Energy Loss Due to Defect Formation from ${}^{206}$Pb Recoils in SuperCDMS Germanium Detectors

The Super Cryogenic Dark Matter Search experiment (SuperCDMS) at the Soudan Underground Laboratory studied energy loss associated with Frenkel defect formation in germanium crystals at mK temperatures using in situ ${}^{210}$Pb sources. We examine the spectrum of ${}^{206}$Pb nuclear recoils near its expected 103 keV endpoint energy and determine an energy loss of $(6.08\pm 0.18)$ %, which we attribute to defect formation. From this result and using TRIM simulations, we extract the first experimentally determined average displacement threshold energy of $\left(19.7_{-0.5}^{+0.6}\right)$ eV for germanium. This has implications for the analysis thresholds of future germanium-based dark matter searches.