Valley-dependent transmission properties of tilted massless Dirac fermions in a two-dimensional salt n − p − n junction

One of the important and fascinating issues in condensed matter physics is the transport phenomena relevant to massless Dirac fermions (MDFs). The $\ensuremath{\alpha}\text{\ensuremath{-}}\text{(}\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF}{\text{)}}₂{\mathrm{I}}₃$ salt is a two-dimensional organic material with tilted and anisotropic Dirac cones, and these tilt and anisotropy affect transport properties of MDFs. In this paper, by using a minimal Weyl Hamiltonian, we study the transport properties of MDFs in a $\ensuremath{\alpha}\text{\ensuremath{-}}\text{(}\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF}{\text{)}}₂{\mathrm{I}}₃$ based $n\text{\ensuremath{-}}p\text{\ensuremath{-}}n$ junction. The Klein tunneling is investigated and discussed in detail and we find that the Klein tunneling depends on valley and it can occur in a wide range of electron incident angles. These properties are in contrast to graphene in which the Klein tunneling is independent of valley and occurs only at zero angle (normal incident). We also show that a $\ensuremath{\alpha}\text{\ensuremath{-}}\text{(}\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF}{\text{)}}₂{\mathrm{I}}₃$-based $n\text{\ensuremath{-}}p\text{\ensuremath{-}}n$ junction can work as a perfect valley filter. This valley filter is controllable by tuning the junction parameters such as the Fermi energy and the top gate voltage. The results of this paper provide deeper insight into the transport phenomena relevant to MDFs with tilted and anisotropic cones and also can be useful in valleytronic devices.