Conductance and shot noise in the helimagnet tunnel junction

As a result of sinusoidal spatial modulation, helimagnet induces spin-dependent diffracted transmission. In this work, we propose a general scattering matrix treatment to the transport properties in helimagnets with arbitrary helical structures. Multiferroic properties can be considered by taking electric polarization and magnetic helix together into account. A monolayer magnetic helix can be treated as a $\delta$-barrier by diffraction theory. The conductance and shot noise properties of the normal metal/helimagnet/normal metal toy model are investigated. It is found that the shot noise is suppressed and demonstrates rise-and-fall variations as a result of interference between different diffracted channels. Sharp change of the shot noise occurs when one and both diffracted beams disappear into evanescent modes at the helimagnet spiral wave vector equal to one and two times the electron Fermi wave vector $q=k_F$ and $2 k_F$. We also considered the conductance and shot noise properties in a real multiferroic helimagnet $\rm{TbMnO_3}$ with ferroelectric and helimagnetism coexistent. It is found that clockwise and counterclockwise spin helix is distinctly separated in the conductance and shot noise spectrum. Their variation pattern is a combined result of helimagnetism and electric polarization.