So far, most theoretically predicted and experimentally confirmed quantum anomalous Hall effect (QAHE) are limited in two-dimensional (2D) materials with out-of-plane magnetization. In this Letter, starting from 2D nodal-line semimetal, a general rule for searching QAHE with in-plane magnetization is mapped out. Due to the spin-orbital-coupling, we found that the magnetization will prefer an in-plane orientation if the orbital of degenerate nodal-line states at Fermi-level have the same absolute value of magnetic quantum number. Moreover, depending on the broken or conserved mirror symmetry, either QAHE or 2D semimetal can be realized. Based on first principles calculations, we further predict a real material of monolayer LaCl to be an intrinsic QAHE with in-plane magnetization. By tuning the directions of in-plane magnetization, the QAHE in LaCl demonstrates a threefold rotational symmetry with Chern number of either +1 or −1, and the transition point is characterized by a 2D semimetal phase. All these features are quantitatively reproduced by tight-binding model calculations, revealing the underlying physics clearly. Our results greatly extend the scope for material classes of QAHE, and hence stimulate immediate experimental interests.

Two-dimensional quadrupole topological insulator (2D QTI), as a new class of second-order topological phases, has been experimentally confirmed in various artificial systems recently. However, its realization in electronic materials has seldom been reported. In this work, we predict that the experimentally synthesized γ-graphyne is a large-gap (∼0.2 eV) 2D QTI. Three characterized features for 2D QTI are simultaneously observed in γ-graphyne: quantized finite bulk quadrupole moment, gapped topological edge states, and in-gap topological corner states. Intriguingly, we found that gapped topological edge states exist on armchair edge with CC (but not CC) termination, and in-gap topological corner states exist at corner with 120° (but not 60°) termination, which can be explained by different edge-hopping textures and corner chiral charges. Moreover, the robustness of in-gap topological corner states is further identified by varying edge-disorder and system-size calculations. Our results demonstrate a realistic electronic material for large-gap 2D QTI, which is expected to draw immediate experimental attention.

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.