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The defining characteristic of hole-doped cuprates is d -wave high temperature superconductivity. However, intense theoretical interest is now focused on whether a pair density wave state (PDW) could coexist with cuprate superconductivity [D. F. Agterberg et al., Annu. Rev. Condens. Matter Phys. 11, 231 (2020)]. Here, we use a strong-coupling mean-field theory of cuprates, to model the atomic-scale electronic structure of an eight-unit-cell periodic, d -symmetry form factor, pair density wave (PDW) state coexisting with d -wave superconductivity (DSC). From this PDW + DSC model, the atomically resolved density of Bogoliubov quasiparticle states N r , E is predicted at the terminal BiO surface of Bi 2 Sr 2 CaCu 2 O 8 and compared with high-precision electronic visualization experiments using spectroscopic imaging scanning tunneling microscopy (STM). The PDW + DSC model predictions include the intraunit-cell structure and periodic modulations of N r , E , the modulations of the coherence peak energy Δ p r , and the characteristics of Bogoliubov quasiparticle interference in scattering-wavevector space q - space . Consistency between all these predictions and the corresponding experiments indicates that lightly hole-doped Bi 2 Sr 2 CaCu 2 O 8 does contain a PDW + DSC state. Moreover, in the model the PDW + DSC state becomes unstable to a pure DSC state at a critical hole density p *, with empirically equivalent phenomena occurring in the experiments. All these results are consistent with a picture in which the cuprate translational symmetry-breaking state is a PDW, the observed charge modulations are its consequence, the antinodal pseudogap is that of the PDW state, and the cuprate critical point at p * ≈ 19% occurs due to disappearance of this PDW. 

High magnetic fields suppress cuprate superconductivity to reveal an unusual density wave (DW) state coexisting with unexplained quantum oscillations. Although routinely labeled a charge density wave (CDW), this DW state could actually be an electron-pair density wave (PDW). To search for evidence of a field-induced PDW, we visualized modulations in the density of electronic states N ( r ) within the halo surrounding Bi 2 Sr 2 CaCu 2 O 8 vortex cores. We detected numerous phenomena predicted for a field-induced PDW, including two sets of particle-hole symmetric N ( r ) modulations with wave vectors Q P and 2 Q P , with the latter decaying twice as rapidly from the core as the former. These data imply that the primary field-induced state in underdoped superconducting cuprates is a PDW, with approximately eight CuO 2 unit-cell periodicity and coexisting with its secondary CDWs. 

Cosmic rays are energetic charged particles from extraterrestrial sources, with the highest-energy events thought to come from extragalactic sources. Their arrival is infrequent, so detection requires instruments with large collecting areas. In this work, we report the detection of an extremely energetic particle recorded by the surface detector array of the Telescope Array experiment. We calculate the particle’s energy as $244\pm 29\left(\text{stat}\text{.}\right){}_{-76}^{+51}\left(\text{syst}\text{.}\right)\text{ exa–electron volts}$ (~40 joules). Its arrival direction points back to a void in the large-scale structure of the Universe. Possible explanations include a large deflection by the foreground magnetic field, an unidentified source in the local extragalactic neighborhood, or an incomplete knowledge of particle physics. 

Abstract Optical emissions associated with Terrestrial Gamma ray Flashes (TGFs) have recently become important subjects in space‐based and ground‐based observations as they can help us understand how TGFs are produced during thunderstorms. In this paper, we present the first time‐resolved leader spectra of the optical component associated with a downward TGF. The TGF was observed by the Telescope Array Surface Detector (TASD) simultaneously with other lightning detectors, including a Lightning Mapping Array (LMA), an INTerFerometer (INTF), a Fast Antenna (FA), and a spectroscopic system. The spectroscopic system recorded leader spectra at 29,900 frames per second (33.44 s time resolution), covering a spectral range from 400 to 900 nm, with 2.1 nm per pixel. The recordings of the leader spectra began 11.7 ms before the kA return stroke and at a height of 2.37 km above the ground. These spectra reveal that optical emissions of singly ionized nitrogen and oxygen occur between 167 s before and 267 s after the TGF detection, while optical emissions of neutrals (H I, 656 nm; N I, 744 nm, and O I, 777 nm) occur right at the moment of the detection. The time‐dependent spectra reveal differences in the optical emissions of lightning leaders with and without downward TGFs. 

Abstract On 11 September 2021, two small thunderstorms developed over the Telescope Array Surface Detector (TASD) that produced an unprecedented number of six downward terrestrial gamma ray flashes (TGFs) within one‐hour timeframe. The TGFs occurred during the initial stage of negative cloud‐to‐ground flashes whose return strokes had increasingly large peak currents up to 223 kA, 147 GeV energy deposit in up to 25 1.2 km‐spaced surface detectors, and intermittent bursts of gamma‐rays with total durations up to 717 s. The analyses are based on observations recorded by the TASD network, complemented by data from a 3D lightning mapping array, broadband VHF interferometer, fast electric field change sensor, high‐speed video camera, and the National Lightning Detection Network. The TGFs of the final two flashes had gamma fluences of and 8, logarithmically bridging the gap between previous TASD and satellite‐based detections. The observations further emphasize the similarity between upward and downward TGF varieties, suggesting a common mechanism for their production. 

Abstract We report the observation of a downward terrestrial gamma‐ray flash (TGF) during the dart‐leader stage in a negative cloud‐to‐ground lightning flash. The observation was recorded by the Telescope Array Surface Detector, in conjunction with a Lightning Mapping Array, an interferometer (INTF), a fast antenna, and a high‐speed camera. The return stroke was the fifth stroke of a negative cloud‐to‐ground lightning flash, which consisted of nine return strokes (RS) with three distinct ground‐strike points. The peak current of the return stroke associated with the TGF was the highest among the nine RS. Its dart leader had the highest propagation speed in the flash, measuring at m/s. The TGF was detected during the final stages of the dart leader, lasting 68 s. The TGF emission was detected within a few microseconds of the return stroke, indicating that it persisted until the final stage of leader development. The total deposited energy of 1,352 MeV was recorded by the TASD; the fluence was estimated to be 8 at the source, and the source altitude was estimated at 1.45 km above the ground. The observation of a downward TGF associated with a dart‐leader stage supports the idea that the production of X‐rays and downward TGFs are part of a continuum of energetic radiation related to lightning leaders. 

We use a new method to estimate the injected mass composition of ultrahigh cosmic rays (UHECRs) at energies higher than 10 EeV. The method is based on comparison of the energy-dependent distribution of cosmic ray arrival directions as measured by the Telescope Array (TA) experiment with that calculated in a given putative model of UHECR under the assumption that sources trace the large-scale structure (LSS) of the Universe. As we report in the companion Letter, the TA data show large deflections with respect to the LSS which can be explained, assuming small extragalactic magnetic fields (EGMF), by an intermediate composition changing to a heavy one (iron) in the highest energy bin. Here we show that these results are robust to uncertainties in UHECR injection spectra, the energy scale of the experiment and galactic magnetic fields. The assumption of weak EGMF, however, strongly affects this interpretation at all but the highest energies E>100 EeV, where the remarkable isotropy of the data implies a heavy injected composition even in the case of strong EGMF. This result also holds if UHECR sources are as rare as 2 ×10−5 Mpc−3, that is the conservative lower limit for the source number density. 

We report an estimation of the injected mass composition of ultra-high energy cosmic rays (UHECRs) at energies higher than 10 EeV. The composition is inferred from an energy-dependent sky distribution of UHECR events observed by the Telescope Array surface detector by comparing it to the Large Scale Structure of the local Universe. In the case of negligible extra-galactic magnetic fields the results are consistent with a relatively heavy injected composition at E ∼ 10 EeV that becomes lighter up to E ∼ 100 EeV, while the composition at E > 100 EeV is very heavy. The latter is true even in the presence of highest experimentally allowed extra-galactic magnetic fields, while the composition at lower energies can be light if a strong EGMF is present. The effect of the uncertainty in the galactic magnetic field on these results is subdominant.