  Quantum phase transitions are intriguing and fundamental cooperative
phenomena in physics. Analyzing a superconducting nanowire with spin-dependent
non-Hermitian hopping, we discover a topological quantum phase transition
driven by infinitesimal cascade instability. The anomalous phase transition is
complementary to the universal non-Bloch wave behavior of non-Hermitian
systems. We show that an infinite small magnetic field drastically suppresses
the non-Hermitian skin effect, inducing a topological phase with Majorana
boundary states. Furthermore, by identifying the bulk topological invariant, we
establish the non-Hermitian bulk-boundary correspondence that does not have a
Hermitian counterpart. We also discuss an experimental realization of the
system by using the spin-current injection to a quantum wire.
