Describing Migdal effects in diamond crystal with atom-centered localized Wannier functions

At a Glance

Metadata	Details
Publication Date	2020-08-10
Journal	Physical review. D/Physical review. D.
Authors	Zheng-Liang Liang, Lin Zhang, Fawei Zheng, Ping Zhang
Institutions	Beijing University of Chemical Technology, University of Chinese Academy of Sciences
Citations	24
Analysis	Full AI Review Included

Technical Documentation & Analysis: Diamond for Migdal Effect Detection

This document analyzes the research paper “Describing Migdal effects in diamond crystal with atom-centered localized Wannier functions” to highlight the critical role of high-quality MPCVD diamond and to align the research requirements with 6CCVD’s advanced material capabilities.

Executive Summary

This paper validates the use of crystalline diamond as a highly promising semiconductor target for next-generation Dark Matter (DM) detection experiments, specifically focusing on the Migdal effect.

Core Application: Theoretical modeling of the Migdal effect (electronic excitation induced by DM-nucleus scattering) in solid-state diamond detectors.
Material Superiority: Diamond is confirmed as superior to traditional Si/Ge detectors due to the light mass of the carbon nucleus, which results in a lower DM mass threshold (sub-GeV range).
Methodology: A Tight-Binding (TB) approach using ab initio Density Functional Theory (DFT) and Maximally Localized Wannier Functions (WFs) was employed to accurately model electron localization and hopping integrals in the crystal.
Key Advantage: Diamond possesses long-lived, hard phonon modes and the ability to withstand strong electric fields, both crucial for efficient collection of ionized electrons across the bulk material.
Sensitivity Demonstrated: Calculations show significant Migdal excitation event rates, such as 0.299/kg/yr for 10 MeV DM, confirming diamond’s high sensitivity in the sub-GeV mass range.
Material Requirement: Successful realization of this detector requires high-purity, low-defect Single Crystal Diamond (SCD) capable of supporting efficient charge transport.

Technical Specifications

The following hard data points were extracted from the computational details and results presented in the paper, defining the parameters for high-performance diamond detectors.

Parameter	Value	Unit	Context
Target Material	Diamond Crystal	N/A	Semiconductor DM detector proof-of-principle
Lattice Constant ($a$)	3.560	Å	Adopted from relaxation
DFT Energy Cut	90	Ry	Plane-wave basis set calculation
DFT k-point Mesh (Initial)	20 x 20 x 20	N/A	Monkhorst-Pack mesh for Bloch states
Wannier Interpolation k-points	16 x 16 x 16	N/A	Used for matrix element calculation
Number of WFs Generated ($J$)	32	N/A	From 72 Bloch wavefunctions
Reciprocal Lattice Value ($2\pi/a$)	3.48	keV	Momentum transfer reference
WF Spread (Max)	$\approx (1.4 \text{ Å})^{2}$	Å²	Localization measure
Example Event Rate 1 ($m_x=500$ MeV)	0.027	/kg/yr	$w=100$ km/s, $\sigma_{\chi n}=10^{-38}$ cm²
Example Event Rate 2 ($m_x=10$ MeV)	0.299	/kg/yr	$w=800$ km/s, $\sigma_{\chi n}=10^{-38}$ cm²
Electron-Hole Pair Energy	13	eV	Assumed average energy for sensitivity estimate

Key Methodologies

The theoretical framework relies on advanced computational physics techniques to accurately model the electronic structure and excitation dynamics within the diamond lattice.

DFT Calculation: Bloch eigenfunctions and eigenvalues for bulk crystalline diamond were obtained using the Quantum Espresso code, employing the Generalized Gradient Approximation (GGA) functional (PBE).
Wannier Function (WF) Generation: The Wannier 90 package was used to generate 32 atom-centered WFs, ensuring that the centers of the WFs were restricted to the lattice sites to properly account for the struck atom.
Tight-Binding (TB) Framework Extension: The Migdal effect formalism, originally developed for isolated atoms, was extended to crystalline solids using the TB approximation. This framework respects both the localized aspects (WFs) and the extensive nature (hopping integrals) of electrons in the crystal.
Impulse Approximation: The electronic excitation was treated under the impulse approximation, valid for momentum transfers $q \gg \sqrt{2\omega_D m_N}$, allowing the Galilean boost operator to be imposed exclusively on the recoiled nucleus.
Transition Amplitude Calculation: The transition amplitude between initial valence states and final conducting states was derived using the Galilean boost operator applied to the WFs of the struck atom.
Event Rate and Form Factor Calculation: The crystal form factor $F(q, E_e)$ and the total transition rate $R(m_x, w)$ were computed by integrating the transition probability over momentum transfer and DM velocity distributions, using Wannier interpolation results.

6CCVD Solutions & Capabilities

The successful implementation of a diamond-based DM detector, as modeled in this research, requires materials with exceptional purity, precise dimensions, and integrated electrode structures. 6CCVD is uniquely positioned to supply the necessary MPCVD diamond components.

Applicable Materials

To replicate or extend this research into a functional detector, the highest quality diamond is essential for maximizing charge collection efficiency and minimizing background noise.

Recommended Material: Optical Grade Single Crystal Diamond (SCD).
- Justification: SCD offers the lowest defect density, ensuring high charge carrier mobility and long carrier lifetimes necessary for efficient transport of the 13 eV electron-hole pairs across the bulk material, as required for low-energy detection.

Customization Potential

6CCVD’s advanced MPCVD growth and fabrication capabilities directly address the engineering needs of solid-state detectors.

Detector Requirement	6CCVD Solution & Capability	Technical Advantage
Bulk Detector Dimensions	Custom SCD Plates/Wafers	We supply SCD material with thicknesses ranging from 0.1 µm up to 500 µm, and can provide PCD plates up to 125 mm in diameter for large-area arrays.
High-Quality Surface Finish	Precision Polishing (Ra < 1 nm)	Ultra-smooth surfaces on SCD are critical for minimizing surface leakage currents and noise, enhancing the signal-to-noise ratio for low-energy ionization events.
Electrode Integration	Custom Metalization Services	We offer in-house deposition of standard detector contacts, including Au, Pt, Pd, Ti, W, and Cu, allowing researchers to define precise electrode geometries for optimal charge collection.
Specific Crystal Orientation	Custom SCD Growth	We provide SCD substrates and films grown along specific crystallographic orientations, which may be optimized for directional detection sensitivity.

Engineering Support

The theoretical complexity of the Migdal effect and the practical challenges of realizing a high-sensitivity detector necessitate expert material consultation.

In-House Expertise: 6CCVD’s in-house PhD team specializes in the electronic and optical properties of MPCVD diamond. We can assist researchers in selecting the optimal material grade (e.g., nitrogen concentration, defect control) and geometry for similar Dark Matter Detection projects.
Process Optimization: We provide consultation on post-processing steps, including annealing and surface termination, to maximize charge collection distance and detector performance based on the specific requirements of the Migdal effect readout.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Recent studies have theoretically investigated the atomic excitation and\nionization induced by the dark matter (DM)-nucleus scattering, and it is found\nthat the suddenly recoiled atom is much more likely to excite or lose its\nelectrons than expected. Such phenomenon is called the “Migdal effect”. In this\npaper, we extend the established strategy to describe the Migdal effect in\nisolated atoms to the case in semiconductors under the framework of\ntight-binding (TB) approximation. Since the localized aspects of electrons are\nrespected in form of the Wannier functions (WFs), the extension of the existing\nMigdal approach for isolated atoms is much more natural, while the extensive\nnature of electrons in solids is reflected in the hopping integrals. We take\ndiamond target as a concrete proof of principle for the methodology, and\ncalculate relevant energy spectra and projected sensitivity of such diamond\ndetector. It turns out that our method as a preliminary attempt is practically\neffective.\n

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevd.102.043007