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Topologically nontrivial electronic structure can often be characterized by the Chern number, the value of which is related to the magnitude of some of the exotic effects predicted to occur in such systems. Many topological phases discovered so far have a Chern number of 1 or 2, but higher values are also theoretically possible. Schröter et al. predicted that the chiral material palladium gallium (PdGa) would have a Chern number of 4, and they confirmed that prediction using photoemission experiments. Interestingly, the sign of the Chern number was opposite for the two enantiomers of PdGa.Science, this issue p. 179Topological semimetals feature protected nodal band degeneracies characterized by a topological invariant known as the Chern number (C). Nodal band crossings with linear dispersion are expected to have at most |C|=4, which sets an upper limit to the magnitude of many topological phenomena in these materials. Here, we show that the chiral crystal palladium gallium (PdGa) displays multifold band crossings, which are connected by exactly four surface Fermi arcs, thus proving that they carry the maximal Chern number magnitude of 4. By comparing two enantiomers, we observe a reversal of their Fermi-arc velocities, which demonstrates that the handedness of chiral crystals can be used to control the sign of their Chern numbers.
