Observation of Kondo condensation in a degenerately doped silicon metal

When a magnetic moment is embedded in a metal, it captures itinerant electrons to form the Kondo cloud1,2, which can spread out over a few micrometres3,4. For a metal with dense magnetic impurities such that Kondo clouds overlap with each other, correlated ground states are formed. When the impurities form a regular lattice, the result is a heavy fermion or anti-ferromagnetic order depending on the dominant interaction5,6. Even in the case of random impurities, overlapping Kondo clouds are expected to form a coherent ground state. Here, we examine this issue by performing electrical transport and high-precision tunnelling density-of-states (DOS) spectroscopy measurements in a highly P-doped crystalline silicon metal where disorder-induced localized magnetic moments exist7. We detect the Kondo effect in the resistivity of the Si metal below 2 K and an exotic pseudogap in the DOS with gap edge peaks at a Fermi energy below 100 mK. The DOS gap and peaks are tuned by applying an external magnetic field and transformed into a metallic Altshuler-Aronov gap8 in the paramagnetic disordered Fermi liquid (DFL) phase. We interpret this phenomenon as the Kondo condensation, the formation of a correlated ground state of overlapping Kondo clouds, and its transition to a DFL. The boundary between the Kondo condensation and DFL phases is identified by analysing distinct DOS spectra in the magnetic field-temperature plane. A detailed theoretical analysis using a holographic method 9 , 10 , 11 reproduces the unusual DOS spectra, 1, supporting our scenario. Our work demonstrates the observation of the magnetic version of Bardeen-Cooper-Shrieffer (BCS) pair condensation and will be useful for understanding complex Kondo systems.