Helical trilayer graphene (HTG) consists of three layers of graphene with successive layers twisted by the same relative angle, resulting in two moire patterns with different orientations. Although HTG is globally C_2z-symmetric, lattice relaxations form large periodic domains where C_2z is broken on the moire scale, resulting in a spatial mosaic of Chern domains. Because domains have valley-contrasting Chern numbers, a network of topological gapless 1D states forms at their boundaries. When the graphene layers are twisted at a magic angle of 1.8 degrees, these topological bands become flat and a rich phase diagram of correlated states emerges, as was recently uncovered. 

Here, we will explore new physics in HTG that arise in finite fields. First, we discuss a special scenario where the network of gapless edge states is no longer topologically protected, leading to the apparent formation of a robustly quantized field-induced Chern insulator. Second, we discuss evidence of possible nematic order at specific integer filling states. These additional findings further highlight HTG as a platform for exploring both strongly correlated and topological phases.