This study investigates the correlated insulator behavior at half-filling in magic-angle twisted bilayer graphene (TwBLG). By twisting two graphene layers at an angle close to the theoretically predicted "magic angle," the researchers observed a flat band structure near charge neutrality, which leads to a strongly correlated electronic system. These flat bands exhibit half-filling insulating phases at zero magnetic field, which are identified as Mott-like insulators due to electron localization in the moiré superlattice. The unique properties of TwBLG open up new possibilities for studying exotic many-body quantum phases in a 2D carbon-based system without the need for an external magnetic field. The flat bands in TwBLG arise from the moiré pattern created by the lattice misorientation of the twisted layers. This pattern results in a long-range modulation that can create a fractal energy spectrum in a strong magnetic field. The interlayer hybridization in the twisted layers modulates the band structure, allowing for the generation of band gaps and band curvatures otherwise absent in the graphene bands. Theoretical calculations predict the existence of flat bands in TwBLG, and experimental results confirm that when the twist angle is close to the magic angle, the interlayer hybridization induces nearly-flat low-energy bands. The low-energy band structure of TwBLG can be considered as two sets of monolayer graphene Dirac cones rotated about the Γ point by the twist angle θ. The difference between the two K (or K') wave vectors gives rise to the mini Brillouin zone (MBZ), which is reciprocal to the moiré superlattice. The Dirac cones near the same valley mix through interlayer hybridization, while interactions between distant Dirac cones are exponentially suppressed. As a result, the valley remains a good quantum number. The theoretically calculated "magic angles" θ_magic^(i) are a series of twist angles at which the Fermi velocity at the Dirac points becomes zero. The resulting low-energy bands near these twist angles are confined to less than about 10 meV. These phenomena can be qualitatively understood from the competition between the kinetic energy and interlayer hybridization energy. The first magic angle θ_magic^(1) is approximately 1.1°, and the labeled flat bands have a bandwidth of 12 meV for the E > 0 branch and 2 meV for the E < 0 branch. The study also demonstrates that the half-filling insulating phases (HFIPs) occur at a narrower density range near half of the superlattice density. These insulating states have a much smaller energy scale and are markedly different from other zero-field insulating behaviors previously reported. The HFIPs are observed at roughly the same density for all four devices and exhibit a much smaller thermal activation gap compared to the superlattice gaps. The emergence of HFIPs is not expected in a single-particle pictureThis study investigates the correlated insulator behavior at half-filling in magic-angle twisted bilayer graphene (TwBLG). By twisting two graphene layers at an angle close to the theoretically predicted "magic angle," the researchers observed a flat band structure near charge neutrality, which leads to a strongly correlated electronic system. These flat bands exhibit half-filling insulating phases at zero magnetic field, which are identified as Mott-like insulators due to electron localization in the moiré superlattice. The unique properties of TwBLG open up new possibilities for studying exotic many-body quantum phases in a 2D carbon-based system without the need for an external magnetic field. The flat bands in TwBLG arise from the moiré pattern created by the lattice misorientation of the twisted layers. This pattern results in a long-range modulation that can create a fractal energy spectrum in a strong magnetic field. The interlayer hybridization in the twisted layers modulates the band structure, allowing for the generation of band gaps and band curvatures otherwise absent in the graphene bands. Theoretical calculations predict the existence of flat bands in TwBLG, and experimental results confirm that when the twist angle is close to the magic angle, the interlayer hybridization induces nearly-flat low-energy bands. The low-energy band structure of TwBLG can be considered as two sets of monolayer graphene Dirac cones rotated about the Γ point by the twist angle θ. The difference between the two K (or K') wave vectors gives rise to the mini Brillouin zone (MBZ), which is reciprocal to the moiré superlattice. The Dirac cones near the same valley mix through interlayer hybridization, while interactions between distant Dirac cones are exponentially suppressed. As a result, the valley remains a good quantum number. The theoretically calculated "magic angles" θ_magic^(i) are a series of twist angles at which the Fermi velocity at the Dirac points becomes zero. The resulting low-energy bands near these twist angles are confined to less than about 10 meV. These phenomena can be qualitatively understood from the competition between the kinetic energy and interlayer hybridization energy. The first magic angle θ_magic^(1) is approximately 1.1°, and the labeled flat bands have a bandwidth of 12 meV for the E > 0 branch and 2 meV for the E < 0 branch. The study also demonstrates that the half-filling insulating phases (HFIPs) occur at a narrower density range near half of the superlattice density. These insulating states have a much smaller energy scale and are markedly different from other zero-field insulating behaviors previously reported. The HFIPs are observed at roughly the same density for all four devices and exhibit a much smaller thermal activation gap compared to the superlattice gaps. The emergence of HFIPs is not expected in a single-particle picture