Broken-symmetry states at half-integer band fillings in twisted bilayer graphene

The dominance of Coulomb interactions over kinetic energy electrons in narrow, non-trivial moir\'{e} bands magic-angle twisted bilayer graphene (TBG) gives rise to a variety correlated phases such as insulators, superconductivity, orbital ferromagnetism, Chern insulators and nematicity. Most these occur at or near an integer number carriers per unit cell. Experimental demonstration ordered states fractional band-fillings zero applied magnetic field $B$, is challenging pursuit. In this letter, we report the observation half-integer $\nu\approx 0.5$ $\pm3.5$ $B\approx 0$ TBG proximitized by tungsten diselenide (WSe$_2$) through magnetotransport thermoelectricity measurements. A series Lifshitz transitions due changes topology Fermi surface implies evolution van Hove singularities (VHSs) diverging density (DOS) discrete set partial fillings flat bands. Furthermore, band filling $\nu\approx-0.5$, symmetry-broken insulator emerges high compatible with structure calculations within translational supercell twice area original Our results are consistent spin/charge wave ground state $B$-field limit.