We introduce twisted trilayer graphene (tTLG) with two independent twist angles as an ideal system for the precise tuning of the electronic interlayer coupling to maximize the effect of correlated ...behaviors. As established by experiment and theory in the related twisted bilayer graphene system, van Hove singularities (VHS) in the density of states can be used as a proxy of the tendency for correlated behaviors. To explore the evolution of VHS in the twist-angle phase space of tTLG, we present a general low-energy electronic structure model for any pair of twist angles. We show that the basis of the model has infinite dimensions even at a finite energy cutoff and that no Brillouin zone exists even in the continuum limit. Using this model, we demonstrate that the tTLG system exhibits a wide range of magic angles at which VHS merge and that the density of states has a sharp peak at the charge-neutrality point through two distinct mechanisms: the incommensurate perturbation of twisted bilayer graphene's flatbands or the equal hybridization between two bilayer moiré superlattices.
We introduce a complete physical model for the single-particle electronic structure of twisted bilayer graphene (TBLG), which incorporates the crucial role of lattice relaxation. Our model, based on ...k·p perturbation theory and openly available, combines the accuracy of density functional theory calculations through effective tight-binding Hamiltonians with the computational efficiency and complete control of the twist angle offered by continuum models. The inclusion of relaxation significantly changes the band structure at the first magic-angle twist corresponding to flat bands near the Fermi level (the “low-energy” states), and eliminates the appearance of a second magic-angle twist. We show that minimal models for the low-energy states of TBLG can be easily modified to capture the changes in electronic states as a function of twist angle.
Electrons in quantum materials exhibiting coexistence of dispersionless (flat) bands piercing dispersive (steep) bands give rise to strongly correlated phenomena and are associated with ...unconventional superconductivity. We show that in twisted sandwiched graphene (TSWG)a three-layer van der Waals heterostructure with a twisted middle layersteep Dirac cones can coexist with dramatic band flattening at the same energy scale, if twisted by 1.5°. This phenomenon is not stable in the simplified continuum models. The key result of this Letter is that the flat bands become stable only as a consequence of lattice relaxation processes included in our atomistic calculations. Further on, external fields can change the relative energy offset between the Dirac cone vertex and the flat bands and enhance band hybridization, which could permit controlling correlated phases. Our work establishes twisted sandwiched graphene as a new platform for research into strongly interacting two-dimensional quantum matter.
Energy efficiency and data reliability are important indicators to measure network performance in wireless sensor networks. In existing research schemes of routing protocols, the impact of node ...coverage on the network is often ignored, and the possibility that multiple sensor nodes may sense the same spatial point is not taken into account, which results in a waste of network resources, especially in large-scale networks. Apart from that, the blindness of geographic routing in data transmission has been troubling researchers, which means that the nodes are unable to determine the validity of data transmission. In order to solve the above problems, this paper innovatively combines the routing protocol with the coverage control technique and proposes the node collaborative scheduling algorithm, which fully considers the correlation characteristics between sensor nodes to reduce the number of active working nodes and the number of packets generated, to further reduce energy consumption and network delay and improve packet delivery rate. In order to solve the problem of unreliability of geographic routing, a highly reliable link detection and repair scheme is proposed to check the communication link status and repair the invalid link, which can greatly improve the packet delivery rate and throughput of the network, and has good robustness. A large number of experiments demonstrate the effectiveness and superiority of our proposed scheme and algorithm.
When surrounded by a transparent emission region, black holes are expected to reveal a dark shadow caused by gravitational light bending and photon capture at the event horizon. To image and study ...this phenomenon, we have assembled the Event Horizon Telescope, a global very long baseline interferometry array observing at a wavelength of 1.3 mm. This allows us to reconstruct event-horizon-scale images of the supermassive black hole candidate in the center of the giant elliptical galaxy M87. We have resolved the central compact radio source as an asymmetric bright emission ring with a diameter of 42 3 as, which is circular and encompasses a central depression in brightness with a flux ratio 10:1. The emission ring is recovered using different calibration and imaging schemes, with its diameter and width remaining stable over four different observations carried out in different days. Overall, the observed image is consistent with expectations for the shadow of a Kerr black hole as predicted by general relativity. The asymmetry in brightness in the ring can be explained in terms of relativistic beaming of the emission from a plasma rotating close to the speed of light around a black hole. We compare our images to an extensive library of ray-traced general-relativistic magnetohydrodynamic simulations of black holes and derive a central mass of M = (6.5 0.7) × 109 M . Our radio-wave observations thus provide powerful evidence for the presence of supermassive black holes in centers of galaxies and as the central engines of active galactic nuclei. They also present a new tool to explore gravity in its most extreme limit and on a mass scale that was so far not accessible.
The Event Horizon Telescope (EHT) is a very long baseline interferometry (VLBI) array that comprises millimeter- and submillimeter-wavelength telescopes separated by distances comparable to the ...diameter of the Earth. At a nominal operating wavelength of ∼1.3 mm, EHT angular resolution (λ/D) is ∼25 as, which is sufficient to resolve nearby supermassive black hole candidates on spatial and temporal scales that correspond to their event horizons. With this capability, the EHT scientific goals are to probe general relativistic effects in the strong-field regime and to study accretion and relativistic jet formation near the black hole boundary. In this Letter we describe the system design of the EHT, detail the technology and instrumentation that enable observations, and provide measures of its performance. Meeting the EHT science objectives has required several key developments that have facilitated the robust extension of the VLBI technique to EHT observing wavelengths and the production of instrumentation that can be deployed on a heterogeneous array of existing telescopes and facilities. To meet sensitivity requirements, high-bandwidth digital systems were developed that process data at rates of 64 gigabit s−1, exceeding those of currently operating cm-wavelength VLBI arrays by more than an order of magnitude. Associated improvements include the development of phasing systems at array facilities, new receiver installation at several sites, and the deployment of hydrogen maser frequency standards to ensure coherent data capture across the array. These efforts led to the coordination and execution of the first Global EHT observations in 2017 April, and to event-horizon-scale imaging of the supermassive black hole candidate in M87.
We present measurements of the properties of the central radio source in M87 using Event Horizon Telescope data obtained during the 2017 campaign. We develop and fit geometric crescent models ...(asymmetric rings with interior brightness depressions) using two independent sampling algorithms that consider distinct representations of the visibility data. We show that the crescent family of models is statistically preferred over other comparably complex geometric models that we explore. We calibrate the geometric model parameters using general relativistic magnetohydrodynamic (GRMHD) models of the emission region and estimate physical properties of the source. We further fit images generated from GRMHD models directly to the data. We compare the derived emission region and black hole parameters from these analyses with those recovered from reconstructed images. There is a remarkable consistency among all methods and data sets. We find that >50% of the total flux at arcsecond scales comes from near the horizon, and that the emission is dramatically suppressed interior to this region by a factor >10, providing direct evidence of the predicted shadow of a black hole. Across all methods, we measure a crescent diameter of 42 3 as and constrain its fractional width to be <0.5. Associating the crescent feature with the emission surrounding the black hole shadow, we infer an angular gravitational radius of GM/Dc2 = 3.8 0.4 as. Folding in a distance measurement of gives a black hole mass of . This measurement from lensed emission near the event horizon is consistent with the presence of a central Kerr black hole, as predicted by the general theory of relativity.
We present the first Event Horizon Telescope (EHT) images of M87, using observations from April 2017 at 1.3 mm wavelength. These images show a prominent ring with a diameter of ∼40 as, consistent ...with the size and shape of the lensed photon orbit encircling the "shadow" of a supermassive black hole. The ring is persistent across four observing nights and shows enhanced brightness in the south. To assess the reliability of these results, we implemented a two-stage imaging procedure. In the first stage, four teams, each blind to the others' work, produced images of M87 using both an established method (CLEAN) and a newer technique (regularized maximum likelihood). This stage allowed us to avoid shared human bias and to assess common features among independent reconstructions. In the second stage, we reconstructed synthetic data from a large survey of imaging parameters and then compared the results with the corresponding ground truth images. This stage allowed us to select parameters objectively to use when reconstructing images of M87. Across all tests in both stages, the ring diameter and asymmetry remained stable, insensitive to the choice of imaging technique. We describe the EHT imaging procedures, the primary image features in M87, and the dependence of these features on imaging assumptions.
The Event Horizon Telescope (EHT) has mapped the central compact radio source of the elliptical galaxy M87 at 1.3 mm with unprecedented angular resolution. Here we consider the physical implications ...of the asymmetric ring seen in the 2017 EHT data. To this end, we construct a large library of models based on general relativistic magnetohydrodynamic (GRMHD) simulations and synthetic images produced by general relativistic ray tracing. We compare the observed visibilities with this library and confirm that the asymmetric ring is consistent with earlier predictions of strong gravitational lensing of synchrotron emission from a hot plasma orbiting near the black hole event horizon. The ring radius and ring asymmetry depend on black hole mass and spin, respectively, and both are therefore expected to be stable when observed in future EHT campaigns. Overall, the observed image is consistent with expectations for the shadow of a spinning Kerr black hole as predicted by general relativity. If the black hole spin and M87's large scale jet are aligned, then the black hole spin vector is pointed away from Earth. Models in our library of non-spinning black holes are inconsistent with the observations as they do not produce sufficiently powerful jets. At the same time, in those models that produce a sufficiently powerful jet, the latter is powered by extraction of black hole spin energy through mechanisms akin to the Blandford-Znajek process. We briefly consider alternatives to a black hole for the central compact object. Analysis of existing EHT polarization data and data taken simultaneously at other wavelengths will soon enable new tests of the GRMHD models, as will future EHT campaigns at 230 and 345 GHz.
We present the calibration and reduction of Event Horizon Telescope (EHT) 1.3 mm radio wavelength observations of the supermassive black hole candidate at the center of the radio galaxy M87 and the ...quasar 3C 279, taken during the 2017 April 5-11 observing campaign. These global very long baseline interferometric observations include for the first time the highly sensitive Atacama Large Millimeter/submillimeter Array (ALMA); reaching an angular resolution of 25 as, with characteristic sensitivity limits of ∼1 mJy on baselines to ALMA and ∼10 mJy on other baselines. The observations present challenges for existing data processing tools, arising from the rapid atmospheric phase fluctuations, wide recording bandwidth, and highly heterogeneous array. In response, we developed three independent pipelines for phase calibration and fringe detection, each tailored to the specific needs of the EHT. The final data products include calibrated total intensity amplitude and phase information. They are validated through a series of quality assurance tests that show consistency across pipelines and set limits on baseline systematic errors of 2% in amplitude and 1° in phase. The M87 data reveal the presence of two nulls in correlated flux density at ∼3.4 and ∼8.3 Gλ and temporal evolution in closure quantities, indicating intrinsic variability of compact structure on a timescale of days, or several light-crossing times for a few billion solar-mass black hole. These measurements provide the first opportunity to image horizon-scale structure in M87.
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