The study of topological materials possessing nontrivial band structures enables exploitation of relativistic physics and development of a spectrum of intriguing physical phenomena. However, previous studies of Weyl physics have been limited exclusively to semimetals. Here, via systematic magnetotransport measurements, two representative topological transport signatures of Weyl physics, the negative longitudinal magnetoresistance and the planar Hall effect, are observed in the elemental semiconductor tellurium. More strikingly, logarithmically periodic oscillations in both the magnetoresistance and Hall data are revealed beyond the quantum limit and found to share similar characteristics with those observed in ZrTe5and HfTe5. The log-periodic oscillations originate from the formation of two-body quasi-bound states formed between Weyl fermions and opposite charge centers, the energies of which constitute a geometric series that matches the general feature of discrete scale invariance (DSI). Our discovery reveals the topological nature of tellurium and further confirms the universality of DSI in topological materials. Moreover, introduction of Weyl physics into semiconductors to develop “Weyl semiconductors” provides an ideal platform for manipulating fundamental Weyl fermionic behaviors and for designing future topological devices.

We have systematically reported the magnetic and magneto-transport properties of two-dimensional itinerant ferromagnetic compound Fe 3 GeTe 2 at high magnetic fields of 58 T and demonstrated the correlation between its transport and magnetism. Anomalous two-steps magnetic ordering and antiferromagnetic-like transitions in zero field-cooling (ZFC) curves for H ab-plane are observed. Additionally, we find that intrinsic negative magnetoresistances in bulk Fe 3 GeTe 2 single crystal are mainly attributed to the suppression of spin-fluctuations in low magnetic fields. Complex evolutions of temperature dependent high field magnetoresistances are detected under different magnetic field and current configurations, which can be explained as a result of the competition between spin-fluctuations, the magnon-scatterings and classical cyclotronic effects.

We revisited the anisotropy of the heavy-fermion material CeCo2Ga8 by measuring the electrical resistivity and magnetic susceptibility along all the principal a-, b-and c-axes. Resistivity along c-axis (ρc) shows clear Kondo coherence below about 17 K, while both ρa and ρ b remain incoherent down to 2 K. The magnetic anisotropy is well understood within the theoretical frame of crystalline electric field effect in combination with magnetic exchange interactions. We found the anisotropy ratio of these magnetic exchange interactions, |J c ex /J a,b ex |, reaches a large value of 4-5. We, therefore, firmly demonstrate that CeCo2Ga8 is a quasi-one-dimensional heavy-fermion compound both electrically and magnetically, and thus provide a realistic example of Kondo chain.

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