Abstract
We investigate the tunneling of pseudospin-1 and pseudospin-3/2 quasiparticles through a barrier consisting of both electrostatic and vector potentials, existing uniformly in a finite region along the transmission axis. First, we find the tunneling coefficients, conductivities and Fano factors in the absence of the vector potential. Then we repeat the calculations by switching on the relevant magnetic fields. The features show clear distinctions, which can be used to identify the type of semimetals, although both of them exhibit linear band crossing points.
Highlights
We investigate the tunneling of pseudospin-1 and pseudospin-3/2 quasiparticles through a barrier consisting of both electrostatic and vector potentials, existing uniformly in a finite region along the transmission axis
In order to study transport, the 3d system is modulated by a scalar potential barrier of strength V0 and width L, resulting in an x-dependent potential energy function: V (x) = V0 for 0 < x < L 0 otherwise
We subject the sample to equal and opposite magnetic fields localized at the edges of the rectangular electric potential, and directed perpendicular to the x-axis.[11,12]. This can be theoretically modeled as Dirac delta functions of opposite signs at x = 0 and x = L respectively, and gives rise to a vector potential with the components: A(x) ≡ {0, Ay, Az} =
Summary
In order to study transport, the 3d system is modulated by a scalar potential barrier (giving rise to an electric field) of strength V0 and width L, resulting in an x-dependent potential energy function:. Some possible methods to achieve this set-up in real experiments (for instance, by placing ferromagnetic stripes at barrier boundaries) have been discussed in Ref. 11. The longitudinal direction corresponds to transport along the x-axis, and for this we need to consider plane wave solutions of the form ei kxx. Given an arbitrary mode of transverse momentum k⊥, we can determine the x-component of the wavevectors of the incoming, reflected, and transmitted waves (denoted by k ), by solving ε+(kx, n) = E. We need to use the piece-wise solutions for the wavefunction (Ψ), applicable in the regions in question (inside or outside the potential barrier). We need to use the boundary conditions to determine the reflection and transmission coefficients.
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