Wavefunction engineering using Mandelbrot, multicorn, and Koch's snowflake fractal quantum rings to control the persistent current

In this work, we have considered the wavefunction, energy levels, and persistent current of two-dimensional quantum rings that created from the less-studied Mandelbrot, multicorn, and Koch's snowflake fractal shapes. The effect of fractality order on the persistent current for different fractal structure, exchanging this fractals as inner and outer border of the rings, composition parameter x in Ga1−xAlxAs/GaAs system are studied. For this purpose, the numerical solution of the Schrödinger equation governing the problem has been used. We study the effect of symmetry on the creation and destruction of the persistent current. Besides, we have addressed the degeneracies of the wave function of the structures mentioned above. •Persistent current of 2D quantum rings (QR) created from the Mandelbrot, multicorn, and Koch's snowflake fractal shapes•Use Multicorns with larger fractal order for Multicorn in Multicorn QRs to have larger persistent current•Use Koch snowflake with smaller fractal order For Koch snowflake QRs to have larger persistent current•If we have not the non-zero wave function at most of QRs the persistent current will not flow•The effect of symmetry on the creation and destruction of the persistent current