Semiconducting transport in Pb10−x_{10-x}Cux_x(PO4_4)6_6O sintered from Pb2_2SO5_5 and Cu3_3P

The very recent claim on the discovery of ambient-pressure room-temperature superconductivity in modified lead-apatite has immediately excited sensational attention in the entire society, which is fabricated by sintering lanarkite (Pb2SO5) and copper(I) phosphide (Cu$_3$P). To verify this exciting claim, we have successfully synthesized Pb$_2$SO$_5$, Cu$_3$P, and finally the modified lead-apatite Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O. Detailed electrical transport and magnetic properties of these compounds were systematically analyzed. It turns out that Pb$_2$SO$_5$ is a highly insulating diamagnet with a room-temperature resistivity of ~7.18x10$^9$ Ohm.cm and Cu$_3$P is a paramagnetic metal with a room-temperature resistivity of ~5.22x10$^{-4}$ Ohm.cm. In contrast to the claimed superconductivity, the resulting Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O compound sintered from Pb$_2$SO$_5$ and Cu$_3$P exhibits semiconductor-like transport behavior with a large room-temperature resistivity of ~1.94x10$^4$ Ohm.cm although our compound shows greatly consistent x-ray diffraction spectrum with the previously reported structure data. In addition, when a pressed Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O pellet is located on top of a commercial Nd$_2$Fe$_{14}$B magnet at room temperature, no repulsion could be felt and no magnetic levitation was observed either. These results imply that the claim of a room-temperature superconductor in modified lead-apatite may need more careful re-examination, especially for the electrical transport properties.Comment: 12 pages, 13 figure

Observation of the Anomalous Hall Effect in a Collinear Antiferromagnet

Time-reversal symmetry breaking is the basic physics concept underpinning many magnetic topological phenomena such as the anomalous Hall effect (AHE) and its quantized variant. The AHE has been primarily accompanied by a ferromagnetic dipole moment, which hinders the topological quantum states and limits data density in memory devices, or by a delicate noncollinear magnetic order with strong spin decoherence, both limiting their applicability. A potential breakthrough is the recent theoretical prediction of the AHE arising from collinear antiferromagnetism in an anisotropic crystal environment. This new mechanism does not require magnetic dipolar or noncollinear fields. However, it has not been experimentally observed to date. Here we demonstrate this unconventional mechanism by measuring the AHE in an epilayer of a rutile collinear antiferromagnet RuO$_2$. The observed anomalous Hall conductivity is large, exceeding 300 S/cm, and is in agreement with the Berry phase topological transport contribution. Our results open a new unexplored chapter of time-reversal symmetry breaking phenomena in the abundant class of collinear antiferromagnetic materials.Comment: 33 pages, 14 figures, 2 table

Publisher Correction: An anomalous Hall effect in altermagnetic ruthenium dioxide

In the version of this article initially published, square brackets and parentheses were incorrect in Fig. 1g and throughout Fig. 2 (excepting lower labels in Fig. 2d–f). Further, in the second paragraph of the “Consistency with theoretical prediction” subsection of the main article, in the text now reading “the reorientation-field scale, namely, HC = (H2 AE − H2 d) /Hd,” the term “H2 AE” wasn’t shown as squared. The changes have been made in the HTML and PDF versions of the article

Convergence rate for the moving least-squares learning with dependent sampling

Abstract We consider the moving least-squares (MLS) method by the regression learning framework under the assumption that the sampling process satisfies the α-mixing condition. We conduct the rigorous error analysis by using the probability inequalities for the dependent samples in the error estimates. When the dependent samples satisfy an exponential α-mixing, we derive the satisfactory learning rate and error bound of the algorithm

The learning performance of the weak rescaled pure greedy algorithms

Abstract We investigate the regression problem in supervised learning by means of the weak rescaled pure greedy algorithm (WRPGA). We construct learning estimator by applying the WRPGA and deduce the tight upper bounds of the K-functional error estimate for the corresponding greedy learning algorithms in Hilbert spaces. Satisfactory learning rates are obtained under two prior assumptions on the regression function. The application of the WRPGA in supervised learning considerably reduces the computational cost while maintaining its powerful generalization capability when compared with other greedy learning algorithms