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 persist under strong structural disorder - even into the amorphous regime. We show that amorphous chiral TSM phases can in particular be stabilized 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 characterize chiral fermions with quantized Berry curvature fluxes in metals with 3D structural disorder. Our findings bridge the crystalline and strongly disordered regimes of chiral TSMs, and indicate a clear route towards engineering geometry-enforced topology in non-crystalline materials and metamaterials.