We clarify the relation between two kinds of statistics for particle excitations in planar systems: the braid statistics of anyons and the Haldane exclusion statistics(HES). It is shown non-perturbatively that the HES exists for incompressible anyon liquid in the presence of a Hall response. We also study the statistical properties of a specific quantum anomalous Hall model with Chern-Simons term by perturbation in both compressible and incompressible regimes, where the crucial role of edge states to the HES is shown.

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Through a thorough magneto-transport study of antiferromagnetic topological insulator MnBi2Te4 (MBT) thick films, a positive linear magnetoresistance (LMR) with a two-dimensional (2D) character is found in high perpendicular magnetic fields and temperatures up to at least 260 K.The nonlinear Hall effect further reveals the existence of high-mobility surface states in addition to the bulk states in MBT. We ascribe the 2D LMR to the high-mobility surface states of MBT, thus unveiling a transport signature of surface states in thick MBT films. A suppression of LMR near the Neel temperature of MBT is also noticed, which might suggest the gap opening of surface states due to the paramagnetic-antiferromagnetic phase transition of MBT. Besides these, the failure of the disorder and quantum LMR model in explaining the observed LMR indicates new physics must be invoked to understand this phenomenon.

To develop the state‐of‐the‐art polymer membrane fuel cells. Both maximization of oxygen reduction reaction (ORR) activity on Pt cathode and minimization of Pt content in the cathode are required. For this challenge, the defect interface on oxide support was modified by proton beam irradiation method. Pt‐CeOx nanowire/C (Pt/C = 0.02) was fabricated using the proton beam irradiation method. Since the radical density generated by proton beam irradiation is two orders of magnitude greater than that of electron beam irradiation, the CeOx nanowire surface was fully converted to a thin layer of Pt‐O‐Ce bonds under proton beam irradiation. The ORR activity observed for fabricated sample with above active surface layer was higher than that of conventional Pt/C (Pt/C = 0.2) and comparable to that of Pt‐CeOx nanowire/C (Pt/C = 0.2) fabricated by conventional methods. From the combination of microanalysis characterization and surface atomistic simulation, we concluded that the Pt‐O‐Ce bond was formed on defect‐rich regions of the CeOx nanowire and this leads to a maximized ORR activity on the fabricated sample. Based on all experimental data, it is concluded that the surface modification of CeOx nanowire support using proton beam irradiation is useful for a lowering the Pt content of the cathode with high ORR activity.