Geometry-enforced topological chiral fermions in amorphous chiral metals
Abstract
Since the prediction and observation of topological Weyl semimetals (chiral TSMs), there have been enormous efforts to characterize further condensed matter realizations of chiral fermions. These efforts were dramatically accelerated by the subsequent discovery of a profound link between low-energy topological and lattice chirality in structurally chiral crystals. Though TSMs are well understood in the limit of perfect translation symmetry, real solid-state materials host defects and disorder, and may even be rendered amorphous down to all but the smallest system length scales. Previous theoretical studies have concluded that chiral TSMs transition into trivial diffusive metals at moderate disorder scales, raising concerns that chiral TSM states may only be accessible in highly crystalline samples. In this work, we in contrast identify large families of chiral TSMs that instead persist under strong structural disorder—even into the amorphous regime. We show that amorphous chiral TSM phases can be stabilized in particular by the presence of long-range order in the local structural chirality. We present extensive analytic and numerical calculations demonstrating the existence of both Weyl and higher-charge chiral fermions in amorphous metals whose topology and spin and orbital angular momentum textures are tunable via the interplay of average symmetry and geometry. To distinguish and generate new realizations of strongly disordered chiral fermions, we introduce an analytic approach grounded in symmetry group theory. We then introduce an amorphous Wilson loop numerical method to identify chiral fermions in metals with 3D structural disorder. Our findings bridge the crystalline and strongly disordered regimes of chiral TSMs, and indicate a clear route toward engineering geometry-enforced topology in noncrystalline materials and metamaterials.
Related
- Symmetry-Enforced Dirac Fermions and Structural Metastability in Pentagonal Monolayers of Transition-Metal Ditellurides
- Symmetry-Enforced Topological Structures in Quantum Phase Diagrams
- Symmetry-enforced topological parity: revisiting 2ℤ classifications beyond cellwise symmetry actions
- A gauge-invariant measure for lattice chiral fermions
- A Note On Lattice Definition of Gauge Theories With Chiral Fermions
BibTeX
@article{schirmann2026geometryenforced,
title = {{Geometry-enforced topological chiral fermions in amorphous chiral metals}},
author = {Justin Schirmann and Adolfo Grushin and Benjamin Wieder},
journal = {Physical Review Materials},
year = {2026},
month = oct,
doi = {10.1103/6lzc-3y6q},
eprint = {2512.19791},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05798453v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - Geometry-enforced topological chiral fermions in amorphous chiral metals
AU - Justin Schirmann
AU - Adolfo Grushin
AU - Benjamin Wieder
PY - 2026
DA - 2026/10/07
JO - Physical Review Materials
DO - 10.1103/6lzc-3y6q
UR - https://hal.science/hal-05798453v1
AB - Since the prediction and observation of topological Weyl semimetals (chiral TSMs), there have been enormous efforts to characterize further condensed matter realizations of chiral fermions. These efforts were dramatically accelerated by the subsequent discovery of a profound link between low-energy topological and lattice chirality in structurally chiral crystals. Though TSMs are well understood in the limit of perfect translation symmetry, real solid-state materials host defects and disorder, and may even be rendered amorphous down to all but the smallest system length scales. Previous theoretical studies have concluded that chiral TSMs transition into trivial diffusive metals at moderate disorder scales, raising concerns that chiral TSM states may only be accessible in highly crystalline samples. In this work, we in contrast identify large families of chiral TSMs that instead persist under strong structural disorder—even into the amorphous regime. We show that amorphous chiral TSM phases can be stabilized in particular by the presence of long-range order in the local structural chirality. We present extensive analytic and numerical calculations demonstrating the existence of both Weyl and higher-charge chiral fermions in amorphous metals whose topology and spin and orbital angular momentum textures are tunable via the interplay of average symmetry and geometry. To distinguish and generate new realizations of strongly disordered chiral fermions, we introduce an analytic approach grounded in symmetry group theory. We then introduce an amorphous Wilson loop numerical method to identify chiral fermions in metals with 3D structural disorder. Our findings bridge the crystalline and strongly disordered regimes of chiral TSMs, and indicate a clear route toward engineering geometry-enforced topology in noncrystalline materials and metamaterials.
SN - 2475-9953
ER -