Generalized WKB theory for electron tunneling in gapped α - T3 lattices

We generalize Wentzel-Kramers-Brillouin (WKB) semiclassical equations for pseudospin-1 alpha - T-3 materials with arbitrary hopping parameter 0 < alpha < 1, which includes the dice lattice and graphene as two limiting cases. In conjunction with a series-expansion method in powers of Planck constant h, we acquired and solved a system of recurrent differential equations for semiclassical electron wave functions in alpha - T-3. Making use of these obtained wave functions, we analyzed the physics-related mechanism and quantified the transmission of pseudospin-1 Dirac electrons across nonrectangular potential barriers in alpha - T-3 materials with both zero and finite band gaps. Our studies reveal several unique features, including the way in which the electron transmission depends on the energy gap, the slope of the potential barrier profile and the transverse momentum of incoming electrons. Specifically, we have found a strong dependence of the obtained transmission amplitude on the geometry-phase phi = tan(-1) alpha of alpha - T-3 lattices. We believe our current findings can be applied to Dirac cone-based tunneling transistors in ultrafast analog RF devices, as well as to tunneling-current control by a potential barrier through a one-dimensional array of scatters.

Automated summary

The study generalizes the WKB semiclassical equations for pseudospin-1 alpha-T-3 materials and analyzes the transmission properties of electrons in these materials, investigating their relationships with energy gap, potential barrier slope, and electron transverse momentum. The results reveal a strong dependence of the transmission amplitude on the geometric phase of the material.