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

Link between T-Linear Resistivity and Quantum Criticality in Ambipolar Black Phosphorus

The interplay between strong Coulomb interactions and kinetic energy leads to intricate many-body competing ground states owing to quantum fluctuations in 2D electron and hole gases. However, the simultaneous observation of quantum critical phenomena in both electron and hole regimes remains elusive. Here, we utilize anisotropic black phosphorus (BP) to show density-driven metal-insulator transition with a critical conductance ∼e2/h which highlights the significant role of quantum fluctuations in both hole and electron regimes. We observe a T-linear resistivity from the deep metallic phase to the metal-insulator boundary at moderate temperatures, while it turns to Fermi liquid behavior in the deep metallic phase at low temperatures in both regimes. An analysis of the resistivity suggests that disorder-dominated transport leads to T-linear behavior in the hole regime, while in the electron regime, the T-linear resistivity results from strong Coulomb interactions, suggestive of strange-metal behavior. Successful scaling collapse of the resistivity in the T-linear region demonstrates the link between quantum criticality and the T-linear resistivity in both regimes. Our study provides compelling evidence that ambipolar BP could serve as an exciting testbed for investigating exotic states and quantum critical phenomena in hole and electron regimes of 2D semiconductors.

Nagaoka ferromagnetism in an array of phosphorene quantum dots

We consider an array of four quantum dots defined in phosphorene containing three excess electrons, i.e., in the conditions of near half filling when itinerant Nagaoka ferromagnetism is expected to appear in a square array with isotropic interdot hopping. The interdot hopping in the array arranged in a square inherits the anisotropy from the form of the phosphorene conduction band. We apply the configuration interaction method for discussion of the appearance and stability of the spin-polarized ground state and discuss the compensation of the effective mass anisotropy by the geometry of the quantum dot array. Our study shows strong stability of Nagaoka ferromagnetism for optimized geometry of the array, with the Nagaoka gap as large as ∼ 230 µeV. A phase diagram for the ground-state spin ordering versus the geometric parameters of the array is presented. We study the suppression of the ferromagnetism in a transition of the [Formula: see text] array to a quasi-1D chain and indicate that the shift of one of the quantum dots away from the array center is enough to transform the system to a quantum dot chain. A shift in the zigzag crystal direction induces the low-spin ground state more effectively than a shift along the armchair direction. We also discuss the robustness of the spin ordering against detuning one of the dots. The ferromagnetic ground-state survives as long as the detuning is not large enough to trap one of the electrons within a single quantum dot (for positive detuning) or remove one of the quantum dots of the accessible energy range (for negative detuning).

Multifrequency on-off modulation and slow light characterization of the patterned black phosphorus metamaterial based on dual plasmon-induced transparency

We present a monolayer patterned black phosphorus (BP) metamaterial for generating a tunable dual plasmon-induced transparency (PIT). We have derived the expression for the theoretical transmittance by introducing the coupled mode theory (CMT), and the calculated results of the expression highly overlap with the simulation results. The quarterly frequency synchronous switch with two different operating bands is designed by the carrier density and scattering rate on the dual PIT modulation effect. Two parameters were selected as important markers to show the performance of the optical switch: the modulation depth (MD) and the insertion loss (IL). The theoretical analysis of this structure shows that the higher modulation depth (5.45d B Collapse

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Vertically grown ultrathin Bi2SiO5 as high-κ single-crystalline gate dielectric

Single-crystalline high-κ dielectric materials are desired for the development of future two-dimensional (2D) electronic devices. However, curent 2D gate insulators still face challenges, such as insufficient dielectric constant and difficult to obtain free-standing and transferrable ultrathin films. Here, we demonstrate that ultrathin Bi₂SiO₅ crystals grown by chemical vapor deposition (CVD) can serve as excellent gate dielectric layers for 2D semiconductors, showing a high dielectric constant (>30) and large band gap (~3.8 eV). Unlike other 2D insulators synthesized via in-plane CVD on substrates, vertically grown Bi₂SiO₅ can be easily transferred onto other substrates by polymer-free mechanical pressing, which greatly facilitates its ideal van der Waals integration with few-layer MoS₂ as high-κ dielectrics and screening layers. The Bi₂SiO₅ gated MoS₂ field-effect transistors exhibit an ignorable hysteresis (~3 mV) and low drain induced barrier lowering (~5 mV/V). Our work suggests vertically grown Bi₂SiO₅ nanoflakes as promising candidates to improve the performance of 2D electronic devices.

Theoretical insights into the epitaxial growth of black arsenene enabled on GeS(001)

Black arsenene exhibits many exotic physical properties, such as Rashba spin-orbital coupling, fractional quantum Hall effect (Sheng 2021Nature59356) as well as some advantages in the field of energy storage (Wuet al2021J. Mater. Chem. A918793). High-quality and large-area BA monolayer can promote the investigations about BA and its device application. Epitaxial growth mechanism of BA is desirable. Here, based on density functional theory calculation, the epitaxial growth of BA monolayer was simulated. GeS(001) is found to be a suitable substrate for BA monolayer to epitaxially grow on. As a common isomer of arsenene, gray arsenene should be considered during the growth, because it is also energetically and thermodynamically stable in freestanding state. However, black arsenene monolayer is more energetically and thermodynamically stable than gray arsenene monolayer on GeS(001) substrate. During the growth, two arsenene atoms easily form a dimer on GeS(001), which diffuses more quickly and isotropically than arsenene monomer. In addition, the heterojunction consisted of balck arsenene and GeS(001) is an indirect gap semiconductor, but it can transform into a direct gap semiconductor with external tensile strain along zigzag direction. Remarkably, optical adsorption spectra range of BA/GeS(001) can be more abroad than that of BA and GeS(001) bilayers. The theatrical insights shed new light on some ideal substrates that can realize the epitaxial growth of high-quality simple substances of group V.

Anisotropic magneto-optical transport properties in black phosphorus induced by in-plane magnetic field

We study the Landau levels and magneto-optical properties of bulk black phosphorus (BP) subjected to an in-plane magnetic field along the armchair direction based on an effectivek⋅pHamiltonian. We analytically obtain the Landau levels by the perturbation method, which agrees well with the results of numerical diagonalization. By using the Kubo formula, we find the magneto-optical transition selection rules and conductance spectra for inter-band transitions are highly anisotropic. In particular, for linearly polarized light along the armchair direction, the magneto-optical transition selection rule isΔn= 0, wherenis the Landau level index. However, for linearly polarized light along the zigzag and stacking direction, the magneto-optical transition selection rules becomeΔn= ±1. The magneto-optical conductance excited by linearly polarized light along the armchair direction is two order of magnitude larger than those excited by linearly polarized light along the zigzag and stacking direction because the inter-band coupling only exists in the armchair direction. Our results are useful to detect the band parameters of BP and design magnetically controlled optical devices based on it.

Impact of the Channel Thickness on the Photoresponse of Black Arsenic Mid-Infrared Photodetectors

Recently explored black arsenic is a layered two-dimensional low-symmetry semiconducting material that, owing to its inherent narrow bandgap (∼0.31 eV) in its bulk form, is attractive for mid-infrared optoelectronics. Several studies have been conducted on its structural, charge-transport, and thermal properties for implementation in nanoelectronics. Herein, the thickness-dependent optoelectronic performance of black arsenic devices for mid-infrared wavelengths (2.0-4.0 μm) is investigated. The device was fabricated over an hBN/SiO2/Si substrate using mechanical exfoliation of black arsenic. It is observed that the optoelectronic properties of the devices vary significantly with the thickness of the black arsenic channel of the devices. A peak photoresponsivity of 244 A/W was achieved at 3.00 μm for a 60 nm-thick black arsenic channel. However, the maximum detectivity of 6.14 × 109 Jones was found for a lower thickness (∼25 nm) of black arsenic, along with an excellent (i.e., the least) noise-equivalent power of ∼89 fW/Hz1/2. Our findings reveal that the optoelectronic properties of black arsenic are excellent and can be tuned through thickness control. The promising results suggest the considerable potential of black arsenic in future opto- and nanoelectronic devices.

Rashba valleys and quantum Hall states in few-layer black arsenic

Exciting phenomena may emerge in non-centrosymmetric two-dimensional electronic systems when spin-orbit coupling (SOC)¹ interplays dynamically with Coulomb interactions^2,3, band topology^4,5 and external modulating forces^6-8. Here we report synergetic effects between SOC and the Stark effect in centrosymmetric few-layer black arsenic, which manifest as particle-hole asymmetric Rashba valley formation and exotic quantum Hall states that are reversibly controlled by electrostatic gating. The unusual findings are rooted in the puckering square lattice of black arsenic, in which heavy 4p orbitals form a Brillouin zone-centred Γ valley with p_z symmetry, coexisting with doubly degenerate D valleys of p_x origin near the time-reversal-invariant momenta of the X points. When a perpendicular electric field breaks the structure inversion symmetry, strong Rashba SOC is activated for the p_x bands, which produces spin-valley-flavoured D^± valleys paired by time-reversal symmetry, whereas Rashba splitting of the Γ valley is constrained by the p_z symmetry. Intriguingly, the giant Stark effect shows the same p_x-orbital selectiveness, collectively shifting the valence band maximum of the D^± Rashba valleys to exceed the Γ Rashba top. Such an orchestrating effect allows us to realize gate-tunable Rashba valley manipulations for two-dimensional hole gases, hallmarked by unconventional even-to-odd transitions in quantum Hall states due to the formation of a flavour-dependent Landau level spectrum. For two-dimensional electron gases, the quantization of the Γ Rashba valley is characterized by peculiar density-dependent transitions in the band topology from trivial parabolic pockets to helical Dirac fermions.

Prediction of nodal-line semimetals in two-dimensional black phosphorous films

Semimetals are a new kind of quantum materials, in which the conduction and valence bands cross each other near the Fermi level. Based on density-functional theory calculations and symmetry analysis, we propose nodal-line semimetals in layered stacked black phosphorus (BP) films which are designed to have a mirror symmetry lying in the BP layer plane and thus rendering them different from the BP film systems previously studied. A closed nodal-line degenerate band can appear around the Fermi level in the BP films after a biaxial compressive strain is applied. The calculated Z2 number of Z2 =  - 1 indicates the robustness of the nodal-line semimetals obtained in the BP films, protected by the in-plane mirror symmetry. Intriguingly, with the increase of the film thickness, a smaller biaxial compressive strain is required to produce the nodal-line semimetals, more accessible in experiments. Our results provide a promising route to carrying out the nodal-line semimetals based on various two-dimensional materials.

Probing the anisotropy of Landau levels in phosphorene by magneto-capacitance with a parabolic potential confinement

We theoretically investigate the Landau levels (LLs) and magneto-capacitance (MC) of monolayer black phosphorus under a perpendicular magnetic field, on which a parabolic potential is applied along with the armchair and zigzag directions, respectively. By both analytically perturbative calculation and numerical diagonalization based on an effectivek⋅pHamiltonian, we find that the LLs parabolically depend on the wave vectors and show strong anisotropy as the parabolic potential is applied along with different crystal directions. Specifically, the analytical LLs obtained by perturbative calculation from a decoupled single-band Hamiltonian are in good agreement with the numerical results. Importantly, the LLs are no longer linearly dependent on the magnetic field and level index even in the low energy regime due to the confinement of parabolic potential which repaints the cyclotron orbits. Moreover, the MC spectrum clearly reflects the structure of the LLs and exhibits strong anisotropic oscillating patterns. It can be used to determine the band parameters of phosphorene, i.e., the effective masses and inter-band coupling in the absence of magnetic and electric fields.

Anomalous magneto-transport properties of bilayer phosphorene

The magneto-transport properties of phosphorene are investigated by employing the generalized tight-binding model to calculate the energy bands. For bilayer phosphorene, a composite magnetic and electric field is shown to induce a feature-rich Landau level (LL) spectrum which includes two subgroups of low-lying LLs. The two subgroups possess distinct features in level spacings, quantum numbers, as well as field dependencies. These together lead to anomalous quantum Hall (QH) conductivities which include a well-shape, staircase and composite quantum structures with steps having varying heights and widths. The Fermi energy-magnetic field-Hall conductivity (EF-Bz-σxy) and Fermi energy-electric field-Hall conductivity (EF-Ez-σxy) phase diagrams clearly exhibit oscillatory behaviors and cross-over from integer to half-integer QH effect. The predicted results should be verifiable by magneto-transport measurements in a dual-gated system.

Unique Landau-level structure of monolayer black phosphorus under an exponentially decaying magnetic field

We study the Landau-level spectrum of a monolayer black phosphorus under an exponentially decaying magnetic field along one spatial dimension. The results show that unlike the case in a constant magnetic field, the number of Landau levels in the inhomogeneous magnetic field is finite, and the Landau-level structure of the system is strongly dependent on the inhomogeneity of the magnetic field. In particular, the crossing of some Landau levels apparently occurs, and the accidental degeneracy points between the levels for the conduction and valence bands are highly anisotropic due to the anisotropic effective masses in monolayer black phosphorus. The above unique characteristics of the Landau-level structure in an exponentially decaying magnetic field could be directly confirmed by the magneto-absorption and transport measurements.

Two-Dimensional Pnictogen for Field-Effect Transistors

Two-dimensional (2D) layered materials hold great promise for various future electronic and optoelectronic devices that traditional semiconductors cannot afford. 2D pnictogen, group-VA atomic sheet (including phosphorene, arsenene, antimonene, and bismuthene) is believed to be a competitive candidate for next-generation logic devices. This is due to their intriguing physical and chemical properties, such as tunable midrange bandgap and controllable stability. Since the first black phosphorus field-effect transistor (FET) demo in 2014, there has been abundant exciting research advancement on the fundamental properties, preparation methods, and related electronic applications of 2D pnictogen. Herein, we review the recent progress in both material and device aspects of 2D pnictogen FETs. This includes a brief survey on the crystal structure, electronic properties and synthesis, or growth experiments. With more device orientation, this review emphasizes experimental fabrication, performance enhancing approaches, and configuration engineering of 2D pnictogen FETs. At the end, this review outlines current challenges and prospects for 2D pnictogen FETs as a potential platform for novel nanoelectronics.

Strong-field nonlinear optical properties of monolayer black phosphorus

Within the past few years, atomically thin black phosphorus (BP) has been demonstrated as a fascinating new 2D material that is promising for novel nanoelectronic and nanophotonic applications, due to its many unique properties such as a direct and widely tunable bandgap, high carrier mobility and remarkable intrinsic in-plane anisotropy. However, its important extreme nonlinear behavior and the ultrafast dynamics of carriers under strong-field excitation have yet to be revealed. Herein, we report nonperturbative high harmonic generation (HHG) in monolayer BP by first-principles simulations. We show that BP exhibits extraordinary HHG properties, with clear advantages over three major types of 2D materials under intensive study, i.e., semimetallic graphene, semiconducting MoS₂, and insulating hexagonal boron nitride, in terms of HHG cutoff energy and spectral intensity. This study advances the scope of current research activities on BP into a new regime, suggesting its promising future in the applications of extreme-ultraviolet and attosecond nanophotonics and also opening doors to investigate the strong-field and ultrafast carrier dynamics of this emerging material.

Bandgap engineering of PbTe ultra-thin layers by surface passivations

We calculate the electronic structures of the PbTe (1 1 1) ultra-thin films by performing the first-principles calculations. The PbTe (1 1 1) ultra-thin films possess direct or indirect band gaps depending sensitively on surface passivations with hydrogen or halogen atoms, and the band gaps depend sensitively on the passivation elements. The bandgaps of PbTe (1 1 1) ultra-thin films with hydrogen passivations can be tuned from 15 meV to 65 meV by applying external strains, making PbTe ultra-thin films promising candidates for optoelectronic device applications in terahertz regime.

Investigating the interlayer electron transport and its influence on the whole electric properties of black phosphorus

Two-dimensional (2D) nanomaterials have attracted great attention in next generation electronic and optoelectronic technologies due to the unique layered structure and excellent physical and chemical properties. However, the mechanism of transmission along the vertical direction of 2D semiconductor materials has not been investigated. Here, we use first-principles calculations to explore the bandgap energies along different directions, and fabricate a vertical, a lateral and a mixture-structured black phosphorus field effect transistor (BPFET) to study the electrical characteristics along different directions under variable temperatures. The variable temperature test indicates that the mixture-structured device performs more like a lateral device, while the conductance along the vertical direction is hard to be tuned by temperature and electrical field. The unchanged conductance under electric field and variable temperatures allows the vertical device to act as a fixed resistor, promising possible application for the prospective electronic and optoelectronic devices.

High-Performance Black Phosphorus Field-Effect Transistors with Long-Term Air Stability

Two-dimensional layered materials (2DLMs) are of considerable interest for high-performance electronic devices for their unique electronic properties and atomically thin geometry. However, the atomically thin geometry makes their electronic properties highly susceptible to the environment changes. In particular, some 2DLMs (e.g., black phosphorus (BP) and SnSe₂) are unstable and could rapidly degrade over time when exposed to ambient conditions. Therefore, the development of proper passivation schemes that can preserve the intrinsic properties and enhance their lifetime represents a key challenge for these atomically thin electronic materials. Herein we introduce a simple, nondisruptive, and scalable van der Waals passivation approach by using organic thin films to simultaneously improve the performance and air stability of BP field-effect transistors (FETs). We show that dioctylbenzothienobenzothiophene (C8-BTBT) thin films can be readily deposited on BP via van der Waals epitaxy approach to protect BP against oxidation in ambient conditions over 20 d. Importantly, the noncovalent van der Waals interface between C8-BTBT and BP effectively preserves the intrinsic properties of BP, allowing us to demonstrate high-performance BP FETs with a record-high current density of 920 μA/um, hole drift velocity over 1 × 10⁷ cm/s, and on/off ratio of 1 × 10⁴ to ∼1 × 10⁷ at room temperature. This approach is generally applicable to other unstable two-dimensional materials, defining a unique pathway to modulate their electronic properties and realize high-performance devices through hybrid heterojunctions.