This is a “just started” endeavour, motivated by many relevant papers, such as [1]: Chiral tunnelling and the Klein paradox in graphene, by Katsnelson, Novoselov and Geim Nature, (2006), and [2]: Klein tunnelling in graphene: optics with massless electrons, by Allain and Fuchs, EPJ (2011). I will study the solutions of the equation

where the potential U(x) is a combination of rectangular barriers and wells. Beside the fascinating occurrence of Klein tunnelling (studied mostly for a single barrier) I will also explore other aspects such as scattering from a periodic (Kronig-Penney) potential, absence of localization in the presence of disorder, and the occurrence of bound-states in symmetric potential, that is intimately related to parity transformation (which is not trivial, see e.g [3] Riazudin, arXiv: 1105.5956). For most cases, the pertinent quantities are given analytically.

Prof. Yshai Avishai is currently a Visiting Professor of Physics at NYU Shanghai. He has received many honors and awards during his academic career, including: Fellow of the American Physical Society, Divisional Associate Editor (Condensed Matter Physics) of Phys. Rev. Lett from 2008 – 2014, Former Director of the Ilse Katz Center for Nanotechnology at Ben Gurion Univeristy, and many more.