Spontaneous Chern-Euler Duality Transitions
This research explores a novel duality in non-Hermitian parity-time symmetric systems where topological invariants switch between Chern numbers and Euler numbers during spontaneous symmetry breaking. It establishes a 'Chern-Euler duality principle' stating that the absolute value of the Chern number equals the absolute value of the Euler number, providing a universal mechanism for generating Chern bands from real bands.