## 4 Conclusions  
We presented an extension to the wave packet dynamical method, where the initial wave packet is constructed from the numerically calculated quasiparticle Bloch states of the pseudopotential that represents the physical system. This method makes it possible to fine-tune the spectral distribution of the initial wave packet and thus to investigate the details of the scattering processes and the nanoscale transport phenomena for different scenarios. The method was applied for a structural defect on a graphene surface, where we studied the scattering of the Bloch function wave packet on the local defect. A hexagonal scattering pattern was seen associated with intervalley scattering. Then we calculated the wave packet time evolution by a second method, where the properties of the infinite crystal (its atomic- and electronic structure) are coded into the kinetic energy operator and the properties of the local defect are represented by a local potential. We show that the hexagonal spreading pattern is already present for the pristine graphene, where the initial wave packet is spatially well localized. This initial WP represents a physical system, where the electrons are injected locally into the graphene surface as in the case of an STM imaging process. We found an anisotropic (hexagonal) scattering pattern emerging even for an isotropic potential, similar to the applied pseudopotential case. The advantage of the method is that it does not require the calculation of a pseudopotential. The only input necessary to represent the infinite crystal is its \(E\bigg{(}\overset{\rightarrow}{k}_{Bloch}\bigg{)}\) band structure, available from, for example, a simple DFT calculation.  
Our extended wave packet dynamical method clearly demonstrated the possibilities to investigate defects in different 2D materials, which serve as a new platform to better understand the basic mechanism of quasiparticle scattering processes at the atomic scale. We intend to apply this method for TMDC materials [35; 36; 37], where the strong spin-orbit coupling leads to large spin splitting with opposite spin directions of the \(K\) and \(K^{\prime}\) valleys, further modifying the possible scattering processes. Another possible application of our method is related to twisted bilayers [38; 39], where symmetry-breaking correlation effects might take place, which have important consequences on the QPI patterns. In all cases, the scattering processes calculated by the wave packet dynamical method and their comparison with the measured QPI patterns by using STM will provide useful information to the application of 2D materials in nanodevices.  
**Supplementary Materials:** The following are available online at [[https://www.mdpi.com/article/10.3390/app11114730/s1](https://www.mdpi.com/article/10.3390/app11114730/s1)]([https://www.mdpi.com/article/10.3390/app11114730/s1](https://www.mdpi.com/article/10.3390/app11114730/s1)), Video S1: time development of a Bloch function wave packet on the graphene surface.  
Conceptualization, G.I.M. and P.V., methodology, software, G.I.M.; STM experiment, P.N.-I., writing--original draft preparation, G.I.M., A.M. and P.V. All authors have read and agreed to the published version of the manuscript.  
The work was supported by the European H2020 GrapheneCore3 Project No. 881603, Graphene Flagship, the NanoFab2D ERC Starting Grant and the Hungarian National Research, Development and Innovation Office (Grant No. KH130413). P.V. acknowledges the support of the Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences. A.M. is funded by the Fund for Scientific Research (F.R.S.-FNRS) of Belgium. P.N.-I. acknowledges support from the Hungarian Academy of Sciences, Lendulet Program, Grant No. LP2017-9/201.  
The authors declare no conflict of interest.