Multiwrapped PT -symmetric topological insulator with complete spin polarization

We theoretically predict a multiwrapped parity-time ($\mathcal{PT}$)-symmetric topological insulator characterized by winding numbers $W=1$ and $W=2$ driven by the nonreciprocal spin-orbit coupling (SOC) in one-dimensional systems. The nonreciprocal SOC triggers a $\mathcal{PT}$-symmetry phase transition, resulting in the emergence of exceptional points. We find that the broken $\mathcal{PT}$ symmetry forbids the $W=1$ topological phase due to the coalescence of the bands. In contrast, the $\mathcal{PT}$-symmetric phase hosts both the single- and double-wrapped topological insulator phases. For the $\mathcal{PT}$-symmetric topological insulator, we can realize complete spin polarization by tuning the nonreciprocal SOC equipped with the bulk-boundary correspondence. The most significant spin polarization can be observed in exceptional points. The nonreciprocal SOC may lead us to unveil novel phases of matter by combining topological and non-Hermitian principles.