Describing the Migdal effect with a bremsstrahlung-like process and many-body effects
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-09-09 |
| Journal | Physical review. D/Physical review. D. |
| Authors | Zheng-Liang Liang, Chongjie Mo, Fawei Zheng, Ping Zhang |
| Institutions | Beijing Institute of Technology, Institute of Applied Physics and Computational Mathematics |
| Citations | 33 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis research introduces a refined quantum field theory (QFT) framework for calculating the Migdal effectâthe electronic excitation caused by Dark Matter (DM) scattering off a nucleusâin bulk semiconductor targets (diamond and silicon).
- Core Methodology: The model coherently integrates a bremsstrahlung-like description for the suddenly recoiling ion with electronic many-body effects, specifically using the Random Phase Approximation (RPA) to calculate the dielectric function.
- Enhanced Low-Energy Rates: The new calculation yields significantly larger event rates in the low energy regime (near the band gap) compared to previous Tight-Binding (TB) or localized Wannier Function (WF) methods. This enhancement is driven by a strong Ï-4 scaling factor in the event rate formula.
- Physical Equivalence: The study finds that the effect of the bremsstrahlung photon mediating the Coulomb interaction between the recoiled ion and the electron-hole pair is physically equivalent to the exchange of a single phonon in the soft limit (impulse approximation).
- Local Field Effects: The use of the microscopic dielectric matrix (calculated using the YAMBO code) successfully incorporates local field effects, which are crucial for accurate modeling in crystalline structures.
- Updated Sensitivity: Provides updated differential event rates and derived cross-section sensitivities for sub-GeV DM detection using 1 kg-yr diamond and silicon detectors, informing future experimental design.
Technical Specifications
Section titled âTechnical SpecificationsâThe following parameters were used in the Density Functional Theory (DFT) and Random Phase Approximation (RPA) calculations for bulk diamond and silicon.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| DM Local Density (ÏÏ) | 0.3 | GeV/cm3 | Standard astrophysical assumption. |
| Earth Velocity (ve) | 230 | km/s | Used in truncated Maxwellian DM velocity distribution. |
| Galactic Escape Velocity (vesc) | 544 | km/s | Used in truncated Maxwellian DM velocity distribution. |
| Diamond Band Gap (Eg) | 5.47 | eV | Experimental value used for scissor correction. |
| Silicon Band Gap (Eg) | 1.12 | eV | Experimental value used for scissor correction. |
| Diamond Lattice Constant | 3.577 | A | Adopted for DFT calculation. |
| Silicon Lattice Constant | 5.429 | A | Adopted for DFT calculation. |
| Diamond k-point Mesh | 6x6x6 | N/A | Uniform mesh for Brillouin Zone integration. |
| Silicon k-point Mesh | 5x5x5 | N/A | Uniform mesh for Brillouin Zone integration. |
| Diamond DFT Energy Cutoff (Ecut) | 200 | Ry | Used in Quantum Espresso calculation. |
| Silicon DFT Energy Cutoff (Ecut) | 70 | Ry | Used in Quantum Espresso calculation. |
| Broadening Parameter (η) | 0.1 | eV | Adopted in dielectric matrix calculation (RPA). |
| Energy Bin Width (ÎÏ) | 0.05 | eV | Used for calculating energy loss spectra F(Ï). |
| Benchmark DM-Nucleon Cross Section (ÏÏn) | 10-38 | cm2 | Reference value for event rate plots. |
Key Methodologies
Section titled âKey MethodologiesâThe Migdal excitation event rates were calculated using a multi-step computational approach combining DFT and QFT linear response theory:
- Electronic Structure Calculation (DFT): Bloch eigenfunctions and eigenvalues for bulk diamond and silicon were obtained using Density Functional Theory (DFT) via the Quantum Espresso package.
- Band Gap Correction: A âscissor correctionâ was applied to the DFT eigenvalues to align the calculated band gaps with experimental values (5.47 eV for diamond, 1.12 eV for silicon).
- Dielectric Matrix Calculation (RPA): The microscopic dielectric matrix ΔG,Gâ(k, Ï) was computed using the Random Phase Approximation (RPA), implemented via the YAMBO code. This step accounts for electronic many-body effects and local field variations.
- Inverse Dielectric Function: The inverse dielectric matrix Δ-1(k, Ï) was calculated by direct matrix inversion, which is necessary to describe the screened Coulomb interaction.
- Energy Loss Function (F(Ï)): The averaged energy loss function F(Ï) was determined by integrating the imaginary part of the inverse dielectric function over the first Brillouin Zone (BZ) using uniform k-point meshes (6x6x6 for diamond, 5x5x5 for silicon).
- Event Rate Integration: The total Migdal event rate (R) was calculated by integrating the energy loss function F(Ï) with the DM velocity distribution and incorporating the critical Ï-4 scaling factor derived from the bremsstrahlung-like process description.
- Sensitivity Analysis: Cross-section sensitivities (90% C.L. upper limits) were derived based on calculated event rates for single-electron and two-electron ionization bins, assuming a 1 kg-yr detector exposure.
Commercial Applications
Section titled âCommercial ApplicationsâThe theoretical advancements in modeling the Migdal effect directly impact the design and interpretation of results from next-generation particle detectors.
- Sub-GeV Dark Matter Direct Detection:
- Provides highly accurate theoretical predictions for event rates in crystalline detectors, essential for interpreting data from experiments like XENON and CDEX.
- Validates the use of wide band gap materials (like diamond) and narrow band gap materials (like silicon) as primary targets for light DM searches.
- Low-Energy Detector Design:
- The identified Ï-4 scaling strongly emphasizes the need for detectors capable of achieving extremely low energy thresholds (near the band gap) to maximize sensitivity to sub-GeV DM.
- Semiconductor Material Characterization:
- The methodology offers a robust framework for calculating electron-hole pair production and collective excitations (plasmon/phonon dynamics) in semiconductors under high-impulse conditions, relevant for radiation damage and high-energy physics applications.
- Quantum Sensing and Metrology:
- The detailed understanding of electronic response and many-body effects in diamond and silicon crystals is foundational for developing highly sensitive solid-state quantum sensors that rely on precise charge or phonon detection.
View Original Abstract
Recent theoretical studies have suggested that the suddenly recoiled atom\nstruck by dark matter (DM) particle is much more likely to excite or lose its\nelectrons than expected. Such Migdal effect provides a new avenue for exploring\nthe sub-GeV DM particles. There have been various attempts to describe the\nMigdal effect in liquids and semiconductor targets. In this paper we\nincorporate the treatment of the bremsstrahlung process and the electronic\nmany-body effects to give a full description of the Migdal effect in bulk\nsemiconductor targets diamond and silicon. Compared with the results obtained\nwith the atom-centered localized Wannier functions (WFs) under the framework of\nthe tight-binding (TB) approximation, the method proposed in this study yields\nmuch larger event rates in the low energy regime, due to a $\omega^{-4}$\nscaling. We also find that the effect of the bremsstrahlung photon mediating\nthe Coulomb interaction between recoiled ion and the electron-hole pair is\nequivalent to that of the exchange of a single phonon.\n