Quantum chaos associated with an emergent ergosurface in the transition layer between type-I and type-II Weyl semimetals

We present emergent ergosurfaces (ES) in a transition layer between type-I and type-II Weyl semimetals (WSMs). The Hawking temperature defined by the surface gravity at the acoustic event horizon which coincides with the ES when the tangent velocity v(vertical bar vertical bar) is small is in a measurable interval. On the type-II WSM side, i.e., inside the ES when v(vertical bar vertical bar) is large, the motion of the quasiparticles may be chaotic after a critical surface as they are governed by an effective inverted oscillator potential induced by the mismatch between the type-I and type-II Weyl nodes. In a relevant lattice model, we calculate out-of-time-ordered correlators (OTOCs). We find that the OTOCs are fast scrambling with a quantum Lyapunov exponent in high temperature and the scrambling is saturated after the Ehrenfest time. This confirms the quantum chaotic behavior.