Carbon allotropes are subject of intense investigations for their superb structural, electronic, and chemical properties, but not for topological band properties because of the lack of strong spin-orbit coupling (SOC). Here, we show that conjugated p-orbital interactions, common to most carbon allotropes, can in principle produce a new type of topological band structure, forming the so-called Weyl-like semimetal in the absence of SOC. Taking a structurally stable interpenetrated graphene network (IGN) as example, we show, by first-principles calculations and tight-binding modeling, that its Fermi surface is made of two symmetry-protected Weyl-like loops with linear dispersion along perpendicular directions. These loops are reduced to Weyl-like points upon breaking of the inversion symmetry. Because of the topological properties of these band-structure anomalies, remarkably, at a surface terminated by vacuum there emerges a flat band in the loop case and two Fermi arcs in the point case. These topological carbon materials may also find applications in the fields of catalysts.

We find theoretically a new quantum state of matter-the valley-polarized quantum anomalous Hall state in silicene. In the presence of Rashba spin-orbit coupling and an exchange field, silicene hosts a quantum anomalous Hall state with Chern number C=2. We show that through tuning the Rashba spin-orbit coupling, a topological phase transition results in a valley-polarized quantum anomalous Hall state, i.e., a quantum state that exhibits the electronic properties of both the quantum valley Hall state (valley Chern number Cv=3) and quantum anomalous Hall state with C=-1. This finding provides a platform for designing dissipationless valleytronics in a more robust manner.

We introduce the concept of three-dimensional Dirac (Weyl) superconductors (SC), which have protected bulk fourfold (twofold) nodal points and surface Majorana arcs at zero energy. We provide a sufficient criterion for realizing them in centrosymmetric SCs with odd-parity pairing and mirror symmetry. Pairs of Dirac nodes appear in a mirror-invariant plane when the mirror winding number is nontrivial. Breaking mirror symmetry may gap Dirac nodes producing a topological SC. Each Dirac node evolves to a nodal ring when inversion-gauge symmetry is broken, whereas it splits into a pair of Weyl nodes when, and only when, time-reversal symmetry is broken.

However, the sluggish kinetics of oxygen evolution reaction (OER) in the electrolysis of water dramatically hinders its development for practical applications. [3] One of the challenges is to develop electrocatalysts with low-cost, abundance, high stability, and high catalytic activity for OER. Noble-metal oxides (such as IrO 2 and RuO 2) are most widely employed as efficient OER catalysts, but their scarcity and high cost limit their commercial application. [4] Therefore, tremendous efforts have been devoted to exploring low-cost earthabundant metals and their compounds for high-efficient and stable OER. [5] Nonprecious transition metal-based compounds, such as sulfides, [4c,6] (oxy)hydroxides, [4a,7] oxides, [4b,8] and phosphides, [4b,9] have been reported for OER owing to their tunable electronic structures and abundant active sites. Recently, 3d transition metal nitrides (TMNs) have been recognized to be promising for the OER process, which are superior to oxides, hydroxides, and sulfides, because of high electrical conductivity and enriched active sites. [10] It should be noted here that the surfaces of TMNs are easily oxidized into oxides and hydroxides. For example, the surface of catalyst was converted to metal oxyhydroxide (*OOH) owing to fast surface reconstruction and phase transition during the electrochemical The sluggish oxygen evolution reaction (OER) is a pivotal process for renewable energy technologies, such as water splitting. The discovery of efficient, durable, and earth-abundant electrocatalysts for water oxidation is highly desirable. Here, a novel trimetallic nitride compound grown on nickel foam (CoVFeN @ NF) is demonstrated, which is an ultra-highly active OER electrocatalyst that outperforms the benchmark catalyst, RuO 2 , and most of the state-of-the-art 3D transition metals and their compounds. CoVFeN @ NF exhibits ultralow OER overpotentials of 212 and 264 mV at 10 and 100 mA cm −2 in 1 m KOH, respectively, together with a small Tafel slop of 34.8 mV dec −1. Structural characterization reveals that the excellent catalytic activity mainly originates from: 1) formation of oxyhydroxide species on the surface of the catalyst due to surface reconstruction and phase transition, 2) promoted oxygen evolution possibly activated by peroxo-like (O 2 2−) species through a combined lattice-oxygen-oxidation and adsorbate escape mechanism, 3) an optimized electronic structure and local coordination environment owing to the synergistic effect of the multimetal system, and 4) greatly accelerated electron 1. Introduction Developing renewable and ecofriendly energy sources/technologies is urgently required to address environmental pollution and energy crisis. [1] Electrically driven water splitting for the production of hydrogen and oxygen has been considered as one

We generalize a semiclassical theory and use the argument of angular momentum conservation to examine the ballistic transport in lightly-doped Weyl semimetals, taking into account various phase-space Berry curvatures. We predict universal transverse shifts of the wave-packet center in transmission and reflection, perpendicular to the direction in which the Fermi energy or velocities change adiabatically. The anomalous shifts are opposite for electrons with different chirality, and can be made imbalanced by breaking inversion symmetry. We discuss how to utilize local gates, strain effects, and circularly polarized lights to generate and probe such a chirality Hall effect.When a strong topological insulator [1, 2] undergoes a phase transition to a trivial band insulator in three dimensions, a gapless Dirac point [3][4][5][6] emerges at the critical point, if both time-reversal (T ) and inversion (P) symmetries are present. Remarkably, when one of the two symmetries is broken, the critical point expands in the phase diagram and the Dirac point splits into pairs of Weyl points related by the unbroken symmetry. This emergent phase [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], dubbed as Weyl semimetal (WSM), is an appealing topological state of matter, with the Fermi surface being those Weyl points.In the simplest case when T symmetry is broken, a WSM at long wavelength only has one pair of Weyl points, which may be described by the HamiltonianHere v's are the Fermi velocities, σ's are Pauli matrices, and τ = ± denote the left-and right-handed Weyl fermions, which are required to come in pairs by the Nielsen-Ninomiya theorem [22]. τ bẑ are the positions of the pair of Weyl points in the Brillouin zone (BZ), and 2b 0 is their energy splitting, which vanishes when P symmetry is not broken. Since all three σ's are used up locally at each Weyl point, small perturbations may renormalize the parameters but cannot open a gap. Indeed, each Weyl point is protected by the Chern number (±1) of the valence band on a constant-energy surface enclosing it. Weyl points can only be annihilated in pairs of opposite chirality, when they are brought together (b, b 0 = 0) or when the translational symmetry is broken by strong interactions or by short-range scatterers.The topological properties of WSM can be best seen by considering a slice of the BZ normal toẑ. The Chern number of the slice changes from 0 to 1 and back to 0 as it crosses the two Weyl points successively. As a consequence, each nontrivial slice contributes an e 2 /h to the Hall conductivity [9-11] producing σ xy = be 2 /πh in the bulk, and also contributes one edge state to the surface forming a surface Fermi arc connecting the two projected Weyl points. Recently, the Weyl points and surface arcs appear to be observed in optical experiments [23][24][25].This progress may herald a flurry of exciting experiments on the appealing transport effects [26][27][28] predicted in WSM, e.g., the chiral magnetic effect [29][30][31][32][33][34][35][36] when b 0 becomes non...