Developing a semiclassical Wentzel-Kramers-Brillouin theory for $\alpha -{\mathcal{T}}_3$ model

Abstract

We have developed a complete semiclassical Wentzel-Kramers-Brillouin (WKB) theory for $\alpha -{\mathcal{T}}_3$ model which describes a wide class of existing pseudospin-1 Dirac cone materials. By expanding the sought wave functions in a series over the powers of Planck constant $\hslash$, we have obtained the leading order expansion term which is the key quantity required for calculating the electronic and transport properties of a semiclassical electron in $\alpha -{\mathcal{T}}_3$. We have derived the transport equations connecting each two consecutive orders of the wave function expansion and solved them to obtained the first order WKB wavefunction. We have also discussed the applicability of the obtained approximation and how these results could be used to investigate various tunneling and transport properties of $\alpha -{\mathcal{T}}_3$ materials with non-trivial potential profiles. Our results could be also helpful for constructing electronics devices and transistors based on innovative flat-band Dirac materials.

17 pages, 5 figures

References in corpus (21)

• The electronic properties of graphene
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Observation of a localized flat-band state in a photonic Lieb lattice
• Observation of bound states in Lieb photonic lattices
• Hall effect of triplons in a dimerized quantum magnet
• All-optical band engineering of gapped Dirac materials
• Effect of electron-hole asymmetry on optical conductivity in 8-Pmmn borophene
• Floquet topological phase transition in $\alpha$-${\mathcal{T}}_3$ lattice
• WKB analysis of edge states in graphene in a strong magnetic field
• Electron states for gapped pseudospin-1 fermions in the field of charged impurity
• Bound states in inhomogeneous magnetic field in graphene: a semiclassical approach
• Optical properties of a semi-Dirac material
• Desiging Artificial Lieb Lattice on Metal Surface
• Dynamics of a quasiparticle in the $\alpha$-T${}_3$ model: Role of pseudospin polarization and transverse magnetic field on \textbf{\textit{zitterbewegung}}
• Anisotropic longitudinal optical conductivities of tilted Dirac bands in 1T${}^{\prime }$-MoS${}_2$
• Generalized WKB theory for electron tunneling in gapped $\alpha -{\mathcal{T}}_3$ lattices
• Gap generation and flat band catalysis in dice model with local interaction
• Many-Body Effects and Optical Properties of Single- and Double Layer $\alpha$-${\mathcal{T}}_3$ Lattices
• Interplay of Lorentz-Berry forces in position-momentum spaces for valley-dependent impurity scattering in alpha-T3 lattices
• Optical response of two-dimensional Dirac materials with a flat band
• Floquet theory of spin dynamics under circularly polarized light pulses

Cited by in corpus (1)

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