Reconfigurable flat bands from cooperative moir\'e and charge order
The formation of flat electronic bands from long-wavelength superperiodic moir\'e potentials in van der Waals heterostructures underpins the creation and control of a host of highly-tunable correlated and topological phases. While the underlying moir\'e periodicity is typically a fixed property of the heterostructure, here we show how the development of a charge-density wave (CDW) in one of the constituent materials can create an emergent moir\'e lattice. We demonstrate this experimentally in TiSe$_2$/graphite epitaxial heterostructures, using angle-resolved photoemission and scanning-tunnelling microscopy and spectroscopy to directly image the resulting long-wavelength moir\'e potential and concomitant flat-band formation. We show how the intrinsically low-energy, deformable landscape of the CDW imparts significant tunability, stabilising quasi-one-dimensional moir\'e domains from symmetry breaking within the CDW, and allowing the complete suppression of flat-band formation by carrier doping across the CDW phase transition. Our findings thus open a new avenue for engineering moir\'e matter by exploiting the rich many-body states of the parent compounds of 2D heterostructures.