General formulas for calculating the ballistic conductance of two-dimensional Dirac materials

One important electrical quantity in devices is the conductance; for systems on the mesoscopic scale and nanoscale, the conductance is given by the Landauer-Buttiker formalism. In this paper, by using the minimal Weyl Hamiltonian, a theoretical study on the ballistic conductance of two-dimensional (2D) Dirac materials is carried out, with the aim of deriving properties of the ballistic conductance. In addition, formulas for calculating and comparing the ballistic conductance of Dirac materials with diverse cones are given. Our study reveals that the ballistic conductance can be both isotropic and anisotropic, depending on the values of the Dirac cone characteristics (i.e., the anisotropy and tilt). The effects of the anisotropy and tilt of the Dirac cone on the ballistic conductance are investigated in detail. For the right Dirac cone, we show that the ballistic conductance in the x direction does not depend on the strength of the anisotropy of Dirac cone, while the ballistic conductance in the y direction varies inversely with the strength of anisotropy. We find that the ballistic conductance of the oblique Dirac cone is greater than that of the right Dirac cone. Also, when the strength of tilt increases, that is, when the Dirac cone becomes more tilted, the ballistic conductance rises. We also investigate symmetry properties of the ballistic conductance. This paper provides a new and deeper insight into properties of the ballistic conductance from massless Dirac fermions and can be useful for designing electronic devices with desired performance.