# Curved spacetime theory of inhomogeneous Weyl materials

## TL;DR

This paper develops a theoretical framework describing inhomogeneous Weyl materials as Weyl fermions in curved spacetime with gauge fields, enabling new ways to engineer and understand topological materials with spatial variations.

## Contribution

It introduces a systematic derivation of an effective curved-space Weyl theory incorporating geometric and gauge structures, applicable to designing inhomogeneous Weyl materials.

## Key findings

- Provides a formalism for fabricating curved spacetimes in topological insulators.
- Accounts for strain-induced effects in Weyl materials.
- Offers a unified framework for studying inhomogeneous Weyl systems.

## Abstract

We show how the universal low-energy properties of Weyl semimetals with spatially varying time-reversal (TR) or inversion (I) symmetry breaking are described in terms of chiral fermions experiencing curved-\emph{spacetime} geometry and synthetic gauge fields. By employing Clifford representations and Schrieffer-Wolff transformations, we present a systematic derivation of an effective curved-space Weyl theory with rich geometric and gauge structure. To illustrate the utility of the formalism, we give a concrete prescription of how to fabricate nontrivial curved spacetimes and event horizons in topological insulators with magnetic textures. Our theory can also account for strain-induced effects, providing a powerful unified framework for studying and designing inhomogeneous Weyl materials.