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Magnetoresistance in quasi-one dimensional Weyl semimetal (TaSe$_4$)$_2$I

Magnetic field effect on linear and nonlinear conductivity in a quasi-one-dimensional Weyl semimetal with a charge density wave (CDW) (TaSe$_4$)$_2$I is studied. Longitudinal magnetoresistance in all known regimes of CDW motion (linear conduction, creep, sliding, "Fröhlich superconductivity") is small, positive and do not exceed a fraction of per cent. Similar magnetotransport measurements were performed in samples profiled by focused ion beams is such a way that motion of the CDW in them is accompanied by phase slip of the CDW. In such samples, a peak-like non-parabolic negative magnetoresistance is observed in relatively small magnetic fields $B \lesssim 4$ T in the nonlinear conduction regime in both longitudinal and transverse geometries. Our results differ significantly from ones obtained earlier and raise the question concerning conditions for observing the axion anomaly in Weyl semimetals in the Peierls state.