When an electron -- or quasiparticle -- in a material scatter off an external impurity potential, interference between the scattered waves generates characteristic patterns in local density of states (LDOS) in real-space which resemble Friedel oscillations. By analyzing the real-space modulation of the LDOS in Fourier space (see picture), useful information about the band structure and dominant scattering processes (which are often detrimental for the electrical and optical material properties) can be obtained.
Experimentally, measurements of the real-space modulation of the LDOS are performed on surfaces via Scanning Tunneling Spectroscopy (STS). For a two-dimensional (2D) material like, e.g., graphene, the surface is basically the bulk of the material, and in this case, STS allows to probe the quasiparticle properties important for device applications etc (see, e.g., Ref. ).
The newest generation of graphene devices are build as socalled van der Waals (vdW) heterostructures where graphene is sandwiched between other types of 2D materials, such as, e.g., hexagonal Boron Nitride (h-BN). In such structures, the small mismatch in the lattice constant between graphene and h-BN leads to the formation of Moiré superlattices (see picture) which give rise to new and unexpected changes in the electronic structure of graphene.
The purpose of this project is to develop a suitable model for such Moiré superlattices within a tight-binding scheme and study their impact on STS spectra for graphene in both real and Fourier space. The calculation of the STS spectra proceeds via the Green's function of the system , which must take into account the details of the Moiré lattice. In addition, the combined effect of Moiré lattice and atomic-scale defects  as well as other exciting 2D materials (silicene, phosphorene, ...) may be investigated.
Altogether, the project will familiarize the student with advanced electronic-structure and quantum-transport theory as well as their practical implementations, and it will provide a solid platform for further courses (e.g., 33206) and projects in this direction.
 Energy-Dependent Chirality Effects in Quasifree-Standing Graphene, Phys. Rev. Lett. 118, 116401 (2017).
 Symmetry-forbidden intervalley scattering by atomic defects in monolayer transition-metal dichalcogenides, Phys. Rev. B 96, 241411(R) (2017) [attached for download].
Condensed matter physics