Integration of Silica in G4CMP for Phonon Simulations: Framework and Tools for Material Integration

TL;DR

This work provides a complete formalism and practical toolkit to integrate new materials into G4CMP for phonon transport simulations, using silica (amorphous SiO$_2$ and $\alpha$-quartz) as a detailed case study. It derives material-specific phonon parameters from SOECs/TOECs, computes anharmonic downconversion through the Tamura framework, and models isotopic scattering, complemented by DOS calculations via Quantum Espresso and Phonopy. The authors validate the approach with phonon caustics and release Python tools, tutorials, and material parameters on the G4CMP repository to enable the community to simulate custom substrates and reduce background uncertainties in sub-eV detectors like BeEST. The work enhances the capability to perform accurate, material-specific phonon simulations in cryogenic detectors, supporting improved background modeling and detector optimization. A DOS tutorial and community-facing resources further promote reproducibility and broad adoption within the superconducting detector community.

Abstract

Superconducting detectors with sub-eV energy resolution have demonstrated success setting limits on Beyond the Standard Model (BSM) physics due to their unique sensitivity to low-energy events. G4CMP, a Geant4-based extension for condensed matter physics, provides a comprehensive toolkit for modeling phonon and charge dynamics in cryogenic materials. This paper introduces a technical formalism to support the superconducting qubit and low-threshold detector community in implementing phonon simulations in custom materials into the G4CMP. As a case study, we present the results of a detailed analysis of silica phonon transport properties relevant for simulating substrate backgrounds in Beryllium Electron capture in Superconducting Tunnel junctions (BeEST)-style experiments using G4CMP. Additionally, Python-based tools were developed to aid users in implementing their own materials and are available on the G4CMP repository.

Figures (4)

• Figure 1: Total density of states (DOS) for $\alpha$-Quartz silica (blue line). (Calculation using Quantum Espresso compared to reference (red line) calculation Togo2023SiO2MDR6922)
• Figure 2: The phonon density of states with contributions from the first three acoustic modes: longitudinal, transverse fast and transverse slow (blue, orange and green). The dashed red line corresponds to the highest possible energy of an acoustic phonon $\omega_{a}$.
• Figure 3: Top: phonon caustic image for $\alpha$-Quartz (SiO$_{2}$) obtained from G4CMP. The crystal direction [1$\bar{1}$00] is at the center of the pattern, oriented out-of-page. Bright regions indicate directions of high phonon flux. Bottom: phonon caustic image for $\alpha$-Quartz measured in Ref. KoosWolfeQuartz1984, where the crystal direction [1$\bar{1}$00] is out of page and scan range is $\pm 56^{\circ}$. The circular spot at the bottom of the image was reported as a laser aberration.
• Figure 4: Top: phonon caustic image for $\alpha$-Quartz (SiO$_{2}$) obtained from G4CMP. The crystal direction [0001] is at the center of the pattern, oriented out-of-page. Bright regions indicate directions of high phonon flux. Bottom: phonon caustic image for $\alpha$-Quartz measured in Ref. KoosWolfeQuartz1984, where the crystal direction [0001] is out of page and scan range is $\pm 56^{\circ}$.