Caustical patterns in circular magnetic dots in graphene

The scattered wavefunction of an incoming plane wave of electrons due to a circular symmetric step-like potential shows an interference pattern which resembles that of ‘cup caustics’. The high intensity maximum located around caustics can be calculated from Snell’s law with negative refractive index. This paper investigates the wavefunction for a plane wave incident on a circular magnetic dot where the magnetic field is nonzero only in a finite, circular disc-like region of space in the presence of a commensurate scalar potential barrier and vanishes outside that region. By formulating the optical analogy, the caustical curves are described inside the scattering region in terms of geometrical optics and analyse the effect of magnetic field on it. The caustical curves obtained in the presence of weak magnetic field are found to be rotated as compared to the case in the absence of magnetic field. This theoretical formulation using geometrical optics also captures the features developed due to bending of classical trajectories in the presence of magnetic field. Graphic abstract Probability density log10| $$\Psi $$ Ψ |2 (scale of logarithmic to base 10) distribution for circular magnetic dot a B = 0 b B = 0.01T c B = 0.05T d B = 0.1T e B = 0.2T f B = 0.3T in the presence of a commensurate circular scalar potential barrier V = 100 meV . Incident energy of charge carriers E = 50 meV . Here x-axis and y-axis corresponds to spatial x and y in the units of R.