Barrier tunneling and loop polarization in Hopf semimetals

Degrees of freedom like charge, spin, and valley in condensed matter have drawn much attention in the past decades. Recently, several kinds of nodal line semimetals have been discovered for which the conduction and valence bands cross along one-dimensional lines, usually forming loops. These distinct loops, similar to valleys, can be used as a possible carrier of information. Here we investigate the loop polarization during quantum transports, i.e., barrier tunneling as well as disorder scattering, in Hopf semimetals with two disconnected loops. We find that in both cases, the loop polarization is mostly dominated by the performance of normal incidence, due to the mirror symmetry of two loop planes and the finite size effect along one direction. After scattered by nonmagnetic disordered potentials, the opposite polarizations can intrinsically reveal the topological structure of two loops, linked or unlinked. The effects from smooth barriers and disorders are also investigated. We find that a long range smooth barrier leads to an even clearer and purer picture of scattering and loop polarization, due to the suppression of large momentum transfer. These effects can be used as a controllable loop filter and detector.