Topological materials with broken inversion symmetry can give rise to nonreciprocal responses, such as the current rectification controlled by magnetic fields via magnetochiral anisotropy. Bulk nonreciprocal responses usually stem from relativistic corrections and are always found to be very small. A large magnetochiral anisotropy of novel origin has been proposed for topological semimetals, but no concrete example has been known so far. Here we report our discovery that ZrTe5 crystals in proximity to a topological quantum phase transition present gigantic magnetochiral anisotropy which is at least 1000 times larger than in any known material. We argue that a very low carrier density, inhomogeneities, and a torus-shaped Fermi surface induced by breaking of inversion symmetry in a Dirac material are central to explain this extraordinary property.
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