The magnetic field-induced changes in the conductivity of metals are the subject of intense interest, both for revealing new phenomena and as a valuable tool for determining their Fermi surface. Here, we report a hitherto unobserved magnetoresistive
effect in ultra-clean layered metals, namely a negative longitudinal magnetoresistance that is capable of overcoming their very pronounced orbital one. This effect is correlated with the inter-layer coupling disappearing for fields applied along the so-called Yamaji angles where the inter-layer coupling vanishes. Therefore, it is intrinsically associated with the Fermi points in the field-induced quasi-one-dimensional electronic dispersion, implying that it results from the axial anomaly among these Fermi points. In its original formulation, the anomaly is predicted to violate separate number conservation laws for left- and right-handed chiral- (e.g. Weyl) fermions. Its observation in PdCoO$_2$, PtCoO$_2$ and Sr$_2$RuO$_4$ suggests that the anomaly affects the transport of clean conductors, particularly near the quantum limit.
Magnetometry measurements in high quality LiFeAs single-crystals reveal a change in the sign of the magnetic hysteresis in the vicinity of the upper critical field $H_{c2}$, from a clear diamagnetic response dominated by the pinning of vortices, to a
considerably smaller net hysteretic response of opposite sign, which emph{disappears} at $H_{c2}$. If the diamagnetic response at high fields results from pinned vortices and associated screening super-currents, this sign change must result from currents circulating in the opposite sense, which give rise to a small field-dependent magnetic moment emph{below} $H_{c2}$. This behavior seems to be extremely sensitive to the sample quality or stoichiometry, as we have observed it only in a few fresh crystals, which also display the de Haas van Alphen-effect. We provide arguments against the surface superconductivity, the flux compression, and the random $pi$ junction scenarios, which have been previously put forward to explain a paramagnetic Meissner effect, below the lower critical field $H_{c1}$. The observed anomalous hysteresis at high fields will be compatible with the existence of chiral gap wave-functions, which possess a field dependent magnetic moment. Within a Landau-Ginzburg framework, we demonstrate how a $(d_{x^2 - y^2} + id_{xy})$ or a $(p_x+ip_y)$ chiral superconducting component can be stabilized in the mixed state of $s_{pm}$ superconductor, due to the combined effects of the magnetic field and the presence of competing pairing channels. The realization of a particular chiral pairing depends on the microscopic details of the strengths of the competing pairing channels.
