Conductivity freeze-out in isotopically pure Si -28 at millikelvin temperatures

Silicon is a key semiconducting material for electrical devices and hybrid quantum systems where low temperatures and zero-spin isotopic purity can enhance quantum coherence. Electrical conductivity in $\mathrm{Si}$ is characterized by carrier freeze out at around 40 K allowing microwave transmission, which is a key component for addressing spins efficiently in silicon quantum technologies. In this work, we report an additional sharp transition of the electrical conductivity in a $\mathrm{Si}$-28 cylindrical cavity at around 1 K. This is observed by measuring microwave resonator whispering gallery mode frequencies and $Q$ factors with changing temperature and comparing these results with finite-element models. We attribute this change to a transition from a relaxation mechanism-dominated to a resonant phononless absorption-dominated hopping conduction regime. Characterizing this regime change represents a deeper understanding of a physical phenomenon in a material of high interest to the quantum technology and semiconductor device community and the impact of these results is discussed.