Microscopic origins of band topology and correlated states in twisted MoTe₂: Part 2

Twisted molybdenum ditelluride (tMoTe₂) exhibits integer and fractional quantum anomalous Hall (I/FQAH) states upon hole doping of its first few moiré valence bands. Additionally, an electric displacement field can be used to induce transitions from these I/FQAH states to topologically trivial correlated insulators. At fractional band fillings, the latter are thought to require charge ordering that spontaneously breaks the translational symmetry of the moiré superlattice. Understanding the competition between topological phases and trivial charge ordered states thus demands an atomic-scale probe such as scanning tunneling microscopy (STM). However, this is highly challenging owing to fundamental difficulties in independently controlling doping and displacement field in conventional STM experiments. We solve this issue by constructing devices using a graphene sensor geometry, in which electrons tunnel into an exposed graphene layer coupled to tMoTe₂ via an ultra-thin boron nitride dielectric. This enables full exploration of the doping and displacement field parameter space in tMoTe₂ while simultaneously providing sub-moiré sensitivity to potential charge orderings. Here, we present STM measurements of tMoTe₂ devices as a function of electrostatic gating and magnetic field. We show that the graphene layer acts as a local probe of the compressibility of the nearby tMoTe₂, providing a pathway for further understanding the microscopic properties of its many-body states.