Emergence of broken-symmetry states at half-integer band fillings in twisted bilayer graphene

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