  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.
