Influence of Aharonov–Bohm flux and dual gaps on electron scattering in graphene quantum dots

Abstract

Abstract We show how the Aharonov–Bohm flux (AB) ϕ i and the dual gaps (Δ 1 , Δ 2 ) can affect the electron scattering in graphene quantum dots (GQDs) of radius r 0 in the presence of an electrostatic potential V . After obtaining the solutions of the energy spectrum, we explicitly determine the radial component of the reflected current <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>J</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> , the square modulus of the scattering coefficients ∣ c m ∣ 2 , and the scattering efficiency Q . Different scattering regimes are identified based on physical parameters such as incident energy E , V , r 0 , dual gaps, and ϕ i . In particular, we show that lower values of E are associated with larger amplitudes of Q . Furthermore, it is found that Q exhibits a damped oscillatory behavior with increasing the AB flux. In addition, increasing the external gap Δ 1 resulted in higher values of Q . By increasing ϕ i , we show that the oscillations in ∣ c m ∣ 2 disappear for larger values of r 0 and are replaced by prominent peaks at certain values of E and angular momentum m . Finally, we show that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>J</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> displays periodic oscillations of constant amplitude, which are affected by the AB flux.