Abstract
Electrical confinement in a spectrum of two-dimensional Dirac materials with classically integrable, mixed, and chaotic dynamics
Highlights
There has been tremendous development of research on two-dimensional (2D) Dirac materials since the experimental realization of graphene [1,2,3,4]
Can confinement be achieved in more general cavities with their geometrical shape deformed from the circular shape, such as the elliptical cavity with mixed classical dynamics or the stadium-shaped chaotic cavity? (There is quantum chaotic scattering [84,85,86,87,88,89] in this case.) For pseudospin-1/2 particles, previous studies based on the method of finite-domain scattering revealed that confinement modes can exist in the stadium cavity [90,91,92,93]
Taking advantage of a recently developed computational method [94] for pseudospin-1 particles based on the multiple multipole (MMP) method in optics [95,96,97,98,99], we have developed an efficient computational method [94] to solve the spinor wave functions associated with the scattering of α-T3 particles from an arbitrary geometric domain (Appendix E)
Summary
There has been tremendous development of research on two-dimensional (2D) Dirac materials since the experimental realization of graphene [1,2,3,4]. Such a structure can be generated by a STM (scanning tunneling microscope) tip induced potential [34,38,39,40] or through the method of doping [41]. The main finding of this paper is that, in the quantumdot regime, among the possible α-T3 materials, the strongest or optimal confinement occurs for hybrid materials in between the pseudospin-1/2 and pseudospin-1 limits but near the graphene end, i.e., for some value of α 0 This result holds for the perfectly circular cavity with classical integrable dynamics and for deformed cavities with mixed or chaotic dynamics in the classical limit. Confinement is still possible, which can be characterized by physically measurable quantities such as the magnetic moment
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