A natural broad energy germanium detector is operated in the China Jinping Underground Laboratory for a feasibility study of building the next generation experiment of the neutrinoless double-beta ($0\nu \beta \beta$) decay of ${}^{76}\mathrm{Ge}$. The setup of the prototype facility, characteristics of the broad energy germanium detector, background reduction methods, and data analysis are described in this paper. A background index of $6.4\times {10}^{-3}\mathrm{counts}/(\mathrm{keV}\mathrm{kg}\mathrm{day})$ is achieved and 1.86 times lower than our previous result of the CDEX-1 detector. No signal is observed with an exposure of 186.4 kg day, thus a limit on the half life of ${}^{76}\mathrm{Ge}$ $0\nu \beta \beta$ decay is set at ${\mathrm{T}}_{1/2}^{0\nu }>5.62\times {10}^{22}\mathrm{yr}$ at 90% C.L. The limit corresponds to an effective Majorana neutrino mass in the range of 4.6–10.3 eV, dependent on the nuclear matrix elements.

• Received 25 May 2022
• Revised 27 July 2022
• Accepted 4 August 2022

DOI:https://doi.org/10.1103/PhysRevD.106.032012