Scattering of Spin-$\frac{1}{2}$ Particles from a $\mathcal{P}\mathcal{T}$-symmetric Complex Potential

In this letter, we study the scattering of spin-$\frac{1}{2}$ particles from a spin-independent parity time ($\mathcal{P}\mathcal{T}$)-symmetric complex potential, and for the first time, theoretically demonstrate the coexistence of $\cal PT$-symmetricand$\cal PT$-broken phases for broadband energy spectra in this system. We also show the existence of anisotropic transmission resonances, accessible through the tuning of energy. Our results are promising for applications in spintronics, semiconductor-based devices, and a better understanding of the topological surface states.