Mie scattering analog in graphene: Lensing, particle confinement, and depletion of Klein tunneling

Abstract

Guided by the analogy to Mie scattering of light on small particles we show that the propagation of a Dirac-electron wave in graphene can be manipulated by a circular gated region acting as a quantum dot. Large dots enable electron lensing, while for smaller dots resonant scattering entails electron confinement in quasibound states. Forward scattering and Klein tunneling can be almost switched off for small dots by a Fano resonance arising from the interference between resonant scattering and the background partition.

Electron dynamics in graphene with gate-defined quantum dots

“…In this regime resonances in the conductance [7,8] and the scattering cross section [9] indicate quasibound states at the dot. Indeed, electrons can be confined in a circular dot surrounded by unbiased graphene as the classical electron dynamics in the dot is integrable and the corresponding Dirac equation is separable [7,10].…”

“…Figure 2 shows our results for E/V < 1 (entailing negative refractive index). For comparison with the continuum model for plane wave scattering, we plot in the upper panel the scattering efficiency Q, that is the scattering cross section divided by the geometric cross section, calculated in the Dirac approximation (for details of the calculation see [9]). A series of resonances a m appears in Q, due to the excitation of normal modes of the dot.…”

Tuning a circular p–n junction in graphene from quantum confinement to optical guiding

“…But, while Klein-tunneling is responsible for the high mobility resulting from the suppression of backscattering, it also makes it difficult to control or shut off carrier-motion, to the detriment of electronic switching. We show that it is possible to control the charge-carriers with a circular p-n junction consisting of a central region acting as a circular potential barrier 22,23 . The junction is created by combining a planar back-gate with a top-gate consisting of an Au decorated tip and it can be continuously tuned from the nanometer to the micrometer scale.…”

“…Its radius, , grows with increasing and diverges at the bulk charge-neutrality point, beyond which it disappears. In graphene the reflection of electrons at a p-n junction is governed by Klein scattering which, for certain oblique angles, can produce perfect reflection 19,23 . As a result, the cavity can support…”

Dirac model of electronic transport in graphene antidot barriers

“…It has previously been shown that the DE on this form can be used to calculate the band structure of GALs [11,12]. In addition, the DE has previously been used to calculate scattering of Dirac electrons on a single circular mass barrier [32], a single circular electrostatic barrier [33] and simple barriers of constant and finite mass [34]. The advantages of our approach are that it works for any antidot shape and for an arbitrary arrangement of antidots.…”