Visualization of hidden topological properties in 2H TMDs

The orbital character of Bloch bands evolves across the Brillouin zone and is intimately connected to their topological properties. Orbital geometry also influences the real space wavefunctions of a band and their spatial structure within the atomic lattice of a solid. Wannier functions (WF) can provide a real space description of the properties of a Bloch band, capturing local properties like orbital hybridization and bonding. The WFs of insulators centered at the covalent bonds between atomic sites were recently shown to be topologically distinct from those centered at atomic sites, giving rise to the classification of “obstructed atomic insulators” (OAI). While the WFs are not observables, the electronic probability density can be mapped with sub-atomic resolution by scanning tunneling microscopy (STM). We show that STM does not image the atoms in transition metal dichalcogenide (TMD) WSe₂, indicating that the WF are localized off the atoms due to the covalent nature of their hybridized d-orbitals. We achieve this by utilizing defects to directly correlate the features in STM images with the underlying atomic lattice. We further confirm the topological character of the WSe₂ by directly mapping the charge density within the atomic lattice at different critical points in the Brillouin zone. Finally, we explore NbSe₂ as a counterexample, showing that in this case the atomic sites are imaged by STM. This work provides deeper insight into the topological properties of 2H TMDs, and demonstrates STM as a useful tool to probe the topology in materials.