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Topological semimetals  are well known for the linear energy band dispersion in the bulk state and topologically protected surface state with arc-like Fermi surface. The angle resolved photoemission spectroscopy experiments help confirm the existence of linear Dirac (Weyl) cone and Fermi arc. Meantime, the transport experiments are very important for its intimate relationship with possible applications. In this concise review, recent developments of quantum transport in two typical topological semimetals, namely Dirac and Weyl semimetals, are described. The 3D Dirac semimetal phase is revealed by the Shubnikov-de Haas oscillations. The Weyl Fermions-related chiral anomaly effect is evident by negative magnetoresistance, thermal power suppression, and nonlocal measurements. The Fermi arc mechanism is discussed and several corresponding transport evidences have been described. The point contact-induced superconductivity in Dirac and Weyl semimetal is also introduced. Perspectives about the development of topological semimetals and topological superconductors are provided.

The recently discovered kagome superconductors offer a promising platform for investigating intertwined orders and novel states, including topology, superconductivity, charge density waves, and more. The interplay among these orders can spontaneously break rotational symmetry, giving rise to exotic phenomena such as nematicity or even nematic superconductivity. Here we present our findings on the two-fold symmetric superconductivity in thin-flake RbV3Sb5 in response to direction-dependent in-plane magnetic fields, in contrast to the inherent six-fold structural symmetry of the crystal lattice. The two-fold symmetry was evidenced through a combination of magnetoresistance transport experiments, critical magnetic field measurements, and observations of anisotropic superconducting gaps. Additionally, by altering the experimental configuration, we also detected the presence of six-fold symmetric components superimposed on the two-fold symmetry at the boundary between normal and superconducting states. Our results underscore the correlation-driven symmetry-breaking phenomena and emphasize the potential of this correlated kagome family as a promising platform for investigating intertwined orders, including unconventional superconductivity.Kagome materials provide a platform to investigate the interplay between a range of ordered phases such as charge density waves, superconductivity, as well as non-trivial topological properties. Here, the authors observed the two-fold symmetric superconductivity in RbV3Sb5, which suggests the presence of unconventional superconductivity involved with nematic states and spin-orbit-parity coupled superconductivity.

Quantum computers have made extraordinary progress over the past decade, and significant milestones have been achieved along the path of pursuing universal fault-tolerant quantum computers. Quantum advantage, the tipping point heralding the quantum era, has been accomplished along with several waves of breakthroughs. Quantum hardware has become more integrated and architectural compared to its toddler days. The controlling precision of various physical systems is pushed beyond the fault-tolerant threshold. Meanwhile, quantum computation research has established a new norm by embracing industrialization and commercialization. The joint power of governments, private investors, and tech companies has significantly shaped a new vibrant environment that accelerates the development of this field, now at the beginning of the noisy intermediate-scale quantum era. Here, we first discuss the progress achieved in the field of quantum computation by reviewing the most important algorithms and advances in the most promising technical routes, and then summarizing the next-stage challenges. Furthermore, we illustrate our confidence that solid foundations have been built for the fault-tolerant quantum computer and our optimism that the emergence of quantum killer applications essential for human society shall happen in the future.

[This corrects the article DOI: 10.1371/journal.pone.0156756.].

Quantum computers have made extraordinary progress over the past decade, and significant milestones have been achieved along the path of pursuing universal fault-tolerant quantum computers. Quantum advantage, the tipping point heralding the quantum era, has been accomplished along with several waves of breakthroughs. Quantum hardware has become more integrated and architectural compared to its toddler days. The controlling precision of various physical systems is pushed beyond the fault-tolerant threshold. Meanwhile, quantum computation research has established a new norm by embracing industrialization and commercialization. The joint power of governments, private investors, and tech companies has significantly shaped a new vibrant environment that accelerates the development of this field, now at the beginning of the noisy intermediate-scale quantum era. Here, we first discuss the progress achieved in the field of quantum computation by reviewing the most important algorithms and advances in the most promising technical routes, and then summarizing the next-stage challenges. Furthermore, we illustrate our confidence that solid foundations have been built for the fault-tolerant quantum computer and our optimism that the emergence of quantum killer applications essential for human society shall happen in the future.

The combination of topology and magnetism is attractive to produce exotic quantum matters, such as the quantum anomalous Hall state, axion insulators and the magnetic Weyl semimetals. MnBi2Te4, as an intrinsic magnetic topological insulator, provides a platform for the realization of various topological phases. Here we report the intermediate Hall steps in the magnetic hysteresis of MnBi2Te4, where four distinguishable magnetic memory states at zero magnetic field are revealed. The gate and temperature dependence of the magnetic intermediate states indicates the noncollinear spin structure in MnBi2Te4, which can be attributed to the Dzyaloshinskii-Moriya interaction as the coexistence of strong spin-orbit coupling and local inversion symmetry breaking on the surface. Moreover, these multiple magnetic memory states can be programmatically switched among each other through applying designed pulses of magnetic field. Our results provide new insights of the influence of bulk topology on the magnetic states, and the multiple memory states should be promising for spintronic devices.

In the original article, we have identified an inappropriate reference in the citation section of the context. To ensure the academic rigor and accuracy of the article, we decided to replace a reference with the new one. Here is the new version of the article.

The emergence of topological order in graphene is in great demand for the realization of quantum spin Hall states. Recently, it is theoretically proposed that the spin textures of surface states in topological insulator can be directly transferred to graphene by means of proximity effect. Here we report the observations of the topological proximity effect in the graphene-topological insulator Bi2Se3 heterojunctions via magnetotransport measurements. The coupling between the p_z orbitals of graphene and the p orbitals of surface states on the Bi2Se3 bottom surface can be enhanced by applying perpendicular negative magnetic field, resulting in a giant negative magnetoresistance at the Dirac point up to about -91%. An obvious resistivity dip in the transfer curve at the Dirac point is also observed in the hybrid devices, which is consistent with the theoretical predictions of the distorted Dirac bands with unique spin textures inherited from Bi2Se3 surface states.

We report an observation of a topologically protected transport of surface carriers in a quasi-ballistic Cd3As2 nanowire.The nanowire is thin enough for the spin-textured surface carriers to form 1D subbands, demonstrating conductance oscillations with gate voltage even without magnetic field. The {\\pi} phase-shift of Aharonov-Bohm oscillations can periodically appear or disappear by tuning gate voltage continuously. Such a {\\pi} phase shift stemming from the Berry's phase demonstrates the topological nature of surface states.The topologically protected transport of the surface states is further revealed by four-terminal nonlocal measurements.