Fig. 6

Experimental results for the \({\cal{P}}{\cal{T}}\)-symmetric broken QW dynamics. a Time-evolution and (b) spin textures of n(k, t) in momentum–time space for a quench process between the initial non-unitary Floquet operator given by \((\theta _1^{\mathrm{i}} = \pi /4,\theta _2^{\mathrm{i}} = - \pi /2)\) and the final \({\cal{P}}{\cal{T}}\)-symmetry-broken Floquet operator given by \(\left[ {\theta _1^{\mathrm{f}} = - \pi /2,\theta _2^{\mathrm{f}} = \frac{1}{2}\left( {\pi - {\mathrm{arccos}}\frac{1}{\alpha }} \right)} \right]\). The quasi-energy spectrum associated with U^f is completely imaginary in this case. (c) Time-evolution and (d) spin textures of n(k, t) in the momentum–time space when the system is quenched from the same initial state as in Fig. 3b into a final \({\cal{P}}{\cal{T}}\)-symmetry-broken Floquet operator given by \((\theta _1^{\mathrm{f}} = - 0.39\pi ,\theta _2^{\mathrm{f}} = 0.3864\pi )\) with ν^f = −2. The quasi-energy spectrum associated with U^f features purely imaginary [red shaded areas in (d)] and purely real regions in momentum space. Only two fixed points of the same kind exist at {−0.4000π, 0.6000π} (dashed lines), whereas no skyrmion structures exist in any momentum–time submanifold. The spin vectors in (c) and (d) are colored according to n₃(k, t)