In a semimetal, both electrons and holes contribute to the density of states at the Fermi level. The small band overlaps and multiband effects engender novel electronic properties. We show that a moderate hydrostatic pressure effectively suppresses the band gap in the elemental semiconductor black phosphorus. An electronic topological transition takes place at approximately 1.2 GPa, above which black phosphorus evolves into a semimetal state that is characterized by a colossal positive magnetoresistance and a nonlinear field dependence of Hall resistivity. The Shubnikov-de Haas oscillations detected in magnetic field reveal the complex Fermi surface topology of the semimetallic phase. In particular, we find a nontrivial Berry phase in one Fermi surface that emerges in the semimetal state, as evidence of a Dirac-like dispersion. The observed semimetallic behavior greatly enriches the material property of black phosphorus and sets the stage for the exploration of novel electronic states in this material.

We present the first-principles studies on the hydrostatic pressure effect of the electronic properties of black phosphorus. We show that the energy bands crossover around the critical pressure Pc=1.23 GPa; with increasing pressure, the band reversal occurs at the Z point and evolves into 4 twofolddegenerate Dirac cones around the Z point, suggesting that pressured black phosphorus is a 3D Dirac semimetal. With further increasing pressure the Dirac cones in the Γ-Z line move toward the Γ point and evolve into 2 hole-type Fermi pockets, and those in the Z-M lines move toward the M point and evolve into 2 tiny electron-type Fermi pockets, and a band above the Z-M line sinks below EF and contributes 4 electron-type pockets. A clear Lifshitz transition occurs at Pc from semiconductor to 3D Dirac semimetal. Such a 3D Dirac semimetal is protected by the nonsymmorphic space symmetry of bulk black phosphorus. These suggest the bright perspective of black phosphorus for optoelectronic and electronic devices due to its easy modulation by pressure. I. MOTIVATIONSThe van der Waals force between layers makes layered compounds graphite, MoS 2 , WTe 2 and TaS 2 , etc.,be easily exfoliated to monolayers as two-dimensional materials, such as graphite to graphene and MoS 2 to its monolayer. As a possible candidate of optoelectronic and electronic material, the energy gap of black phosphorus varies from 0.3 eV in bulk to about 2 eV in monolayer, filling the optical interval between small energy gap 0-0.3 eV in graphene and large energy gap of 1-2 eV in semiconductive dichalcogenides [1]. Recently, black phosphorus in bulk, multilayers and monolayers have received considerable interests [2][3][4]. Zhang et al. demonstrated that multilayer black phosphorus exhibits as high as 10 5 drain current modulation and 10 3 cm 2 V −1 s −1 charge mobility [5], showing that black phosphorus thin film might be a good potential candidate for field effect transistor [6]. More recently it is shown that a moderate hydrostatic pressure could not only drive semiconductive black phosphorus to metallic, but also tune multiple Fermi surfaces and Lifshitz point in the magnetotransport and ShubnikovDe Haas oscillation measurements [7]. These properties make black phosphorus a new exciting field both in material sciences and condensed matter physics [8].Hydrostatic pressure could easily change the crystal structure of black phosphorus and modify its electronic properties [3,9]. As the most stable allotrope of phosphorus, black phosphorus exhibits three different phases under moderate high hydrostatic pressures: the orthorhombic phase with wrinkled hexagons, the graphene-like rhombohedral phase with hexagonal lattice for the pressure P >4.5 GP a [10], and the simple cubic phase for P >10.3 GP a [10]. Under high pressure the P-P bond lengths and bond angle of black phosphorus display strong pressure dependence, and exhibit highly anisotropy in compressibility [9]. Though a strain may crucially modify the energy gap of monolayer black phosphorus [3], it is com...

All-solid-state sodium batteries (ASSBs) have attracted ever-increasing attention due to their enhanced safety, high energy density, and the abundance of raw materials. One of the remaining key issues for the practical ASSB is the lack of good superionic and electrochemical stable solid-state electrolytes (SEs). Design and manufacturing specific functional materials used as high-performance SEs require an in-depth understanding of the transport mechanisms and electrochemical properties of fast sodium-ion conductors on an atomic level. On account of the continuous progress and development of computing and programming techniques, the advanced computational tools provide a powerful and convenient approach to exploit particular functional materials to achieve that aim. Herein, this review primarily focuses on the advanced computational methods and ion migration mechanisms of SEs. Second, we overview the recent progress on state-of-the-art solid sodium-ion conductors, including Na-β-alumina, sulfide-type, NASICON-type, and antiperovskite-type sodium-ion SEs. Finally, we outline the current challenges and future opportunities. Particularly, this review highlights the contributions of the computational studies and their complementarity with experiments in accelerating the study progress of high-performance sodium-ion SEs for ASSBs.