  Chiral crystals are materials whose lattice structure has a well-defined
handedness due to the lack of inversion, mirror, or other roto-inversion
symmetries. These crystals represent a broad, important class of quantum
materials; their structural chirality has been found to allow for a wide range
of phenomena in condensed matter physics, including skyrmions in chiral
magnets, unconventional pairing in chiral superconductors, nonlocal transport
and unique magnetoelectric effects in chiral metals, as well as
enantioselective photoresponse. Nevertheless, while these phenomena have been
intensely investigated, the topological electronic properties of chiral
crystals have still remained largely uncharacterized. While recent theoretical
advances have shown that the presence of crystalline symmetries can protect
novel band crossings in 2D and 3D systems, we present a new class of Weyl
fermions enforced by the absence of particular crystal symmetries. These
"Kramers-Weyl" fermions are a universal topological electronic property of all
nonmagnetic chiral crystals with spin-orbit coupling (SOC); they are guaranteed
by lattice translation, structural chirality, and time-reversal symmetry, and
unlike conventional Weyl fermions, appear at time-reversal-invariant momenta
(TRIMs). We cement this finding by identifying representative chiral materials
in the majority of the 65 chiral space groups in which Kramers-Weyl fermions
are relevant to low-energy physics. By combining our analysis with the results
of previous works, we determine that all point-like nodal degeneracies in
nonmagnetic chiral crystals with relevant SOC carry nontrivial Chern numbers.
We further show that, beyond the previous phenomena allowed by structural
chirality, Kramers-Weyl fermions enable unusual phenomena, such as a novel
electron spin texture, chiral bulk Fermi surfaces over large energy windows.
