Weyl fermions are a new ingredient for correlated states of electronic matter. A key difficulty has been that real materials also contain non-Weyl quasiparticles, and disentangling the experimental signatures has proven challenging. We use magnetic fields up to 95 tesla to drive the Weyl semimetal TaAs far into its quantum limit (QL), where only the purely chiral 0th Landau levels (LLs) of the Weyl fermions are occupied. We find the electrical resistivity to be nearly independent of magnetic field up to 50 tesla: unusual for conventional metals but consistent with the chiral anomaly for Weyl fermions. Above 50 tesla we observe a two-order-of-magnitude increase in resistivity, indicating that a gap opens in the chiral LLs. Above 80 tesla we observe strong ultrasonic attenuation below 2 kelvin, suggesting a mesoscopically-textured state of matter. These results point the way to inducing new correlated states of matter in the QL of Weyl semimetals.
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