Geodesic geometry of 2+1-D Dirac materials subject to artificial, quenched gravitational singularities

Abstract

The spatial modulation of the Fermi velocity for gapless Dirac electrons in quantum materials is mathematically equivalent to the problem of massless fermions on a certain class of curved spacetime manifolds. We study null geodesic lensing through these manifolds, which are dominated by curvature singularities, such as nematic singularity walls (where the Dirac cone flattens along one direction). Null geodesics lens across these walls, but do so by perfectly collimating to a local transit angle. Nevertheless, nematic walls can trap null geodesics into stable or metastable orbits characterized by repeated transits. We speculate about the role of induced one-dimensionality for such bound orbits in 2D dirty d-wave superconductivity.

v2: Added quantum calculations for singular geometries, 47 pages, 16 figures, published version

References in corpus (5)

• The electronic properties of graphene
• The $8Pmmn$ borophene sheet: A solid-state platform for space-time engineering
• Transport across twist angle domains in moiré graphene
• Artificial event horizons in Weyl semimetal heterostructures and their non-equilibrium signatures
• Geodesic scattering by surface deformations of a topological insulator

Cited by in corpus (5)

• Tunning the tilt of a Dirac cone by atomic manipulations: application to 8Pmmn borophene
• Anisotropic optics and gravitational lensing of tilted Weyl fermions
• Unruh Effect and Takagi's Statistics Inversion in Strained Graphene
• Analog Unruh effect of inhomogeneous one-dimensional Dirac fermions
• Emergence of curved momentum-spacetime and its effect on the cyclotron motion in the antiferromagnetic quantum critical metal