relation to earlier tools, scope, and limitations

EXCEED-DM is positioned as an extension beyond earlier material-response tools used in dark-matter direct detection. The paper states explicitly that, unlike QEDark, which is “tightly coupled to Quantum Espresso,” EXCEED-DM can work with any electronic-structure code that can provide wave functions in one of the supported basis forms [2210.14917]. It also notes interoperability with DarkELF, where EXCEED-DM can provide $\varepsilon(\mathbf{q},\omega)$ while DarkELF performs rate integrals for simplified models [2210.14917].

The framework’s generality is nevertheless bounded by its approximations. The electronic structure is only as accurate as the supplied wave functions and band energies; standard DFT can underestimate band gaps and misplace bands, and many-body corrections must be incorporated upstream by the user if needed [2210.14917]. The dielectric response is computed in an independent-particle RPA/Lindhard-type approximation with a phenomenological broadening parameter $\delta(\omega)$, so strong-correlation effects and excitonic structure may be missed [2210.14917]. Finite $k$-point grids and band truncation are additional numerical uncertainties [2210.14917].

The astrophysical treatment is similarly conventional rather than exhaustive. EXCEED-DM adopts the Standard Halo Model by default, with user-selectable values of $v_0$, $v_{\rm esc}$, $\mathbf{v}_e$, and $\rho_\chi$ [2210.14917]. Real halo substructure, streams, or anisotropy are not modeled in the default setup, although the interface is presented as extensible [2210.14917].

These limitations are not incidental; they delimit the intended role of the framework. EXCEED-DM is best understood as an extensible engine for rate prediction in realistic materials rather than as a complete end-to-end experimental inference package. The paper explicitly identifies future directions including more basis types, wider dark-matter EFT support, additional materials such as anisotropic and spin-orbit-coupled systems, improved screening models, direct ingestion of experimentally measured dielectric functions, more general velocity distributions, and closer integration with detector response and likelihood pipelines [2210.14917].

## 7. Significance and conceptual place in direct-detection research

EXCEED-DM occupies a specific niche in the development of light-dark-matter direct detection: it brings ab initio electronic structure, a reusable operator basis, in-medium screening, and modulation physics into a single computational framework [2210.14917]. This is significant because sub-GeV dark matter cannot be treated reliably with free-electron intuition alone; the observable rates depend sensitively on crystal-band structure, screening, and the availability of bound, valence, core, and continuum states [2210.14917].

The paper’s main conceptual contribution is the factorization of the problem into three layers: electronic structure, primitive transition matrix elements, and dark-matter–model-dependent combinations of those matrix elements plus halo integrals [2210.14917]. This architecture makes the framework simultaneously material-specific and interaction-general. It also suggests a methodological shift in the field: rather than deriving bespoke analytic rate formulas separately for each target and interaction, one computes a common set of transition objects and reuses them across models.

Within the direct-detection literature, this makes EXCEED-DM especially relevant for semiconductor and other electronic-excitation targets, and for phenomenological studies that require consistent comparisons across mediators, operator structures, materials, or astrophysical assumptions [2210.14917]. The Si and Ge results in the paper illustrate this role by providing updated calculations for screened dark-photon scattering, velocity-dependent interactions, extended absorption channels, and annual modulation within the same software environment [2210.14917].

In summary, EXCEED-DM is a general-purpose ab initio framework for computing dark-matter–induced electronic excitations in materials, with explicit support for scattering, absorption, dielectric response, and modulation in realistic crystalline targets. Its importance lies less in a single benchmark result than in the infrastructure it provides for systematically connecting microscopic dark-matter models to experimentally relevant material responses in the light-dark-matter regime [2210.14917].

Source: https://www.emergentmind.com/topics/exceed-dm