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Black phosphorus (BP), a layered van der Waals material, reportedly has a band gap sensitive to external perturbations and manifests a Dirac-semimetal phase when its band gap is closed. Previous studies were focused on effects of each perturbation, lacking a unified picture for the band-gap closing and the Dirac-semimetal phase. Here, using pseudospins from the glide-reflection symmetry, we study the electronic structures of mono- and bilayer BP and construct the phase diagram of the Dirac-semimetal phase in the parameter space related to pressure, strain, and electric field. We find that the Dirac-semimetal phase in BP layers is singly connected in the phase diagram, indicating the phase is topologically identical regardless of the gap-closing mechanism. Our findings can be generalized to the Dirac semimetal phase in anisotropic layered materials and can play a guiding role in search for a new class of topological materials and devices.
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Motivated by recent experimental observation of an hydrostatic pressure induced transition from semiconductor to semimetal in black phosphorus [Chen et al. in arXiv:1504.00125], we present the first principles calculation on the pressure effect of the electronic structures of black phosphorus. It is found that the band crossover and reversal at the Z point occur around the critical pressure Pc1=1.23 Gpa, and the band inversion evolves into 4 twofold-degenerate Dirac cones around the Z point, suggesting a 3D Dirac semimetal. With further increasing pressure the Dirac cones in the Gamma-Z line move toward the Gamma point and evolve into two hole-type Fermi pockets, and those in the Z-M lines move toward the M point and evolve into 2 hole-type Fermi pockets up to P=4.0 Gpa. It demonstrates clearly that the Lifshitz transition occurs at $P_{c1}$ from semiconductor to 3D Dirac semimetal protected by the nonsymmorphic space symmetry of bulk. This suggests the bright perspective of black phosphorus for optoelectronic and electronic devices due to its easy modulation by pressure.
Black phosphorus (bP) is the second known elemental allotrope with a layered crystal structure that can be mechanically exfoliated down to atomic layer thickness. We have fabricated bP naked quantum wells in a back-gated field effect transistor geometry with bP thicknesses ranging from $6pm1$ nm to $47pm1$ nm. Using an encapsulating polymer superstrate, we have suppressed bP oxidation and have observed field effect mobilities up to 600 cm$^2$/Vs and on/off current ratios exceeding $10^5$. Importantly, Shubnikov-de Haas (SdH) oscillations observed in magnetotransport measurements up to 35 T reveal the presence of a 2-D hole gas with Schrodinger fermion character in an accumulation layer at the bP/oxide interface. Our work demonstrates that 2-D electronic structure and 2-D atomic structure are independent. 2-D carrier confinement can be achieved in layered semiconducting materials without necessarily approaching atomic layer thickness, advantageous for materials that become increasingly reactive in the few-layer limit such as bP.
Very recently, in spite of various efforts in searching for two dimensional topological Dirac semimetals (2D TDSMs) in phosphorene, there remains a lack of experimentally efficient way to activate such phase transition and the underlying mechanism for the topological phase acquisition is still controversial. Here, from first-principles calculations in combination with a band-sorting technique based on k.p theory, a layer-pressure topological phase diagram is obtained and some of the controversies are clarified. We demonstrate that, compared with tuning by external electric-fields, strain or doping by adsorption, hydrostatic pressure can be an experimentally more feasible way to activate the topological phase transition for 2D TDSM acquisition in phosphorene. More importantly, the resultant TDSM state is a pristine phase possessing a single pair of symmetry-protected Dirac cones right at the Fermi level, in startling contrast to the pressured bulk black phosphorous where only a carrier-mixed Dirac state can be obtained. We corroborate that the Dirac points are robust under external perturbation as long as the glide-plane symmetry preserves. Our findings provide a means to realize 2D pristine TDSM in a more achievable manner, which could be crucial in the realization of controllable TDSM states in phosphorene and related 2D materials.
The three dimensional (3D) topological insulators are predicted to exhibit a 3D Dirac semimetal state in critical regime of topological to trivial phase transition. Here we demonstrate the first experimental evidence of 3D Dirac semimetal state in topological insulator Bi2Se3 with bulk carrier concentration of ~ 10^19 cm^{-3}, using magneto-transport measurements. At low temperatures, the resistivity of our Bi2Se3 crystal exhibits clear Shubnikov-de Haas (SdH) oscillations above 6T. The analysis of these oscillations through Lifshitz-Onsanger and Lifshitz-Kosevich theory reveals a non-trivial pi Berry phase coming from 3D bands, which is a decisive signature of 3D Dirac semimetal state. The large value of Dingle temperature and natural selenium vacancies in our crystal suggest that the observed 3D Dirac semimetal state is an outcome of enhanced strain field and weaker effective spin-orbit coupling.
Two-dimensional Dirac semimetals have attracted much attention because of their linear energy dispersion and non-trivial Berry phase. Graphene-like 2D Dirac materials are gapless only within certain approximations, e.g., if spin-orbit coupling (SOC) is neglected. It has recently been reported that materials with nonsymmorphic crystal lattice possess symmetry-enforced Dirac-like band dispersion around certain high-symmetry momenta even in the presence of SOC. Here we calculate the optical absorption coefficient of nonsymmorphic semimetals, such as $alpha$-bismuthene, which hosts two anisotropic Dirac cones with different Fermi velocities along $x$ and $y$ directions.We find that the optical absorption coefficient depends strongly on the anisotropy factor and the photon polarization. When a magnetic field is applied perpendicular to the plane of the material, the absorption coefficient also depends on an internal parameter we termed the mixing angle of the band structure. We further find that an in-plane magnetic field, while leaving the system gapless, can induce a Van-Hove singularity in the joint density of states: this causes a significant enhancement of the optical absorption at the frequency of the singularity for one direction of polarization but not for the orthogonal one, making the optical properties even more strongly dependent on polarization. Due to the anisotropy present in our model, the Dirac cones at two high-symmetry momenta in the Brillouin zone contribute very differently to the optical absorbance. Consequently, it might be possible to preferentially populate one valley or the other by varying photon polarization and frequency. These results suggest that nonsymmorphic 2D Dirac semimetals are excellent candidate materials for tunable magneto-optic devices.
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