Revival resonant scattering, perfect caustics, and isotropic transport of pseudospin-1 particles

Abstract

We report drastically new physics associated with wave scattering in pseudospin-1 systems whose band structure consists of a conventional Dirac cone and a topologically flat band. First, for small scatterer size, we find a surprising revival resonant scattering phenomenon and identify a peculiar type of boundary trapping profile through the formation of unusual vortices as the physical mechanism. Second, for larger scatterer size, a perfect caustic phenomenon arises as a manifestation of the super-Klein tunneling effect, leading to the scatterer's being effectively as a Veselago lens. Third, in the far scattering field, an unexpected isotropic behavior emerges at low energies, which can be attributed to the vanishing Berry phase for massless pseudospin-1 particles and, consequently, to constructive interference between the time-reversed backscattering paths. We develop an analytic theory based on the generalized Dirac-Weyl equation to fully explain these phenomena and articulate experimental schemes with photonic or electronic systems.

Electrical confinement in a spectrum of two-dimensional Dirac materials with classically integrable, mixed, and chaotic dynamics

“…where S α denotes the generalized Pauli matrices that depend on the material parameter α. The details for solving the corresponding eigenvalue problem are presented in Appendix A. Quantum scattering from a circular cavity has been studied for graphene (α = 0) [52,54,68,69] and pseudospin-1 (α = 1) [33,70] systems. There has also been a study of scattering from a centrally symmetric potential in α-T 3 materials [16].…”

“…For graphene, due to the π/2 Berry phase, in the low-energy regime backscattering is ruled out [52,74]. For pseudospin-1 systems, scattering in the far field is isotropic [33]. What is the far-field behavior in the scattering of α-T 3 particles for 0 < α < 1?…”

“…Similar to optics [24], such a structure can be exploited for storage and energy transfer in spintronics and valleytronics [25,26]. However, even in a perfectly circular cavity generated by, e.g., an electrostatic potential, confinement of pseudospin-1/2 particles in graphene is already a nontrivial issue [27], due to the phenomenon of Klein tunneling [28][29][30][31][32][33][34]. To confine pseudospin-1 particles is also difficult, due to super-Klein tunneling [33], in which particles can penetrate through a high and wide potential barrier at any angle.…”

“…However, even in a perfectly circular cavity generated by, e.g., an electrostatic potential, confinement of pseudospin-1/2 particles in graphene is already a nontrivial issue [27], due to the phenomenon of Klein tunneling [28][29][30][31][32][33][34]. To confine pseudospin-1 particles is also difficult, due to super-Klein tunneling [33], in which particles can penetrate through a high and wide potential barrier at any angle. Confinement becomes even more difficult in realistic situations where geometric deformations from the circular shape are inevitable, which can lead to chaotic dynamics in the classical limit [35][36][37].…”

“…The geometric shape of the cavity can be chosen to generate integrable (e.g., a circle), mixed (e.g., an ellipse), or chaotic (e.g., a stadium) dynamics in the classical limit. In order to confine an electron inside the cavity, its energy should be far away from the Klein tunneling regime that occurs for E ≈ U/2 for graphene [28][29][30][31][32][33][34] and pseudospin-1 materials [33]. For the confinement problem to have physical and applied significance, we focus on the quantum-dot regime where the effect of Klein tunneling is weak [15,27,42].…”