Scattering in graphene quantum dots under generalized uncertainty principle

Abstract

In this article, the Dirac electron scattering problem on circular barrier of radius [Formula: see text] is studied under the generalized uncertainty principle (GUP). The expressions of scattering coefficients, scattering cross-section and scattering efficiency of massless Dirac particle are obtained by solving the massless Dirac equation under GUP and discussed by numerical methods. It shows that the scattering coefficient, the scattering cross-section, and the scattering efficiency depend explicitly on the GUP parameter [Formula: see text]. For the scattering coefficient [Formula: see text], GUP may cause slight shift in the oscillation position of [Formula: see text] and make some peaks value of [Formula: see text] smaller. For scattering cross-section and scattering efficiency, GUP may also lead to slight shift in their oscillation position and increase of amplitude when the GUP parameter increases.

Quantum Dot Scattering in Monolayer Molybdenum Disulfide

“…However, when ρ grows, the scattering efficiency Q roughly linearly until it reaches a maximum value Q max ¼ 2:9 relates to a certain value of ρ. Furthermore, by raising ρ and for the four energy levels, the four curves display oscillating attitude [35]. In this domain (ε > U), we find attitudes of symmetry Q (Q Àτ, s z ðÞ ¼ Q τ, Às z ðÞ ) with regard to s z and τ comparable with those of the previous domain (ε < U).…”

Scattering in Monolayer Molybdenum Disulfide Quantum Dot

“…We observe that for zero energy or close to zero energy all scattering coefficients are zero except the case corresponding to m = 0. Also, by increasing the energy the scattering coefficients |c m | 2 tend to oscillatory behavior [35]. We can see that the application of the spin-orbit interaction leads to an increase in the number of oscillations.…”

“…As the radius R increases, the height of the peak is reduced but its width becomes larger which shows the peculiarity of the energy dispersion becomes apparent. Moreover, by comparing Figures 2(a Q max = 2.9 corresponds to a specific value of R. However, by increasing R and for the four values of energy, the four curves are exhibits oscillatory behavior [35]. In this regime (E > V ), we find behaviors of symmetry Q (Q(−τ, s z ) = Q(τ, −s z )) with respect to s z and τ similar to those of the preceding regime (E < V ).…”

Electron flow in Monolayer Molybdenum Disulfide Quantum Dot with Magnetic Flux

“…In figures 2(c) and 2(d), we show the scattering efficiency Q as a function of the radius of the quantum dot R, for the quantum states (spin-up (↑), τ = ±1, φ = 3/2) and (spin-down (↓), τ = ±1, φ = 3/2), with E = 0.01 and V = 1. The scattering efficiency Q has a sharply damped oscillatory behaviour with the appearance of sharp transverse resonant peaks [29], As the radius R increases, the height of the peak decreases but its width becomes larger, which shows that the peculiarity of the energy dispersion becomes apparent. Moreover, by comparing figures 2(a) and 2(b) with figures 2(c) and 2(d), we find that the dependence of Q for the spin-up (↑) and spin-down (↓) states in the two valleys ±τ depends sharply on φ, as a consequence, the resonance peak height decreases when φ increases and the resonance peak width increases when φ increases vice versa.…”

“…By focusing on the reflected wave, from (29) we show that the corresponding radial current can be written as…”