Fully spin-polarised quantum Hall effect at sub-tesla magnetic fields

The integer quantum Hall effect provides one of the most precise and robust manifestations of topological quantum transport. Yet, in semiconductor systems, its development to a fully spin-polarised state typically requires magnetic fields of several tesla and milli-Kelvin temperatures to overcome disorder, Landau-level broadening, and thermal smearing. Here we report a fully spin-polarised ν = 1 quantum Hall state in a two-dimensional (2D) hole gas hosted in a compressively strained germanium quantum well grown on silicon, stabilised at magnetic fields as low as 0.25 - 0.3 T and temperatures up to 1.5 K. This unusually low-field quantisation is enabled by an ultra-dilute carrier regime combined with extremely large Zeeman energy that approaches the cyclotron energy of free carriers over a wide density range, resulting in dominant spin splitting of Landau levels at sub-tesla fields to reach ν= 1 fully spin-polarized quantum limit. Magnetotransport and 2D Landau-fan measurements demonstrate that Landau-level broadening remains smaller than the spin splitting throughout the whole magnetic field range down to 0.25 mT, allowing robust quantisation of the Hall resistance at h/e ². These results establish access to an experimentally unexplored regime of spin-polarised quantum Hall physics in a semiconductor platform and open new opportunities for exploring exchange-driven and correlated many-body states of dilute systems in small magnetic fields.