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

## TL;DR

This paper investigates emergent ergosurfaces in transition layers between type-I and type-II Weyl semimetals, revealing quantum chaos and fast scrambling behavior through OTOC calculations, with implications for understanding quantum chaos in condensed matter systems.

## Contribution

It introduces the concept of emergent ergosurfaces in Weyl semimetals and demonstrates quantum chaos via OTOC analysis in a lattice model.

## Key findings

- Emergent ergosurfaces occur at the transition layer between Weyl semimetal types.
- OTOCs exhibit fast scrambling with a measurable quantum Lyapunov exponent.
- Quantum chaotic behavior is confirmed through saturation of scrambling after the Ehrenfest time.

## Abstract

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 $v_{\parallel}$ is small is in a measurable interval. On the type-II WSM side, i.e., inside the {ES when $v_{\parallel}$ 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.