One of the most remarkable feats achieved with a scanning tunneling microscope, in addition to the possibility to visualize material surfaces with atomic resolution, was the possibility to image the standing waves associated with the interference of quasi-free electron wave functions. In this talk we present the scanning tunneling microscopy technique and the different method to use this technique. We will give an overview of the use of standing waves pattern around specific defects with the technique of Fourier Transform Scanning Tunneling Spectroscopy (FT-STS) allowing the local determination of Fermi surface, band structures [1]. In the case of free electrons at the surface of metal and then on 2D systems such as graphene functionalized with different methods [2-5]. The band structure of graphene and other types of Dirac Fermion will be also explained.

[1] L. Simon et al J. Phys. D : Appl. Phys. 44 (2011) 464010

[2] L Daukiya et al Review Article Progress in Surface Science (in press)

[3] M. Nair Phys. Rev. B 94 (2016) 075427

[4] L. Daukiya et al ACS Nano, (2017), 11 (1), 627–634

[5] L. Daukiya et al Phys. Rev. B 97, 035309 (2018)