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At least 1,675 records · Page 93
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Topological quantum computation based on chiral Majorana fermions

Here, the chiral Majorana fermion is a massless self-conjugate fermion which can arise as the edge state of certain 2D topological matters. It has been theoretically predicted and experimentally observed in a hybrid device of a quantum anomalous Hall insulator and a conventional superconductor. Its closely related cousin, the Majorana zero mode in the bulk of the corresponding topological matter, is known to be applicable in topological quantum computations. Here we show that the propagation of chiral Majorana fermions leads to the same unitary transformation as that in the braiding of Majorana zero modes and propose a platform to perform quantum computation with chiral Majorana fermions. A Corbino ring junction of the hybrid device can use quantum coherent chiral Majorana fermions to implement the Hadamard gate and the phase gate, and the junction conductance yields a natural readout for the qubit state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1972

Development of low-cost welding procedures for thick sections of HY-150 steel

Low cost welding procedures were developed for welding 6-inch thick HY-150 steel to be used in the manufacture of large diameter motor case Y rings and nozzle attachment flanges. An extensive investigation was made of the mechanical and metallurgical properties and fracture toughness of HY-150 base plate and welds made with manual shielded metal arc process and semi-automatic gas metal arc process in the flat position. Transverse tensiles, all-weld metal tensiles, Charpy V-notch specimens and edge notched bend specimens were tested in the course of the program. In addition metallographic studies and hardness tests were performed on the weld, weld HAZ and base metal. The results of the work performed indicate that both the shielded metal arc and gas metal arc processes are capable of producing consistently sound welds as determined by radiographic and ultrasonic inspection. In addition, the weld metal, deposited by each process was found to exhibit a good combination of strength and toughness such that the selection of a rolled and welded procedure for fabricating rocket motor case components would appear to be technically feasible.

Schmidt, P. M.↗
NASA NTRS1995

Detection and Location of Transverse Matrix Cracks in Cross-Ply Gr/Ep Composites Using Acoustic Emission

Transverse matrix cracking in cross-ply gr/ep laminates was studied with advanced acoustic emission (AE) techniques. The primary goal of this research was to measure the load required to initiate the first transverse matrix crack in cross-ply laminates of different thicknesses. Other methods had been previously used for these measurements including penetrant enhanced radiography, optical microscopy, and audible acoustic microphone measurements. The former methods required that the mechanical test be paused for measurements at load intervals. This slowed the test procedure and did not provide the required resolution in load. With acoustic microphones, acoustic signals from cracks could not be clearly differentiated from other noise sources such as grip damage, specimen slippage, or test machine noise. A second goal for this work was to use the high resolution source location accuracy of the advanced acoustic emission techniques to determine whether the crack initiation site was at the specimen edge or in the interior of the specimen.In this research, advanced AE techniques using broad band sensors, high capture rate digital waveform acquisition, and plate wave propagation based analysis were applied to cross-ply composite coupons with different numbers of 0 and 90 degree plies. Noise signals, believed to be caused by grip damage or specimen slipping, were eliminated based on their plate wave characteristics. Such signals were always located outside the sensor gage length in the gripped region of the specimen. Cracks were confirmed post-test by microscopic analysis of a polished specimen edge, backscatter ultrasonic scans, and in limited cases, by penetrant enhanced radiography. For specimens with three or more 90 degree plies together, there was an exact 1-1 correlation between AE crack signals and observed cracks. The ultrasonic scans and some destructive sectioning analysis showed that the cracks extended across the full width of the specimen. Furthermore, the locations of the cracks from the AE data were in excellent agreement with the locations measured with the microscope. The high resolution source location capability of this technique, combined with an array of sensors, was able to determine that the cracks initiated at the specimen edges, rather than in the interior. For specimens with only one or two 90 degree plies, the crack-like signals were significantly smaller in amplitude and there was not a 1-1 correlation to observed cracks. This was similar to previous results. In this case, however, ultrasonic and destructive sectioning analysis revealed that the cracks did not extend across the specimen. They initiated at the edge, but did not propagate any appreciable distance into the specimen. This explains the much smaller AE signal amplitudes and the difficulty in correlating these signals to actual cracks in this, as well as in the previous study.

Prosser, W. H.↗
DOE OSTI2019

Hollow pellet injection for magnetic fusion

The precise delivery of mass to burning plasmas is an area of growing interest in magnetic fusion (MF). The amount of mass that is necessary and sufficient can vary depending on such parameters as the type of atoms involved, the type of applications, plasma conditions, mass injector, and injection timing. Motivated by edge localized mode (ELM) control in H-mode plasmas, disruption mitigation and other applications in MF, we report the progress and new possibilities in mass delivery based on hollow pellets. Here, a hollow pellet refers to a spherical shell mass structure with a hollow core. Based on an empirical model of pellet ablation, coupled with BOUT++ simulations of the ELM triggering threshold, hollow pellets are found to be attractive in comparison with solid spheres for ELM control. By using hollow pellets, it is possible to tailor mass delivery to certain regions of edge plasmas while minimizing core contamination and reducing the total amount of mass needed. We also include the experimental progress in mass delivery experiments, in situ diagnostics and hollow pellet fabrication, and emphasize new experimental possibilities for ELM control based on hollow pellets. A related application is the disruption mitigation scheme using powder encapsulated inside hollow shells. Further experiments will also help to resolve known discrepancies between theoretical predictions and experiments in using mass injection for ELM control and leading to better predictive models for ELM stability and triggering.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Efficient hydrogen peroxide generation using reduced graphene oxide-based oxygen reduction electrocatalysts

Electrochemical oxygen reduction has garnered attention as an emerging alternative to the traditional anthraquinone oxidation process to enable the distributed production of hydrogen peroxide. Here, we demonstrate a selective and efficient non-precious electrocatalyst, prepared through an easily scalable mild thermal reduction of graphene oxide, to form hydrogen peroxide from oxygen. During oxygen reduction, certain variants of the mildly reduced graphene oxide electrocatalyst exhibit highly selective and stable peroxide formation activity at low overpotentials (<10 mV) under basic conditions, exceeding the performance of current state-of-the-art alkaline catalysts. Spectroscopic structural characterization and in situ Raman spectroelectrochemistry provide strong evidence that sp 2 -hybridized carbon near-ring ether defects along sheet edges are the most active sites for peroxide production, providing new insight into the electrocatalytic design of carbon-based materials for effective peroxide production.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Correction of absorption-edge artifacts in polychromatic X-ray tomography in a scanning electron microscope for 3D microelectronics

X-ray tomography is widely used in materials science. However, X-ray scanners are often based on polychromatic radiation that creates artifacts such as dark streaks. We show this artifact is not always due to beam hardening. It may appear when scanning samples with high-Z elements inside a low-Z matrix because of the high-Z element absorption edge: X-rays whose energy is above this edge are strongly absorbed, violating the exponential decay assumption for reconstruction algorithms and generating dark streaks. A method is proposed to limit the absorption edge effect and is applied on a microelectronic case to suppress dark streaks between interconnections.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

On hybrid scenarios in KSTAR

We report the status of hybrid scenario experiments in Korea Superconducting Tokamak Advanced Research (KSTAR). The hybrid scenario is defined as stationary discharges with ${\beta _{\rm{N}}}$ $ \geqslant $ 2.4 and ${H_{89}}$ $ \geqslant $ 2.0 at ${q_{95}}$ < 6.5 without or with very mild sawtooth activities in KSTAR. It is being developed towards reactor-relevant conditions. High performance of ${\beta _{\rm{N}}} \lesssim 3.0$, ${H_{89}} \lesssim 2.4$ and G-factor ($ \equiv {\beta _{\rm{N}}}{H_{89}}/q_{95}^2$) $ \lesssim 0.4$6 has been achieved and sustained for $ \gtrsim 40{{\tau }_{\text{E}}}$ at ne/nGW ~ 0.7 with heating power of $ \lesssim $5 MW. Some KSTAR hybrid discharges exhibit a unique feature of a slow transition from conventional H-mode to hybrid mode after the third neutral beam injection. The reason for the confinement enhancement is extensively studied in this transition period of a representative discharge exhibiting a common feature of KSTAR hybrid scenarios. 0D performance analysis with magnetohydrodynamic activities, 1D kinetic profile dynamics, power balance analysis, linear gyro-kinetic analysis and edge pedestal stability analysis were conducted. The enhancement is thought to be from both the core and the pedestal. The improvement in the core region of the ion energy channel is observed from the linear gyro-kinetic analysis considering the electromagnetic, the fast ion, the Shafranov shift, ${\it{\omega }_{E \times B}}$, and the magnetic shear effect. The electromagnetic finite $\beta $ stabilisation plays a role in the inner core region at ${\rho _{\rm{tor}}}\sim0.35$ together with the fast ion effect. The alpha stabilisation effect is also found at ${\rho _{\rm{tor}}}\sim0.5$. ${\omega _{E \times B}}$, which could reduce the linear growth of the ion temperature gradient mode in the outer core region at ${\rho _{\rm{tor}}}\sim0.5 - 0.7$ with the highest contribution from the toroidal rotation. Furthermore, regarding the improvement in the pedestal, Shafranov shift broadens the stability boundary of the pedestal in support of the diamagnetic effect. The pedestal height and width could be reproduced by the EPED model, while a realistic current profile is used to calculate the internal inductance for Shafranov shift. Based on these findings, a comprehensive confinement enhancement mechanism has been proposed by considering the core-edge interplay.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems

Discrete dynamical systems are used to model various realistic systems in network science, from social unrest in human populations to regulation in biological networks. A common approach is to model the agents of a system as vertices of a graph, and the pairwise interactions between agents as edges. Agents are in one of a finite set of states at each discrete time step and are assigned functions that describe how their states change based on neighborhood relations. Full characterization of state transitions of one system can give insights into fundamental behaviors of other dynamical systems. In this work, we describe a discrete graph dynamical systems (GDSs) application called GDSCalc for computing and characterizing system dynamics. It is an open access system that is used through a web interface. We provide an overview of GDS theory. This theory is the basis of the web application; i.e., an understanding of GDS provides an understanding of the software features, while abstracting away implementation details. We present a set of illustrative examples to demonstrate its use in education and research. Finally, we compare GDSCalc with other discrete dynamical system software tools. Our perspective is that no single software tool will perform all computations that may be required by all users; tools typically have particular features that are more suitable for some tasks. We situate GDSCalc within this space of software tools.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Quantum anomalous Hall effect in two-dimensional magnetic insulator heterojunctions

Abstract Recent years have witnessed tremendous success in the discovery of topological states of matter. Particularly, sophisticated theoretical methods in time-reversal-invariant topological phases have been developed, leading to the comprehensive search of crystal database and the prediction of thousands of topological materials. In contrast, the discovery of magnetic topological phases that break time reversal is still limited to several exemplary materials because the coexistence of magnetism and topological electronic band structure is rare in a single compound. To overcome this challenge, we propose an alternative approach to realize the quantum anomalous Hall (QAH) effect, a typical example of magnetic topological phase, via engineering two-dimensional (2D) magnetic van der Waals heterojunctions. Instead of a single magnetic topological material, we search for the combinations of two 2D (typically trivial) magnetic insulator compounds with specific band alignment so that they can together form a type-III broken-gap heterojunction with topologically non-trivial band structure. By combining the data-driven materials search, first-principles calculations, and the symmetry-based analytical models, we identify eight type-III broken-gap heterojunctions consisting of 2D ferromagnetic insulators in the MXY compound family as a set of candidates for the QAH effect. In particular, we directly calculate the topological invariant (Chern number) and chiral edge states in the MnNF/MnNCl heterojunction with ferromagnetic stacking. This work illustrates how data-driven material science can be combined with symmetry-based physical principles to guide the search for heterojunction-based quantum materials hosting the QAH effect and other exotic quantum states in general.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Recent progress towards a physics-­based understanding of the H-­mode transition

Results from recent experiment and numerical simulation point towards a picture of the L-H transition in which edge shear flows interacting with edge turbulence create the conditions needed to produce a non-zero turbulent Reynolds stress at and just inside the LCFS during L-mode discharges. This stress acts to reinforce the shear flow at this location and the flow drive gets stronger as heating is increased. The L-H transition ensues when the rate of work done by this stress is strong enough to drive the shear flow to large values, which then grows at the expense of the turbulence intensity. The drop in turbulence intensity momentarily reduces the heat flux across the magnetic flux surface, which then allows the edge plasma pressure gradient to build. A sufficiently strong ion pressure gradient then locks in the H-mode state. These results are in general agreement with previously published reduced 0D and 1D predator prey models. An extended predator–prey model including separate ion and electron heat channels yields a non-monotonic power threshold dependence on plasma density provided that the fraction of heat deposited on the ions increases with plasma density. Possible mechanisms to explain other macroscopic transition threshold criteria are identified. A number of open questions and unexplained observations are identified, and must be addressed and resolved in order to build a physics-based model that can yield predictions of the macroscopic conditions needed for accessing H-mode.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Flow adjustment inside homogeneous canopies after a leading edge – An analytical approach backed by LES

A two-dimensional analytical model for describing the mean flow behavior inside a vegetation canopy after a leading edge in neutral conditions was developed and tested by means of large eddy simulations (LES) employing the LES code PALM. The analytical model is developed for the region directly after the canopy edge, the adjustment region, where one-dimensional canopy models fail due to the sharp change in roughness. The derivation of this adjustment region model is based on an analytic solution of the two-dimensional Reynolds averaged Navier–Stokes equation in neutral conditions for a canopy with constant plant area density (PAD). The main assumptions for solving the governing equations are separability of the velocity components concerning the spatial variables and the neglection of the Reynolds stress gradients. These two assumptions are verified by means of LES. To determine the emerging model parameters, a simultaneous fitting scheme was applied to the velocity and pressure data of a reference LES simulation. Furthermore a sensitivity analysis of the adjustment region model, equipped with the previously calculated parameters, was performed varying the three relevant length, the canopy height ( h ), the canopy length and the adjustment length ( L c ), in additional LES. Even if the model parameters are, in general, functions of h / L c , it was found out that the model is capable of predicting the flow quantities in various cases, when using constant parameters. Subsequently the adjustment region model is combined with the one-dimensional model of Massman, which is applicable for the interior of the canopy, to attain an analytical model capable of describing the mean flow for the full canopy domain. As a result, the model is tested against an analytical model based on a linearization approach.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Edge-Functionalized Graphene Nanoribbon Encapsulation To Enhance Stability and Control Kinetics of Hydrogen Storage Materials

Hydrogen is a long-term clean energy carrier that enables completely carbon-free energy production. However, practical implementation of hydrogen fuel technologies is restricted because of lack of safe and high-performing storage materials. Here, we report Mg nanocrystals encapsulated by narrow, bottom-up synthesized graphene nanoribbons (GNRs) as environmentally stable and high-capacity hydrogen storage materials. As an encapsulation medium, GNRs offer similar functionalities as reduced graphene oxide to protect the encapsulated Mg nanocrystals from extensive oxidation, while allowing penetrations of hydrogen. In addition, the GNRs can be edge functionalized to tune the (de-)hydrogenation kinetics, in particular for the processes occurred at the GNR–Mg interfaces. In this work, four different types of edge-functional groups were introduced into GNRs with the goal of comparing their cycling performances because of edge functionalization. On the basis of detailed kinetic analysis coupled with first-principles calculations, we propose that edge-functional groups can contribute to the reduction of kinetic barriers for surface hydrogen reactions at the interface with the GNR by stabilizing surface defects. Furthermore, the GNR–Mg composite exhibited higher hydrogen storage capacity (7.1 wt % of hydrogen based on the total composite) compared with the current literature while demonstrating long-term air stability. This work suggests that the rational design of edge-functional groups in graphene derivatives can provide a general and novel paradigm for simultaneous encapsulation and hydrogen storage catalysis in simple metal or complex metal nanocrystals.

08 HYDROGEN↗
DOE OSTI2022

A Fast and Scalable Genetic Algorithm-Based Approach for Planning of Microgrids in Distribution Networks: Preprint

As a result of climate change, extreme weather events are occurring more frequently and with increasing impact. This trend poses a significant challenge for distribution utilities and system operators to ensure that there is uninterrupted power supply to critical loads in their networks; thus, the level of proactive preparation of the distribution system to be able to handle severe impacts of extreme weather events represents the system's resilience. One method that distribution systems use to prepare for extreme events is to form multiple microgrids and thereby isolate themselves from the grid supply by using local generation as much as possible to supply critical loads. But partitioning an existing system into multiple feasible islands capable of supporting critical loads is still challenging for distribution systems - first, because of the size of the graph partitioning problem and, second, because of the difficulty in properly formulating the desired attributes of such islands or microgrids. Therefore, this paper presents a genetic algorithmbased approach that facilitates incorporating multiple objectives for grid partitioning by formulating two types of problems - node allocation and edge elimination - and it considers multiple topological and resilience-enhancing objectives. The performance of the proposed genetic algorithm-based approach is numerically evaluated on multiple test systems as well as on a real distribution feeder in Colorado, USA.

edge elimination↗
NASA NTRS2004

Ultrasensitive Label-free Electronic Chip for DNA Analysis Using Carbon Nanotube Nanoelectrode Arrays

There is a strong need for faster, cheaper, and simpler methods for nucleic acid analysis in today s clinical tests. Nanotechnologies can potentially provide solutions to these requirements by integrating nanomaterials with biofunctionalities. Dramatic improvement in the sensitivity and multiplexing can be achieved through the high-degree miniaturization. Here, we present our study in the development of an ultrasensitive label-free electronic chip for DNA/RNA analysis based on carbon nanotube nanoelectrode arrays. A reliable nanoelectrode array based on vertically aligned multi-walled carbon nanotubes (MWNTs) embedded in a SiO2 matrix is fabricated using a bottom-up approach. Characteristic nanoelectrode behavior is observed with a low-density MWNT nanoelectrode array in measuring both the bulk and surface immobilized redox species. The open-end of MWNTs are found to present similar properties as graphite edge-plane electrodes, with a wide potential window, flexible chemical functionalities, and good biocompatibility. A BRCA1 related oligonucleotide probe with 18 bases is covalently functionalized at the open ends of the MWNTs and specifically hybridized with an oligonucleotide target as well as a PCR amplicon. The guanine bases in the target molecules are employed as the signal moieties for the electrochemical measurements. Ru(bpy)3(2+) mediator is used to further amplify the guanine oxidation signal. This technique has been employed for direct electrochemical detection of label-free PCR amplicon through specific hybridization with the BRCAl probe. The detection limit is estimated to be less than approximately 1000 DNA molecules, approaching the limit of the sensitivity by laser-based fluorescence techniques in DNA microarray. This system provides a general electronic platform for rapid molecular diagnostics in applications requiring ultrahigh sensitivity, high-degree of miniaturization, simple sample preparation, and low- cost operation.

Li, Jun↗
DOE OSTI2022

Real-Time Hardware-in-the-Loop Testbed to Evaluate FLISR Implemented with OpenFMB

With the increasing complexity of the distribution smart grid architecture, algorithms such as the fault location, isolation, and service restoration (FLISR) scheme rely on robust communications that are resilient to natural and man-made adverse conditions and exhibit robustness. Existing communications infrastructure for information exchange are centralized at the distribution management system, with very little autonomy or intelligence at the grid-edge. As a first step towards achieving grid-edge self-healing, this paper aims to bridge this shortcoming by implementing a centrally coordinated rules-based FLISR scheme and integrating it with Open Field Message Bus (OpenFMB), which is a flexible publish-subscribe architecture with the potential to enable point-to-multipoint communications and is more robust and resilient to natural and man-made adverse conditions. A proof of concept is developed to validate the centrally coordinated FLISR and OpenFMB mounted on an SEL-3360 computer that interacts with a simple feeder network of five SEL-651R relays, an SEL-3530 RTAC, and a hardware-in-the-loop testbed. Results demonstrate the efficacy of this approach in enabling direct, low-latency information exchange. OpenFMB's publish-subscribe data model also opens new ways to enable grid-edge interoperability among devices of different vendors interacting with different protocols.

Sundararajan, Aditya↗
DOE OSTI2014

X-ray relative intensities at incident photon energies across the L{sub i} (i=1–3) absorption edges of elements with 35≤Z≤92

The intensity ratios, I{sub Lk}/I{sub Lα1} (k=l,η,α{sub 2},β{sub 1},β{sub 2,15},β{sub 3},β{sub 4},β{sub 5,7},β{sub 6},β{sub 9,10},γ{sub 1,5},γ{sub 6,8},γ{sub 2,3},γ{sub 4}) and I{sub Lj}/I{sub Lα} (j=β,γ), have been evaluated at incident photon energies across the L{sub i} (i=1–3) absorption edge energies of all the elements with 35≤Z≤92. Use is made of what are currently considered to be more reliable theoretical data sets of different physical parameters, namely, the L{sub i} (i=1–3) sub-shell photoionization cross sections based on the relativistic Hartree–Fock–Slater (RHFS) model, the X-ray emission rates based on the Dirac–Fock model, and the fluorescence and Coster–Kronig yields based on the Dirac–Hartree–Slater model. In addition, the Lα{sub 1} X-ray production cross sections for different elements at various incident photon energies have been tabulated so as to facilitate the evaluation of production cross sections for different resolved L X-ray components from the tabulated intensity ratios. Further, to assist evaluation of the prominent (L{sub i}−S{sub j}) (S{sub j}=M{sub j}, N{sub j} and i=1–3, j=1–7) resonant Raman scattered (RRS) peak energies for an element at a given incident photon energy (below the L{sub i} sub-shell absorption edge), the neutral-atom electron binding energies based on the relaxed orbital RHFS calculations are also listed so as to enable identification of the RRS peaks, which can overlap with the fluorescent X-ray lines. -- Highlights: •The L X-ray relative intensities and Lα{sub 1} XRP cross sections are evaluated using physical parameters based on the IPA models. •Comparison of the intensity ratios evaluated using the DHS and DF models based photoionization cross sections is presented. •Importance of many body effects including electron exchange effects is highlighted.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2021

Coupling of the FUN3D Unstructured Flow Solver and the LASTRAC Stability Code to Model Transition

We develop an iterative automated method to predict transition locations in boundary-layer flows by using the FUN3D solver to perform flow simulations and the LASTRAC code for linear stability computations. The coupling of FUN3D and LASTRAC allows for a robust physics-based approach to model boundary-layer transition by analyzing the growth of different instability waves and then using that information to iteratively update the resulting transition location. There is no user involvement during the iterative computations. We apply this automated method to subsonic flow over a flat plate with a sharp leading edge. The final solution has regions of laminar and turbulent flow with a transition onset location that agrees with experiments and stability-based correlations. This iterative automated method is also applied to an NLF(1)-0416 airfoil for conditions with and without a separation bubble. Along with predicting transition locations, we compare the streamwise distributions of surface-pressure and skin-friction coefficients to a transport-equation-based model. We consider a 6:1 prolate spheroid at three angles of attack, namely, five, ten, and fifteen degrees, where mixed-mode transition occurs due to both Tollmien-Schlichting and crossflow instabilities. The skin-friction contours and transition fronts at every angle of attack from our iterative automated method show good agreement with past experimental and computational results in the literature for the 6:1 prolate spheroid.

Transition↗
DOE OSTI2013

Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides

We present a three-band tight-binding (TB) model for describing the low-energy physics in monolayers of group-VIB transition metal dichalcogenides MX2 (M = Mo, W; X = S, Se, Te). As the conduction- and valence-band edges are predominantly contributed by the dz2 , dxy, and dx2 y2 orbitals of M atoms, the TB model is constructed using these three orbitals based on the symmetries of the monolayers. Parameters of the TB model are fitted from the first-principles energy bands for all MX2 monolayers. The TB model involving only the nearest-neighbor M-M hoppings is sufficient to capture the band-edge properties in the K valleys, including the energy dispersions as well as the Berry curvatures. The TB model involving up to the third-nearest-neighbor M-M hoppings can well reproduce the energy bands in the entire Brillouin zone. Spin-orbit coupling in valence bands is well accounted for by including the on-site spin-orbit interactions ofM atoms. The conduction band also exhibits a small valley-dependent spin splitting which has an overall sign difference between MoX2 and WX2. We discuss the origins of these corrections to the three-band model. The three-band TB model developed here is efficient to account for low-energy physics in MX2 monolayers, and its simplicity can be particularly useful in the study of many-body physics and physics of edge states.

Liu, G. B.↗