Sharif Digital Repository

Beenakker noticed that the peculiar band structure of Dirac fermions in two-dimensional (2D) solids allows for the specular Andreev reflection in these systems, which has no analogue in other 2D electron systems. An interesting deformation of the Dirac equation in the solid state is to tilt it, which has now been realized in materials. In this paper we report another peculiar feature of the Andreev reflection in tilted 2D Dirac cone systems. The tilt deformation of the Dirac equation is characterized by two parameters ζ=ζ(cosθ,sinθ). We show that when the tilt parameter is tuned to its "horizon value" ζ=1, irrespective of the incidence angle of electrons, the Andreev reflected hole is always... 

In a graphene-based Josephson junction, the Andreev reflection can become specular, which gives rise to propagating Andreev modes. These propagating Andreev modes are essentially charge neutral and therefore they transfer energy but not electric charge. One main result of this work is that when the Dirac theory of graphene is deformed into a tilted Dirac cone, the breaking of charge conjugation symmetry of the Dirac equation renders the resulting Andreev modes electrically charged. We calculate an otherwise zero charge conductance arising solely from the tilt parameters ζâ -=(ζx,ζy). The distinguishing feature of such a form of charge transport from the charge transport caused by normal...