Imaging and Controlling Pseudospin and Berry Phase of Dirac Fermions by Symmetry-Assisted Coherent Scattering

In lattice materials, the solution of the Schrödinger equation is a set of Bloch waves. The dispersion of these components defines the band structure and is crucial to electronic transport and thermodynamic properties. Scanning tunneling microscopy (STM) is a powerful tool to study electronic properties with exceptional spatial resolution. Because coherent scattering induced by impurities strongly depends on the band structure of a material, by imaging the pattern of coherent scattering, the band structure can be probed in momentum space as well. Using atom manipulation with STM, we show that the coherent scattering term can be separated from the non-scattering term. As a result, the contrast of the coherent scattering pattern is amplified and the details of the band structure of Dirac fermions in graphene, including complete Dirac cones and their trigonal warping, are revealed. Furthermore, by tuning the symmetry of the scattering center using atom manipulation, we show that pseudospin can be resolved and that a signature of the underlying Berry phase can be observed. The results indicate that the interplay of the symmetry of wave functions and that of a single scattering center provides a new way to image and control the internal degrees of freedom of quantum matter.