Scattering of two-dimensional Dirac fermions on gate-defined oscillating quantum dots

Abstract

Within an effective Dirac-Weyl theory we solve the scattering problem for massless chiral fermions impinging on a cylindrical time-dependent potential barrier. The set-up we consider can be used to model the electron propagation in a monolayer of graphene with harmonically driven quantum dots. For static small-sized quantum dots scattering resonances enable particle confinement and interference effects may switch forward scattering on and off. An oscillating dot may cause inelastic scattering by excitation of states with energies shifted by integer multiples of the oscillation frequency, which significantly modifies the scattering characteristics of static dots. Exemplarily the scattering efficiency of a potential barrier with zero bias remains finite in the limit of low particle energies and small potential amplitudes. For an oscillating quantum dot with finite bias, the partial wave resonances at higher energies are smeared out for small frequencies or large oscillation amplitudes, thereby dissolving the quasi-bound states at the quantum dot.

Imaging electrostatically confined Dirac fermions in graphene quantum dots

“…Due to Klein tunneling, a graphene pn junction perfectly transmits quasiparticles at normal incidence to the boundary but reflects them at larger angles of incidence 1,4,5 . In a potential well with circular symmetry electrons with high angular momenta are obliquely incident on the barrier and are internally reflected, thus leading to particle confinement and the formation of quasi-bound quantum dot states [19][20][21][22][23][24] . As angular momentum is increased, electrons are repelled from the center of the potential by the centrifugal barrier, leading to an increase in the number of dI/dV s resonances that should be observable in spectroscopy measured away from the center 30 .…”

Numerical study of Klein quantum dots in graphene systems

“…In most of the previous theoretical studies, the quasibound states are obtained by solving continuous Dirac equation under potential U , where only one valley is considered. The intervalley scattering, which is inevitable in experiments, is neglected [29][30][31][32][33][34][35] . However, such different treatment in theory and experiment actually lead to the same results, which has puzzled physicists for a long time [19][20][21] .…”

“…It is worth to note that the decreasing of hopping energy can cause strong intervalley scattering, which is discovered in Dirac systems 36 . Nevertheless, the effects of hopping term are not considered in previous graphene KQD studies [29][30][31][32][33][34][35] . Therefore, we consider the situation that both hopping t and potential U take hyperbolic form, say, t = t 1 (1 − | tanh r−R S |) and U = V 2(1−tanh r−R S ) in the boundary region, respectively, where t 1 is the hopping strength.…”

“…During the numerical calculations, the hopping energy between nearest neighbor sites in a pristine graphene denoted by t is set as the energy unit. Comparing to the previous analytic methods [29][30][31][32][33][34][35] , the intervalley scattering is included in our numerical calculations. Moreover, our method is applicable for any type of confined potential, thus can be applied to KQD with arbitrary geometry.…”

Excitonic physics in a Dirac quantum dot

“…[18][19][20]. Similarly, the circular geometry leads to quasi-bound states [21][22][23][24][25][26], and may even lead to bound states if a confining potential enters as a mass term in the Dirac equation [27]. Here we will use the circular set-up with a confining mass term that was used in Ref.…”