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

TL;DR

This paper constructs lattice models of tilted Weyl semimetals to simulate Dirac fermion dynamics in curved spacetime, revealing gravitational analogies and horizon phenomena through numerical wave packet analysis.

Contribution

It introduces spatially varying hopping models that mimic curved spacetime effects and explores horizon formation at finite energies in lattice systems.

Findings

Wave packet propagation matches geodesic trajectories in curved spacetime.

Exponential suppression of noncontinuous quasimomentum changes observed.

Horizons can be engineered at finite energies using specific tilting profiles.

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.