Horizon physics of quasi-one-dimensional tilted Weyl cones on a lattice

Abstract

To simulate the dynamics of massless Dirac fermions in curved spacetimes with one, two, and three spatial dimensions we construct tight-binding Hamiltonians with spatially varying hoppings. These models represent tilted Weyl semimetals where the tilting varies with position, in a manner similar to the light cones near the horizon of a black hole. We illustrate the gravitational analogies in these models by numerically evaluating the propagation of wave packets on the lattice and then comparing them to the geodesics of the corresponding curved spacetime. We also show that the motion of electrons in these spatially varying systems can be understood through the conservation of energy and the quasi-conservation of quasimomentum. This picture is confirmed by calculations of the scattering matrix, which indicate an exponential suppression of any noncontinuous change in the quasimomentum. Finally, we show that horizons in the lattice models can be constructed also at finite energies using specially designed tilting profiles.

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Cited by in corpus (8)

• Black hole mirages: electron lensing and Berry curvature effects in inhomogeneously tilted Weyl semimetals
• Anisotropic optics and gravitational lensing of tilted Weyl fermions
• Optimally scrambling chiral spin-chain with effective black hole geometry
• Tilted Dirac superconductor at quantum criticality: Restoration of Lorentz symmetry
• Yukawa-Lorentz Symmetry of Tilted Non-Hermitian Dirac Semimetals at Quantum Criticality
• Smart Holes: Analogue black holes with the right temperature and entropy
• Analog charged black hole formation via percolation: Exploring cosmic censorship and Hoop conjecture
• Synthetic horizons in an atomic chain: Horizon-induced effects and connections to quantum Hall systems