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

TL;DR

This paper explores how artificial gravitational singularities in 2+1-D Dirac materials influence the paths of massless fermions, revealing phenomena like geodesic lensing and trapping near curvature singularities, with implications for quantum materials.

Contribution

It introduces a geometric framework for understanding electron behavior in Dirac materials with engineered gravitational-like singularities, highlighting null geodesic dynamics and potential bound states.

Findings

Null geodesics are collimated across curvature singularities.

Nematic walls can trap geodesics in stable or metastable orbits.

Implications for bound states in disordered d-wave superconductors.

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.