Spin-charge mixing effects on resonant tunneling in a polarized Luttinger liquid

We investigate spin-charge mixing effect on resonant tunneling in spin-polarized Tomonaga-Luttinger liquid with double impurities. The mixing arises from Fermi velocity difference between two spin species due to Zeeman effect. Zero bias conductance is calculated as a function of gate voltage V-g, gate magnetic field B-g, temperature, and magnetic field applied to the system. Mixing effect is shown to cause rotation of the lattice pattern of the conductance peaks in (V-g,B-g) plane, which can be observed in experiments. At low temperatures, the contour shapes are classified into three types, reflecting the fact that effective barrier potential is renormalized towards "perfect reflection," "perfect transmission," and magnetic field induced "spin-filtering," respectively.