Circular current in a one-dimensional open quantum ring in the presence of magnetic field and spin-orbit interaction

Abstract: In an open quantum system having a channel in the form of loop geometry, the current inside the channel, namely circular current, and overall junction current, namely transport current, can be different. A quantum ring has doubly degenerate eigen energies due to periodic boundary condition that is broken in an asymmetric ring where the ring is asymmetrically connected to the external electrodes. Kramers' degeneracy and spin degeneracy can be lifted by considering non-zero magnetic field and spin-orbit interaction (SOI), respectively. Here, we find that symmetry breaking impacts the circular current density vs energy ($E$) spectra in addition to lifting the degeneracy. For charge and spin current densities, the corresponding effects are not the same. Under symmetry-breaking they may remain symmetric or anti-symmetric or asymmetric around $E = 0$ whereas the transmission function (which is proportional to the junction current density) vs energy characteristic remains symmetric around $E = 0$. This study leads us to estimate the qualitative nature of the circular current and the choices of Fermi-energy/chemical potential to have a net non-zero current. As a result, we may manipulate the system to generate pure currents of charge, spin, or both, which is necessary for any spintronic and electronic applications.