Pressure-Induced Electronic Transition in Black Phosphorus

Pressure-Driven Polymorphic Transition, Emergent Insulator-To-Metal Transition, and Photoconductivity Switching in Violet Phosphorus

Polymorphic phase transition is an essential phenomenon in condensed matter that the physical properties of materials may undergo significant changes due to the structural transformation. Phase transition has thus become an important means and dimension for regulating material properties. Herein, this study demonstrates the pressure-induced multi-transition of both structure and physical properties in violet phosphorus, a novel phosphorus allotrope. Under compression, violet phosphorus undergoes sequential polymorphic phase transitions. Concomitant with the first phase transition, violet phosphorus exhibits emergent insulator-metal transition, superconductivity, and dramatic switching from positive to negative photoconductivity. Remarkably, the resistance of violet phosphorus shows a sudden drop of around 107 along with the phase transition. In addition, piezochromism from translucent red to opaque black and suppression of photoluminescence are observed upon compression. Of particular interest is that the sample irreversibly transforms into black phosphorus with a pronounced discrepancy in physical properties from the pristine violet phosphorus after decompression. The abundant polymorphic transitions and property changes in violet phosphorus have significant implications for designing novel pressure-responsive electronic/optoelectronic devices and exploring concealed polymorphic transition materials.

Effect of tensile deformation on the optoelectronic properties of black phosphine-doped lithium atoms

CONTEXT

First-principles calculations based on the generalized gradient approximation gradient and the Perdew-Burke-Ernzerhof function (GGA-PBE generalized function) are carried out on the intrinsic and lithium-doped black phosphine systems to investigate the effects of different uniaxial tensile deformations on the electronic and optical properties of the systems. It is shown that the structural stability of the intrinsic and lithium-doped systems decreases with increasing tensile deformation, and all systems are most stable at 0% tensile deformation. The intrinsic black phosphazene system is a direct band gap semiconductor, and its band gap increases and then decreases with tensile deformation and reaches a maximum value of 1.086 eV at 4%. Lithium doping closes the band gap of the black phosphazene system, which is metallic in nature, but the band gap is opened up when the tensile deformation is 4-6%. From the density of states analysis, the density of states of all systems is basically contributed by the s and p orbitals, with little contribution from the d orbitals, and the contribution from the p orbitals is dominant. From the analysis of optical properties, the increase of tensile deformation causes the absorption peaks of the intrinsic system to redshift then blueshift then redshift, causes the absorption peaks of the lithium-doped system to redshift, and causes the reflection peaks of all systems to redshift. In addition, lithium doping blueshifts the absorption and reflection peaks of the systems compared to the intrinsic black phosphazene system.

METHODS

Using the CASTEP section of the Materials Studio software, first-principle calculations based on density functional theory are done on the top-site doped lithium atoms of monolayer black phosphine under uniaxial stretching deformation in the a-direction, and the generalized gradient approximation gradients and Perdew-Burke-Ernzerhof functions (GGA-PBE generalized functionals) are used for the optimization and approximation process. The optimization parameters are set for the supercell structure: its plane-wave truncation energy is set to 400 eV, its Brillouin zone K-point grid is set to 3*3*3, its self-consistent field iteration accuracy convergence value is 2.0e-6 eV/atom, the convergence basis of its structural optimization is 0.02 eV/ Å, and the convergence of the stress value is 0.05 gpa. During the optimization period, the interaction force between atoms is 0.03 eV/ Å and the atomic displacement is less than 0.001 Å. To eliminate the effect of interlayer forces, a vacuum layer with a thickness of 15 Å is placed in its vertical direction (i.e., c-axis direction).

Imaging Ultrafast Dynamics of Pressure-Driven Phase Transitions in Black Phosphorus and Anomalous Coherent Phonon Softening

Applying high pressure to effectively modulate the electronic and lattice structures of materials could unravel various physical properties associated with phase transitions. In this work, high-pressure-compatible femtosecond pump-probe microscopy was constructed to study the pressure-dependent ultrafast dynamics in black phosphorus (BP) thin films. We observed pressure-driven evolution of the electronic topological transition and three structural phases as the pressure reached ∼22 GPa, which could be clearly differentiated in the transient absorption images containing spatially resolved ultrafast carrier and coherent phonon dynamics. Surprisingly, an anomalous coherent acoustic phonon mode with pressure softening behavior was observed within the range of ∼3-8 GPa, showing distinct laser power and time dependences. Density functional theory calculations show that this mode, identified as the shear mode along the armchair orientation, gains significant electron-phonon coupling strength from out-of-plane compression that leads to decreased phonon frequency. Our results provide insights into the structure evolution of BP with pressure and hold potential for applications in microelectromechanical devices.

Effects of spin-orbit coupling on transmission and absorption of electromagnetic waves in strained armchair phosphorene nanoribbons

We compute the optical conductivity, both the imaginary and real parts of the dielectric constant, and the optical coefficients of armchair phosphorene nanoribbons under application of biaxial and uniaxial strains. The Kane-Mele model Hamiltonian has been applied to obtain the electronic band structure of phosphorene nanoribbons in the presence of a magnetic field. The effects of uniaxial and biaxial in-plane strain on the frequency behavior of the optical dielectric constant, and the frequency behavior of the optical absorption and refractive index of phosphorene nanoribbons have been studied, in terms of magnetic field, spin-orbit coupling and strain effects. Linear response theory and the Green's function approach have been exploited to obtain the frequency behavior of the optical properties of the structure. Moreover, the transmissivity and reflectivity of electromagnetic waves between two media separated by a phosphorene-nanoribbon layer are determined. Our numerical results indicate that the frequency dependence of the optical absorption includes a peak due to applying a magnetic field. Moreover, the effects of both in-plane uniaxial and biaxial strains on the refractive index of single-layer phosphorene have been addressed. Also, the frequency dependence of the transmissivity and reflectivity of electromagnetic waves between two media separated by armchair phosphorene nanoribbons for normal incidence has been investigated in terms of the effects of magnetic field and strain parameters. Both compressive and tensile strain have been considered for the armchair phosphorene nanoribbons in order to study the optical properties of the structure. In particular, the control of the optical properties of phosphorene nanoribbons could lead to extensive applications of phosphorene in the optoelectronics industry. Also, such a study of the optical properties of phosphorene nanoribbons has further applications in light sensors. Meanwhile, the effects of spin-orbit coupling on the optical absorption and transmissivity of electromagnetic waves in phosphorene nanoribbons could be a novel topic in condensed-matter physics.

Pressure-Induced Structural Phase Transition and Enhanced Interlayer Coupling in Two-Dimensional Ferromagnet CrSiTe3

The two-dimensional van der Waals ferromagnetic semiconductor CrSiTe₃ has attracted growing interest as an intrinsic topological magnet. Both superconductivity and enhancement of ferromagnetism, usually competing for orders, have been observed in CrSiTe₃ at high pressure. However, the high-pressure structure of CrSiTe₃ is still unclear, setting obstacles in understanding pressure-induced novel physics. Here, combining the Raman spectra and first-principles calculations, the structure of CrSiTe₃ at high pressure has been clarified. The interlayer breathing mode located at ∼42.1 cm^-1 has been observed for the first time in CrSiTe₃ by ultralow-frequency Raman spectroscopy at high pressure. Theoretical calculations confirm a phase transition from the R3̅ phase to the R3 phase accompanying noticeable enhancement of the Curie temperature. Our results highlight ultralow-frequency Raman spectroscopy combined with high pressure for detecting and modulating the structure and interlayer coupling of two-dimensional materials.

Giant Density of States Enhancement Driven by a Zero-Mode Landau Level in Semimetallic Black Phosphorus under Pressure

Dirac fermion systems form a unique Landau level at the Fermi level-the so-called zero mode-whose observation itself will provide strong evidence of the presence of Dirac dispersions. Here, we report the study of semimetallic black phosphorus under pressure by ^{31}P-nuclear magnetic resonance measurements in a wide range of magnetic field up to 24.0 T. We have found a field-induced giant enhancement of 1/T_{1}T, where 1/T_{1} is the nuclear spin lattice relaxation rate: 1/T_{1}T at 24.0 T reaches more than 20 times larger than that at 2.0 T. The increase in 1/T_{1}T above 6.5 T is approximately proportional to the squared field, implying a linear relationship between the density of states and the field. We also found that, while 1/T_{1}T at a constant field is independent of temperature in the low-temperature region, it steeply increases with temperature above 100 K. All these phenomena are well explained by considering the effect of Landau quantization on three-dimensional Dirac fermions. The present study demonstrates that 1/T_{1} is an excellent quantity to probe the zero-mode Landau level and to identify the dimensionality of the Dirac fermion system.

Ultrafast Carrier-Coupled Interlayer Contraction, Coherent Intralayer Motions, and Phonon Thermalization Dynamics of Black Phosphorus

Black phosphorus (bP) exhibits highly anisotropic properties and dynamical behavior that are unique even among two-dimensional and van der Waals (vdW) layered materials. Here, we show that an interlayer lattice contraction and concerted, symmetric intralayer vibrations occur concurrently within few picoseconds following the photoinjection and relaxation of carriers, using ultrafast electron diffraction in the reflection geometry to probe the out-of-plane motions. A strong coupling between the photocarriers and bP's puckered structure, with the alignment of the electronic band structure, is at work for such directional atomic motions without a photoinduced phase transition. Three temporal regimes can be identified for the phonon thermalization dynamics where a quasi-equilibrium without anisotropy is reached in about 50 ps, followed by propagation of coherent acoustic phonons and heat diffusion into the bulk. The early time out-of-plane dynamics reported here have important implications for single- and few-layer bP and other vdW materials with strong electronic-lattice correlations.

Manipulating the electronic structure and physical properties in monolayer Mo2I3Br3via strain and doping

Identifying new two-dimensional intrinsic ferromagnets with high transition temperatures is a key step of improving device performance. Here we used first-principles calculations to demonstrate that the monolayer Janus Mo₂I₃Br₃ is an intrinsic ferromagnetic bipolar semiconductor with a large out-of-plane spin orientation. The calculated phonon dispersion and ab initio molecular dynamic simulations indicate the stability dynamically and thermally. Furthermore, we investigated the effect of electrostatic doping or in-plane biaxial strain on the electronic structures and magnetic and optical properties of monolayer Mo₂I₃Br₃. We find that the magnetic anisotropy energy and Curie temperature are enhanced more than 4 and 2 times with the hole doping compared with those in the pristine monolayer Mo₂I₃Br₃, respectively. The calculated electronic structures show that the stable half-metallic states are formed by electron or hole doping due to the strong spin polarization of the electronic states around the Fermi level. Furthermore, the spin orientation in the metallic channel of the doped monolayer Mo₂I₃Br₃ can be flipped with the increase of electron doping concentration. In addition, the magnetic anisotropy energy and Curie temperature can also be effectively manipulated by in-plane biaxial strain. The spin polarization of the conduction band minimum can be reversed by the tensile strain of 3% for the monolayer Mo₂I₃Br₃, transforming it into an indirect band gap semiconductor. Finally, the calculated large and tunable optical absorption coefficient indicates that monolayer Mo₂I₃Br₃ is a promising candidate for potential optoelectronic applications. Our results may open up more opportunities for few-layer van der Waals crystals in magnetic storage, spintronics, and optoelectronic devices.

Anomalous non-equilibrium response in black phosphorus to sub-gap mid-infrared excitation

The competition between the electron-hole Coulomb attraction and the 3D dielectric screening dictates the optical properties of layered semiconductors. In low-dimensional materials, the equilibrium dielectric environment can be significantly altered by the ultrafast excitation of photo-carriers, leading to renormalized band gap and exciton binding energies. Recently, black phosphorus emerged as a 2D material with strongly layer-dependent electronic properties. Here, we resolve the response of bulk black phosphorus to mid-infrared pulses tuned across the band gap. We find that, while above-gap excitation leads to a broadband light-induced transparency, sub-gap pulses drive an anomalous response, peaked at the single-layer exciton resonance. With the support of DFT calculations, we tentatively ascribe this experimental evidence to a non-adiabatic modification of the screening environment. Our work heralds the non-adiabatic optical manipulation of the electronic properties of 2D materials, which is of great relevance for the engineering of versatile van der Waals materials.

Here, the authors investigate the optical response of bulk black phosphorus to mid-infrared pulses, and find that while above-gap excitation leads to a broadband light-induced transparency, sub-gap pulses drive an anomalous response, peaked at the single-layer exciton resonance.

Engineering Near-Infrared Light Emission in Mechanically Exfoliated InSe Platelets through Hydrostatic Pressure for Multicolor Microlasing

γ-indium selenide (InSe) is a van der Waals semiconductor and holds great potentials for low-energy-consumption electronic and optoelectronic devices. Herein, we investigated the hydrostatic pressure engineered near-infrared (NIR) light emission of mechanically exfoliated γ-InSe crystals using the diamond anvil cell (DAC) technique. A record-wide spectral tuning range of 185 nm and a large linear pressure coefficient of 40 nm GPa^-1 were achieved for spontaneous emissions, leading to ultrabroadband microlasing spectrally ranging from 1022 to 911 nm. This high emission tunability can be attributed to the compression of the soft intralayer In-Se bonds under high pressure, which suppressed the band gap shrinkage by increasing the interlayer interaction. Furthermore, two band gap crossovers of valence (direct-to-indirect) and conduction bands were resolved at approximately 4.0 and 7.0 GPa, respectively, resulting in pressure-sensitive emission lifetime and intensity. These findings pave the pathways for pressure-sensitive InSe-based NIR light sources, sensors and so on.

Moiré bands in twisted trilayer black phosphorene: effects of pressure and electric field

Twist-induced moiré bands and accompanied correlated phenomena have been extensively investigated in twisted hexagonal lattices with weak interlayer coupling. However, the formation of moiré bands in strongly coupled layered materials and their controlled tuning remain largely unexplored. Here, we systematically study the moiré bands in twisted trilayer black phosphorene (TTbP) and the influences of pressure and electric field on them. Moiré states can form in various TTbPs even when the twist angle is larger than 16° similar to that of twisted bilayer bP. However, different TTbPs show different localization patterns depending on the twisting layer, leading to distinct dipolar behaviors. While these moiré states become quasi-one-dimensional (1D) as the twist angle decreases, external pressure causes the crossover of moiré states from quasi-1D to 0D with a dramatic change in localization areas and greatly reduced bandwidth. Interestingly, compared to twisted bilayer and pristine bP, TTbPs show a much larger electric-field induced Stark effect, controllable by either the twist angle or twist layer. Our work thus demonstrates TTbP as an attractive platform to explore moiré-controlled electronic and optical properties, as well as tunable optoelectronic applications.

Layer-Dependent Pressure Effect on the Electronic Structure of 2D Black Phosphorus

Through infrared spectroscopy, we systematically study the pressure effect on electronic structures of few-layer black phosphorus (BP) with layer number ranging from 2 to 13. We reveal that the pressure-induced shift of optical transitions exhibits strong layer dependence. In sharp contrast to the bulk counterpart which undergoes a semiconductor to semimetal transition under ∼1.8  GPa, the band gap of 2 L increases with increasing pressure until beyond 2 GPa. Meanwhile, for a sample with a given layer number, the pressure-induced shift also differs for transitions with different indices. Through the tight-binding model in conjunction with a Morse potential for the interlayer coupling, this layer- and transition-index-dependent pressure effect can be fully accounted. Our study paves a way for versatile van der Waals engineering of two-dimensional BP.

Unambiguous determination of crystal orientation in black phosphorus by angle-resolved polarized Raman spectroscopy

Angle-resolved polarized Raman spectroscopy (ARPRS) is widely used to determine the crystal orientations of anisotropic layered materials (ALMs), which is an essential step to study all of their anisotropic properties. However, the understanding of the ARPRS response of black phosphorous (BP) as a most widely studied ALM is still unsatisfactory. Here, we clarify two key controversies about the physical origin of the intricate ARPRS response and the determination of crystal orientations in BP. Through systematic ARPRS measurements, we show that the degree of anisotropy of the response evolves gradually and periodically with the BP thickness, eventually leading to the intricate response. Meanwhile, we find that using the Raman peak intensity ratio of the two A_g phonon modes, the crystal orientations of BP can be unambiguously distinguished via a concise inequality . Comprehensive analysis and first-principles calculations reveal that the external anisotropic interference effect and the intrinsic electron-phonon coupling are responsible for the observations.

Ultrafast dynamical Lifshitz transition

Fermi surface is at the heart of our understanding of metals and strongly correlated many-body systems. An abrupt change in the Fermi surface topology, also called Lifshitz transition, can lead to the emergence of fascinating phenomena like colossal magnetoresistance and superconductivity. While Lifshitz transitions have been demonstrated for a broad range of materials by equilibrium tuning of macroscopic parameters such as strain, doping, pressure, and temperature, a nonequilibrium dynamical route toward ultrafast modification of the Fermi surface topology has not been experimentally demonstrated. Combining time-resolved multidimensional photoemission spectroscopy with state-of-the-art TDDFT+U simulations, we introduce a scheme for driving an ultrafast Lifshitz transition in the correlated type-II Weyl semimetal T _d-MoTe₂ We demonstrate that this nonequilibrium topological electronic transition finds its microscopic origin in the dynamical modification of the effective electronic correlations. These results shed light on a previously unexplored ultrafast scheme for controlling the Fermi surface topology in correlated quantum materials.

Systematic competition between strain and electric field stimuli in tuning EELS of phosphorene

The strongly anisotropic properties of phosphorene makes it an attractive material for applications in deciding the specific direction for different purposes. Here we have particularly reported the competition between strain and electric field stimuli in evaluating the band gap and electron energy loss spectrum (EELS) of single-layer black phosphorus using the tight-binding method and the Kubo conductivity. We construct possible configurations for this competition and evaluate the interband optical excitations considering the corresponding band gap variations. The band gap increases with the individual electric field, while it increases (decreases) with tensile (compressive) uniaxial in-plane strain. Contrary to the in-plane strains, the uniaxial out-of-plane strain shows a critical strain at which the system suffers from a phase transition. Furthermore, the presence of these stimuli simultaneously results in an extraordinary band gap engineering. Based on the EELS response in the electromagnetic spectrum, the armchair (zigzag) direction is classified into the infrared and visible (ultraviolet) region. We report that the electric field gives rise to the blue shift in the interband optical transitions along the armchair direction, while the compressive/tensile (tensile/compressive) in-plane/out-of-plane strain provides a red (blue) shift. Moreover, we observe an inverse behavior of EELS response to the individual and combined effects of electric field and strains compared to the band gap behavior except at critical out-of-plane strain for which the physical theory of interband excitation is simply violated. Our results provide a new perspective on the applicability of phosphorene in stimulated optical applications.

Kinetics-Limited Two-Step Growth of van der Waals Puckered Honeycomb Sb Monolayer

Puckered honeycomb Sb monolayer, the structural analog of black phosphorene, has been recently successfully grown by means of molecular beam epitaxy. However, little is known to date about the growth mechanism for such a puckered honeycomb monolayer. In this study, by using scanning tunneling microscopy in combination with first-principles density functional theory calculations, we unveil that the puckered honeycomb Sb monolayer takes a kinetics-limited two-step growth mode. As the coverage of Sb increases, the Sb atoms first form the distorted hexagonal lattice as the half layer, and then the distorted hexagonal half-layer transforms into the puckered honeycomb lattice as the full layer. These results provide the atomic-scale insight in understanding the growth mechanism of puckered honeycomb monolayer and can be instructive to the direct growth of other monolayers with the same structure.

Prediction of topological nontrivial semimetals and pressure-induced Lifshitz transition in 1T'-MoS2 layered bulk polytypes

Recently, bulk MoS2 crystals stacked by 1T'-MoS2 monolayers have been synthesized successfully, but little is known about their stacking sequences and topological properties. Based on first-principles calculations and symmetry-based indicator theory, we discovered that three predicted bulk structures of MoS2 (named 2M-, 1T'- and β-MoS2) stacked by 1T' monolayers are topological insulators and nodal line semimetals with and without spin-orbit coupling. Their stacking stability, electronic structure and the topology origin were systematically investigated. Further research proves that in the absence of SOC the open- and closed-type nodal lines can coexist in the momentum space of 2M-MoS2, which also possesses drumhead-like surface state. Moreover, we predicted a pressure-induced Lifshitz transition at about 1.3 GPa in 2M-MoS2. Our findings greatly enrich the topological phases of MoS2 and probably bring MoS2 to the rapidly growing family of layered topological semimetals.

Reversible Pressure-Induced Partial Phase Transition in Few-Layer Black Phosphorus

The experimental identification of structural transitions in layered black phosphorus (BP) under mechanical stress is essential to extend its application in microelectromechanical (MEMS) devices under harsh conditions. High-pressure Raman spectroscopic analysis of BP flakes suggests a transition pressure at ∼4.2 GPa, where the BP's crystal structure progressively transforms from an orthorhombic to a rhombohedral symmetry (blue phosphorus, bP). The phase transition has been identified by observing a transition from blueshift to redshift of the in-plane characteristic Raman modes (B_2g and A_g²) with increasing pressure. Recovery of the vibrational frequencies for all three characteristic Raman modes confirms the reversibility of the structural phase transition. First-principles calculations provide insight into the behavior of the Raman modes of BP under high pressure and reveal the mechanism responsible for the partial phase transition from BP to bP, corresponding to a metastable equilibrium state where both phases coexist.

Structure refinement of black phosphorus under high pressure

The structure refinement of black phosphorus was performed at pressures of up to 3.2 GPa at room temperature by powder neutron diffraction techniques. The bond lengths and bond angles between the phosphorus atoms at pressures were precisely determined and confirmed to be consistent with those of the previous single crystal x-ray analysis [A. Brown and S. Rundqvist, Acta Cryst. 19, 684 (1965)]. Although the lattice parameters exhibited an anisotropic compressibility, the covalent P1-P2 and P1-P3 bond lengths were almost independent of pressure and only the P3-P1-P2 bond angle was reduced significantly. On the basis of our results, the significant discrepancy in the bond length reported by Cartz et al. [J. Chem. Phys. 71, 1718 (1979)] has been resolved. Our structural data will contribute to the elucidation of the Dirac semimetal state of black phosphorus under high pressure.

Temperature-Induced Lifshitz Transition and Possible Excitonic Instability in ZrSiSe

The nodal-line semimetals have attracted immense interest due to the unique electronic structures such as the linear dispersion and the vanishing density of states as the Fermi energy approaching the nodes. Here, we report temperature-dependent transport and scanning tunneling microscopy (spectroscopy) [STM(S)] measurements on nodal-line semimetal ZrSiSe. Our experimental results and theoretical analyses consistently demonstrate that the temperature induces Lifshitz transitions at 80 and 106 K in ZrSiSe, which results in the transport anomalies at the same temperatures. More strikingly, we observe a V-shaped dip structure around Fermi energy from the STS spectrum at low temperature, which can be attributed to co-effect of the spin-orbit coupling and excitonic instability. Our observations indicate the correlation interaction may play an important role in ZrSiSe, which owns the quasi-two-dimensional electronic structures.

Spin-splitting effects on the interband optical conductivity and activity of phosphorene

Being able to tune the anisotropic interband transitions in phosphorene at finite temperature offers an enormous amount of possibilities in finding new insights in the optoelectronic community. To contribute to this goal we propose a Zeeman spin-splitting field aiming at absorbing various frequencies of the incident light. Employing the tight-binding Hamiltonian to describe the carrier dynamics and the Kubo formalism to formulate the orientation-dependent interband optical conductivity (IOC) and optical activity of phosphorene we investigate the absorption and scattering mechanisms in phosphorene depending on the Zeeman field strength and optical energy parameters. The optical activity features are characterized by exploring the eccentricity and shift phase of reflected and transmitted electromagnetic waves of the incident light. Different electronic phases in the absence and presence of Zeeman field ultimate different types of interband transitions of which in all cases the IOC along the armchair direction is larger than the zigzag one. However, we observed an irregular (regular) process for IOC with the Zeeman field along the armchair (zigzag) direction, resulting in irregular (regular) absorption and scattering mechanisms. Additionally, a little to no effects for temperature-dependent IOC are provided with the Zeeman field in undoped phosphorene. Further, almost linearly and elliptically polarizations are reported for the transmitted and reflected waves, respectively, indicating that the phosphorene is almost transparent. The emergence of Zeeman spin-splitting effects in optoelectronic properties of phosphorene is pleasant to make it a great potential candidate for logic applications.

Exploring the Limits of Transition-Metal Fluorination at High Pressures

Fluorination is a proven method for challenging the limits of chemistry, both structurally and electronically. Here we explore computationally how pressures below 300 GPa affect the fluorination of several transition metals. A plethora of new structural phases are predicted along with the possibility for synthesizing four unobserved compounds: TcF₇ , CdF₃ , OsF₈ , and IrF₈ . The Ir and Os octaflourides are both predicted to be stable as quasi-molecular phases with an unusual cubic ligand coordination, and both compounds formally correspond to a high oxidation state of +8. Electronic-structure analysis reveals that otherwise unoccupied 6p levels are brought down in energy by the combined effects of pressure and a strong ligand field. The valence expansion of Os and Ir enables ligand-to-metal F 2p→M 6p charge transfer that strengthens M-F bonds and decreases the overall bond polarity. The lower stability of IrF₈ , and the instability of PtF₈ and several other compounds below 300 GPa, is explained by the occupation of M-F antibonding orbitals in octafluorides with a metal-valence-electron count exceeding 8.

Pressure-induced metallization of black arsenic

Black arsenic (bAs), a cousin of black phosphorus, has attracted increasing attention due to its excellent physical properties such as high carrier mobility and high on/off ratio, which provide new opportunities for future field-effect transistors and photodetectors. As a clear and powerful means, hydrostatic pressure is commonly used to tune the structure and electronic properties of materials. However, there have been few reports to date about bAs under pressure. In this work, a theoretical study is presented on the structure, stability, and electronic properties of bAs under high pressure. The calculation results show that bAs becomes unstable at pressures above 3 GPa. A transition from direct band gap to indirect band gap occurs at 1.2 GPa, and with a further increase of pressure, bAs undergoes a phase transition from semiconductor to metal at a critical pressure of 2.2 GPa. In addition, the carrier effective masses can be modulated slightly by hydrostatic pressure.

Pressure-induced phase transitions and superconductivity in a quasi-1-dimensional topological crystalline insulator α-Bi4Br4

Great progress has been achieved in the research field of topological states of matter during the past decade. Recently, a quasi-1-dimensional bismuth bromide, Bi₄Br₄, has been predicted to be a rotational symmetry-protected topological crystalline insulator; it would also exhibit more exotic topological properties under pressure. Here, we report a thorough study of phase transitions and superconductivity in a quasihydrostatically pressurized α-Bi₄Br₄ crystal by performing detailed measurements of electrical resistance, alternating current magnetic susceptibility, and in situ high-pressure single-crystal X-ray diffraction together with first principles calculations. We find a pressure-induced insulator-metal transition between ∼3.0 and 3.8 GPa where valence and conduction bands cross the Fermi level to form a set of small pockets of holes and electrons. With further increase of pressure, 2 superconductive transitions emerge. One shows a sharp resistance drop to 0 near 6.8 K at 3.8 GPa; the transition temperature gradually lowers with increasing pressure and completely vanishes above 12.0 GPa. Another transition sets in around 9.0 K at 5.5 GPa and persists up to the highest pressure of 45.0 GPa studied in this work. Intriguingly, we find that the first superconducting phase might coexist with a nontrivial rotational symmetry-protected topology in the pressure range of ∼3.8 to 4.3 GPa; the second one is associated with a structural phase transition from monoclinic C2/m to triclinic P-1 symmetry.

Pressure-induced enhancement of thermoelectric power factor in pristine and hole-doped SnSe crystals

We evaluate the influence of pressure on the thermoelectric power factors PF ≡ S²σ of pristine and Na-doped SnSe crystals by measuring their electrical conductivity σ(T) and Seebeck coefficient S(T) up to ∼22 kbar with a self-clamped piston-cylinder cell. For both cases, σ(T) is enhanced while S(T) reduced with increasing pressure as expected, but their imbalanced variations lead to a monotonic enhancement of PF under pressure. For pristine SnSe, σ(290 K) increases by ∼4 times from ∼10.1 to 38 S cm⁻¹, while S(290 K) decreases by only ∼12% from 474 to 415 μV K⁻¹, leading to about three-fold enhancement of PF from 2.24 to 6.61 μW cm⁻¹ K⁻², which is very close to the optimal value of SnSe above the structural transition at ∼800 K at ambient pressure. In comparison, the PF of Na-doped SnSe at 290 K is enhanced moderately by ∼30% up to 20 kbar. In contrast, the PF of isostructural black phosphorus with a simple band structure was found to decrease under pressure. The comparison with black phosphorus indicates that the multi-valley valence band structure of SnSe is beneficial for the enhancement of PF by retaining a large Seebeck coefficient under pressure. Our results also provide experimental confirmation on the previous theoretical prediction that high pressure can be used to optimize the thermoelectric efficiency of SnSe.

The thermoelectric power factor of SnSe is enhanced by three times under a hydrostatic pressure of 22.5 kbar.

Magnetic field-induced electronic phase transition in the Dirac semimetal state of black phosphorus under pressure

Different instabilities have been confirmed to exist in the three-dimensional (3D) electron gas when it is confined to the lowest Landau level in the extreme quantum limit. The recently discovered 3D topological semimetals offer a good platform to explore these phenomena due to the small sizes of their Fermi pockets, which means the quantum limit can be achieved at relatively low magnetic fields. In this work, we report the high-magnetic-field transport properties of the Dirac semimetal state in pressurized black phosphorus. Under applied hydrostatic pressure, the band structure of black phosphorus goes through an insulator-semimetal transition. In the high pressure topological semimetal phase, anomalous behaviors are observed on both magnetoresistance and Hall resistivity beyond the relatively low quantum limit field, which is demonstrated to indicate the emergence of an exotic electronic state hosting a density wave ordering. Our findings bring the first insight into the electronic interactions in black phosphorus under intense field.

Coexistence of pressure-induced structural phases in bulk black phosphorus: a combined x-ray diffraction and Raman study up to 18 GPa

We report a study of the structural phase transitions induced by pressure in bulk black phosphorus by using both synchrotron x-ray diffraction for pressures up to 12.2 GPa and Raman spectroscopy up to 18.2 GPa. Very recently black phosphorus attracted large attention because of the unique properties of few-layers samples (phosphorene), but some basic questions are still open in the case of the bulk system. As concerning the presence of a Raman spectrum above 10 GPa, which should not be observed in an elemental simple cubic system, we propose a new explanation by attributing a key role to the non-hydrostatic conditions occurring in Raman experiments. Finally, a combined analysis of Raman and XRD data allowed us to obtain quantitative information on presence and extent of coexistences between different structural phases from ~5 up to ~15 GPa. This information can have an important role in theoretical studies on pressure-induced structural and electronic phase transitions in black phosphorus.

Quantum Hall Effect in Electron-Doped Black Phosphorus Field-Effect Transistors

The advent of black phosphorus field-effect transistors (FETs) has brought new possibilities in the study of two-dimensional (2D) electron systems. In a black phosphorus FET, the gate induces highly anisotropic 2D electron and hole gases. Although the 2D hole gas in black phosphorus has reached high carrier mobilities that led to the observation of the integer quantum Hall effect, the improvement in the sample quality of the 2D electron gas (2DEG) has however been only moderate; quantum Hall effect remained elusive. Here, we obtain high quality black phosphorus 2DEG by defining the 2DEG region with a prepatterned graphite local gate. The graphite local gate screens the impurity potential in the 2DEG. More importantly, it electrostatically defines the edge of the 2DEG, which facilitates the formation of well-defined edge channels in the quantum Hall regime. The improvements enable us to observe precisely quantized Hall plateaus in electron-doped black phosphorus FET. Magneto-transport measurements under high magnetic fields further revealed a large effective mass and an enhanced Landé g-factor, which points to strong electron-electron interaction in black phosphorus 2DEG. Such strong interaction may lead to exotic many-body quantum states in the fractional quantum Hall regime.

Pressure-induced phase transitions and superconductivity in a black phosphorus single crystal

We report a thorough study of the transport properties of the normal and superconducting states of black phosphorus (BP) under magnetic field and high pressure with a large-volume apparatus that provides hydrostatic pressure to induce transitions from the layered A17 phase to the layered A7 phase and to the cubic phase of BP. Quantum oscillations can be observed at P ≥ 1 GPa in both resistivity and Hall voltage, and their evolutions with pressure in the A17 phase imply a continuous enlargement of Fermi surface. A significantly large magnetoresistance (MR) at low temperatures is observed in the A7 phase that becomes superconducting below a superconducting transition temperature Tc ∼ 6-13 K. Tc increases continuously with pressure on crossing the A7 to the cubic phase boundary. The strong MR effect can be fit by a modified Kohler's rule. A correlation between Tc and fitting parameters suggests that phonon-mediated interactions play dominant roles in driving the Cooper pairing, which is further supported by our density functional theory (DFT) calculations. The change of effective carrier mobility in the A17 phase under pressure derived from the MR effect is consistent with that obtained from the temperature dependence of the quantum oscillations. In situ single-crystal diffraction under high pressure indicates a total structural reconstruction instead of simple stretching of the A17 phase layers in the A17-to-A7-phase transition. This finding helps us to interpret transport properties on crossing the phase transition under high pressure.

Photoinduced Nonequilibrium Topological States in Strained Black Phosphorus

Black phosphorus (BP), an elemental semiconductor, has attracted tremendous interest because it exhibits a wealth of interesting electronic and optoelectronic properties in equilibrium condition. The nonequilibrium electronic structures of bulk BP under a periodic field of laser remain unexplored, but can lead to intriguing topological optoelectronic properties. Here we show that, under the irradiation of circularly polarized light (CPL), BP exhibits a photon-dressed Floquet-Dirac semimetal state, which can be continuously tuned by changing the direction, intensity, and frequency of the incident laser. The topological phase transition from type-I to type-II Floquet-Dirac fermions manifests a new form of type-III phase, which exists in a wide range of intensities and frequencies of the incident laser. Furthermore, topological surface states exhibit nonequilibrium electron transport in a direction locked by the helicity of CPL. Our findings not only deepen our understanding of fundamental properties of BP in relation to topology but also extend optoelectronic device applications of BP to the nonequilibrium regime.

Observation of Poiseuille flow of phonons in black phosphorus

The travel of heat in insulators is commonly pictured as a flow of phonons scattered along their individual trajectory. In rare circumstances, momentum-conserving collision events dominate, and thermal transport becomes hydrodynamic. One of these cases, dubbed the Poiseuille flow of phonons, can occur in a temperature window just below the peak temperature of thermal conductivity. We report on a study of heat flow in bulk black phosphorus between 0.1 and 80 K. We find a thermal conductivity showing a faster than cubic temperature dependence between 5 and 12 K. Consequently, the effective phonon mean free path shows a nonmonotonic temperature dependence at the onset of the ballistic regime, with a size-dependent Knudsen minimum. These are hallmarks of Poiseuille flow previously observed in a handful of solids. Comparing the phonon dispersion in black phosphorus and silicon, we show that the phase space for normal scattering events in black phosphorus is much larger. Our results imply that the most important requirement for the emergence of Poiseuille flow is the facility of momentum exchange between acoustic phonon branches. Proximity to a structural transition can be beneficial for the emergence of this behavior in clean systems, even when they do not exceed silicon in purity.

Recent Progress on Stability and Passivation of Black Phosphorus

From a fundamental science perspective, black phosphorus (BP) is a canonical example of a material that possesses fascinating surface and electronic properties. It has extraordinary in-plane anisotropic electrical, optical, and vibrational states, as well as a tunable band gap. However, instability of the surface due to chemical degradation in ambient conditions remains a major impediment to its prospective applications. Early studies were limited by the degradation of black phosphorous surfaces in air. Recently, several robust strategies have been developed to mitigate these issues, and these novel developments can potentially allow researchers to exploit the extraordinary properties of this material and devices made out of it. Here, the fundamental chemistry of BP degradation and the tremendous progress made to address this issue are extensively reviewed. Device performances of encapsulated BP are also compared with nonencapsulated BP. In addition, BP possesses sensitive anisotropic photophysical surface properties such as excitons, surface plasmons/phonons, and topologically protected and Dirac semi-metallic surface states. Ambient degradation as well as any passivation method used to protect the surface could affect the intrinsic surface properties of BP. These properties and the extent of their modifications by both the degradation and passivation are reviewed.

Stacking sequences of black phosphorous allotropes and the corresponding few-layer phosphorenes

Possible bulk black phosphorus (BP) allotropes are constructed based on single-layer BP with various stacking sequences. Our stacking algorithm shows that there are eight possible allotropes with two stacking layers in their unit cells possessing relatively high symmetries, and six of them are retained after structural relaxation using a van der Waals correction of optB88-vdW. The AF, AG, and AH bulk structures are presented for the first time. The structural relationship of these configurations has been explained via an interlayer slipping process. The total energy of the AF allotrope is closest to the most stable bulk BP structure (AB stacking) among all explored 2-layer stacked bulk structures. The calculated band structure of the AF allotrope using HSE06 shows a direct band gap of 0.48 eV with anisotropic electronic structures. We also presented six possible BP allotropes with three stacking layers in their unit cells. The newly reported AAF and ABC stacked structures show semiconducting and metallic features, respectively. After the bulk structures were explored, we further built the corresponding few-layer phosphorene structures and investigated their electronic properties. The results show that all the few-layer phosphorenes show semiconducting features. The AE, AAE, and AEA phosphorenes have indirect band gaps while the other explored phosphorenes possess direct band gaps located at the Γ point.

Topological nature of the node-arc semimetal PtSn4 probed by de Haas-van Alphen quantum oscillations

Dirac node arc semimetal state is a new topological quantum state which is proposed to exist in PtSn₄ (Wu et al 2016 Dirac node arcs in PtSn₄ Nat. Phys. 12 667-71). We present a systematic de Haas-van Alphen quantum oscillation study on this compound. Two intriguing oscillation branches, i.e. F ₁ and F ₂, are detected in the fast Fourier transformation spectra, both of which are characterized to possess tiny effective mass and ultrahigh quantum mobility. And the F ₂ branch exhibits an angle-dependent nontrivial Berry phase. The features are consistent with the existence of the node arc semimetal state and shed new light on its complicated Fermi surfaces and topological nature.

Weak antilocalization effect in exfoliated black phosphorus revealed by temperature- and angle-dependent magnetoconductivity

Recently, there have increasingly been debates on whether there exists a surface resonance state (SRS) in black phosphorus (BP), as suggested by recent angle-resolved photoemission spectroscopy results. To resolve this issue, we have performed temperature- and angle-dependent magnetoconductivity measurements on exfoliated, high-quality BP single crystals. A pronounced weak-antilocalization (WAL) effect was observed within a narrow temperature range of 8-16 K, with the electrical current flowing parallel to the cleaved ac-plane (along the a- or c-axis) and the magnetic field along the b-axis. The angle-dependent magnetoconductivity and the Hikami-Larkin-Nagaoka model-fitted results have revealed that the observed WAL effect shows surface-bulk coherent features, which supports the existence of SRS in BP.

All-Electrical Determination of Crystal Orientation in Anisotropic Two-Dimensional Materials

The crystal orientation of an exfoliated black phosphorous flake is determined by purely electrical means. A sequence of three resistance measurements on an arbitrarily shaped flake with five contacts determines the three independent components of the anisotropic in-plane resistivity tensor, thereby revealing the crystal axes. The resistivity anisotropy ratio decreases linearly with increasing temperature T and carrier density reaching a maximum ratio of 3.0 at low temperatures and densities, while mobility indicates impurity scattering at low T and acoustic phonon scattering at high T.

Growth of Black Phosphorus Nanobelts and Microbelts

Black phosphorus nanobelts are fabricated with a one-step solid-liquid-solid reaction method under ambient pressure, where red phosphorus is used as the precursor instead of white phosphorus. The thickness of the as-fabricated nanobelts ranges from micrometers to tens of nanometers as studied by scanning electron microscopy. Energy dispersive X-ray spectroscopy and X-ray diffraction indicate that the nanobelts have the composition and the structure of black phosphorus, transmission electron microscopy reveals a typical layered structure stacked along the b-axis, and scanning transmission electron microscopy with energy dispersive X-ray spectroscopy analysis demonstrates the doping of bismuth into the black phosphorus structure. The nanobelt can be directly measured in scanning tunneling microscopy in ambient conditions.

2D library beyond graphene and transition metal dichalcogenides: a focus on photodetection

Two-dimensional materials beyond graphene and TMDs can be promising candidates for wide-spectra photodetection.

Commensurability oscillations in a periodically modulated phosphorene

The recent experimental realization of high-quality phosphorene leads to novel electronic and optical properties with possible new device applications due to its huge direct band gap. We study the commensurability or Weiss oscillations in monolayer phosphorene in the presence of a weak perpendicular magnetic field B and a weak and periodic, electric or magnetic one-dimensional modulation. Either modulation broadens the Landau levels into bands, whose width oscillates with B, and the oscillations appear in the electrical conductivity perpendicular to the modulation taken along the direction (x) of the smaller effective mass. Compared with the oscillations of the diffusive conductivity in a two-dimensional electron gas (2DEG) for typical electron densities [Formula: see text], the ones in phosphorene, with typical [Formula: see text], have approximately similar height but a period significantly smaller when plotted versus [Formula: see text] while plotted versus B they occur at significantly higher fields. The Shubnikov-de Haas oscillations exhibit a similar behaviour. When the modulation is taken along the direction (y) of the larger effective mass, the oscillation period is close to that of a 2DEG. For equal modulation strengths the bandwidth due to a magnetic modulation is one order of magnitude larger than that due to an electric one and the amplitude of the oscillations in the diffusive conductivity about 50 times larger. Numerical results are presented for experimentally relevant parameters.

Strain-Modulated Bandgap and Piezo-Resistive Effect in Black Phosphorus Field-Effect Transistors

Energy bandgap largely determines the optical and electronic properties of a semiconductor. Variable bandgap therefore makes versatile functionality possible in a single material. In layered material black phosphorus, the bandgap can be modulated by the number of layers; as a result, few-layer black phosphorus has discrete bandgap values that are relevant for optoelectronic applications in the spectral range from red, in monolayer, to mid-infrared in the bulk limit. Here, we further demonstrate continuous bandgap modulation by mechanical strain applied through flexible substrates. The strain-modulated bandgap significantly alters the density of thermally activated carriers; we for the first time observe a large piezo-resistive effect in black phosphorus field-effect transistors (FETs) at room temperature. The effect opens up opportunities for future development of electromechanical transducers based on black phosphorus, and we demonstrate an ultrasensitive strain gauge constructed from black phosphorus thin crystals.

Compressed few-layer black phosphorus nanosheets from semiconducting to metallic transition with the highest symmetry

The high-pressure response of few-layer black phosphorus (BP) nanosheets remains elusive, despite the special interest in it particularly after the achievement of an exotic few-layer BP based field effect transistor. Here, we identified a pressure-induced reversible phase transition on few-layer BP nanosheets by performing in situ ADXRD and Raman spectroscopy with the assistance of DAC apparatus. The few-layer BP nanosheets transformed from orthorhombic semiconductors to simple cubic metal with increasing pressure, which is well interpreted using the pressure-induced inverse Peierls distortion. The obtained simple cubic BP nanosheets exhibited an enhanced isothermal bulk modulus of 147.0(2) GPa, and negative Grüneisen parameters that were attributed to the pressure-driven softening of phonon energies. Note that the simple cubic BP nanosheets adopted the highest symmetry which is in stark contrast to the general phase transformation under high pressure. First-principles calculations indicated that the metallic BP was significantly related to the band overlapped metallization, resulting from the traversing of density of states across the Fermi level at high pressure. Such findings paved a potential pathway to design targeted BP nanostructures with functional properties at extremes, and opened up possibilities for conceptually new devices.

Achieving Ultrahigh Carrier Mobility in Two-Dimensional Hole Gas of Black Phosphorus

We demonstrate that a field-effect transistor (FET) made of few-layer black phosphorus (BP) encapsulated in hexagonal boron nitride (h-BN) in vacuum exhibits a room-temperature hole mobility of 5200 cm²/(Vs), being limited just by the phonon scattering. At cryogenic temperatures, the FET mobility increases up to 45 000 cm²/(Vs), which is five times higher compared to the mobility obtained in earlier reports. The unprecedentedly clean h-BN-BP-h-BN heterostructure exhibits Shubnikov-de Haas oscillations and a quantum Hall effect with Landau level (LL) filling factors down to v = 2 in conventional laboratory magnetic fields. Moreover, carrier density independent effective mass of m^* = 0.26 m₀ is measured, and a Landé g-factor of g = 2.47 is reported. Furthermore, an indication for a distinct hole transport behavior with up- and down-spin orientations is found.

Substantial Band-Gap Tuning and a Strain-Controlled Semiconductor to Gapless/Band-Inverted Semimetal Transition in Rutile Lead/Stannic Dioxide

By first-principle calculations, we have systematically studied the effect of strain/pressure on the electronic structure of rutile lead/stannic dioxide (PbO₂/SnO₂). We find that pressure/strain has a significant impact on the electronic structure of PbO₂/SnO₂. Not only can the band gap be substantially tuned by pressure/strain, but also a transition between a semiconductor and a gapless/band-inverted semimetal can be manipulated. Furthermore, the semimetallic state is robust under strain, indicating a bright perspective for electronics applications. In addition, a practical approach to realizing strain in SnO₂ is then proposed by substituting tin (Sn) with lead (Pb), which also can trigger the transition from a large-band-gap to a moderate-gap semiconductor with enhanced electron mobility. This work is expected to provide guidance for full utilization of the flexible electronic properties in PbO₂ and SnO₂.

Tunable Electrical Performance of Few-Layered Black Phosphorus by Strain

Strain engineering shows promising applications in low-dimensional materials. It is demonstrated that the bandgap of few-layered black phosphorus can be effectively reduced by out-of-plane compressive strain, resulting in a significant modulation of the vertical electrical performance of black phosphorus and even inducing a nonlinear current-voltage curve to linear current-voltage curve transition.

Transport studies in 2D transition metal dichalcogenides and black phosphorus

Two-dimensional (2D) materials are a new family of materials with interesting physical properties, ranging from insulating hexagonal boron nitride, semiconducting or semi-metallic transition metal dichalcogenides, to gapless metallic graphene. In this review, we provide a brief discussion of transport studies in transition metal dichalcogenides, including both semiconducting and semi-metallic phases, as well as a discussion of the newly emerged narrow bandgap layered material, black phosphorus, in terms of its electrical and quantum transport properties at room and cryogenic temperatures. Ultra-thin layered channel materials with atomic layer thickness in the cross-plane direction, together with relatively high carrier mobility with appropriate passivation techniques, provide the promise for new scientific discoveries and broad device applications.

Black Phosphorus Nanosheets: Synthesis, Characterization and Applications

Black phosphorus (BP) is an emerging two-dimensional (2D) material with a natural bandgap, which has unique anisotropy and extraordinary physical properties. Due to its puckered structure, BP exhibits strong in-plane anisotropy unlike other layered materials. The bandgap tunability of BP enables a wide range of ultrafast electronics and high frequency optoelectronic applications ranging from telecommunications to thermal imaging covering the nearly entire electromagnetic spectrum, whereas no other 2D material has this functionality. Here, recent advances in the synthesis, fabrication, anisotropic physical properties, and BP-based devices including field effect transistors (FETs) and photodetectors, are discussed. Recent passivation approaches to address the degradation of BP, which is one of the main challenges to bring this material into real world applications, are also introduced. Finally, a comment is made on the recent developments in other emerging applications, future outlook and challenges ahead in BP research.

Large and Anisotropic Linear Magnetoresistance in Single Crystals of Black Phosphorus Arising From Mobility Fluctuations

Black Phosphorus (BP) is presently attracting immense research interest on the global level due to its high mobility and suitable band gap for potential application in optoelectronics and flexible devices. It was theoretically predicted that BP has a large direction-dependent electrical and magnetotransport anisotropy. Investigations on magnetotransport of BP may therefore provide a new platform for studying the nature of electron transport in layered materials. However, to the best of our knowledge, magnetotransport studies, especially the anisotropic magnetoresistance (MR) effect in layered BP, are rarely reported. Here, we report a large linear MR up to 510% at a magnetic field of 7 Tesla in single crystals of BP. Analysis of the temperature and angle dependence of MR revealed that the large linear MR in our sample originates from mobility fluctuations. Furthermore, we reveal that the large linear MR of layered BP in fact follows a three-dimensional behavior rather than a two-dimensional one. Our results have implications to both the fundamental understanding and magnetoresistive device applications of BP.

Emergent Non-Fermi-Liquid at the Quantum Critical Point of a Topological Phase Transition in Two Dimensions

We study the effects of Coulomb interaction between 2D Weyl fermions with anisotropic dispersion which displays relativistic dynamics along one direction and nonrelativistic dynamics along the other. Such a dispersion can be realized in phosphorene under electric field or strain, in TiO_{2}/VO_{2} superlattices, and, more generally, at the quantum critical point between a nodal semimetal and an insulator in systems with a chiral symmetry. Using the one-loop renormalization group approach in combination with the large-N expansion, we find that the system displays interaction-driven non-Fermi liquid behavior in a wide range of intermediate frequencies and marginal Fermi liquid behavior at the smallest frequencies. In the non-Fermi liquid regime, the quasiparticle residue Z at energy E scales as Z∝E^{a} with a>0, and the parameters of the fermionic dispersion acquire anomalous dimensions. In the marginal Fermi-liquid regime, Z∝(|logE|)^{-b} with universal b=3/2.

'Hard' crystalline lattice in the Weyl semimetal NbAs

We report the effect of hydrostatic pressure on the magnetotransport properties of the Weyl semimetal NbAs. Subtle changes can be seen in the ρ(xx)(T) profiles with pressure up to 2.31 GPa. The Fermi surfaces undergo an anisotropic evolution under pressure: the extremal areas slightly increase in the k(x)-k(y) plane, but decrease in the k(z)-k(y)(k(x)) plane. The topological features of the two pockets observed at atmospheric pressure, however, remain unchanged at 2.31 GPa. No superconductivity can be seen down to 0.3 K for all the pressures measured. By fitting the temperature dependence of specific heat to the Debye model, we obtain a small Sommerfeld coefficient γ(0) = 0.09(1) mJ (mol·K(2))(-1) and a large Debye temperature, Θ(D) = 450(9) K, confirming a 'hard' crystalline lattice that is stable under pressure. We also studied the Kadowaki-Woods ratio of this low-carrier-density massless system, R(KW) = 3.2 × 10(4) μΩ cm mol(2) K(2) J(-2). After accounting for the small carrier density in NbAs, this R(KW) indicates a suppressed transport scattering rate relative to other metals.