Black hole mirages: electron lensing and Berry curvature effects in inhomogeneously tilted Weyl semimetals

Abstract

We study electronic transport in Weyl semimetals with spatially varying nodal tilt profiles. We find that the flow of electrons can be guided precisely by judiciously chosen tilt profiles. In a broad regime of parameters, we show that electron flow is described well by semiclassical equations of motion similar to the ones governing gravitational attraction. This analogy provides a physically transparent tool for designing tiltronic devices like electronic lenses. The analogy to gravity circumvents the notoriously difficult full-fledged description of inhomogeneous solids. A comparison to microscopic lattice simulations shows that it is only valid for trajectories sufficiently far from analogue black holes. We finally comment on the Berry curvature-driven transverse motion and relate the latter to spin precession physics.

Replaced with revised version for SciPost resubmission. 38 pages, 12 figures

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• Optimally scrambling chiral spin-chain with effective black hole geometry
• Quantum geometric tensors from sub-bundle geometry
• Bayesian analysis of analog gravity systems with the Rezzolla-Zhidenko metric
• Spinning Black Hole in a Fluid
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• Emergent quantum field theories on curved spacetimes in spinor Bose-Einstein condensates: from scalar to Proca fields