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The problem of matrix completion and decomposition in the cone of positive semidefinite (PSD) matrices is a well-understood problem, with many important applications in areas such as linear algebra, optimization, and control theory. This paper considers the completion and decomposition problems in a broader class of cones, namely phase-bounded cones. We show that most of the main results from the PSD case carry over to the phase-bounded case. More precisely, this is done by first unveiling a duality between the completion and decomposition problems, using a dual cone interpretation. Based on this, we then derive necessary and sufficient conditions for the phase-bounded completion and decomposition problems, and also characterize all phase-bounded completions of a completable partial matrix with a banded pattern.

A conventional superconducting state may be replaced by another dissipationless state hosting Cooper pairs with a finite momentum, leaving thermodynamic footprints for such a phase transition. Recently, a novel type of finite momentum pairing, so-called orbital Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, has been proposed to occur in spin-orbit coupled superconductors such as bilayer $2\mathrm{H-NbSe_{2}}$. So far, a thermodynamic demonstration, which is key for establishing this exotic phase, has been lacking. Here, we reveal a first-order quantum phase transition to the orbital FFLO state in tunneling spectroscopic measurements on multilayer $2\mathrm{H-NbSe_{2}}$. The phase transition manifests itself as a sudden enhancement of the superconducting gap at an in-plane magnetic field $B_{//}$ well below the upper critical field. Furthermore, this transition shows prominent hysteresis by sweeping $B_{//}$ back and forth and quickly disappears once the magnetic field is tilted away from the sample plane by less than one degree. We obtain a comprehensive phase diagram for the orbital FFLO state and compare it with the theoretical calculation that takes into account the rearrangement of Josephson vortices. Our work elucidates the microscopic mechanism for the emergence of the orbital FFLO state.

Vortices in superconductors can help identify emergent phenomena but certain fundamental aspects of vortices, such as their entropy, remain poorly understood. Here, we study the vortex entropy in underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ by measuring both magneto-resistivity and Nernst effect on ultrathin flakes ($\le$2 unit-cell). We extract the London penetration depth from the magneto-transport measurements on samples with different doping levels. It reveals that the superfluid phase stiffness $\rho_s$ scales linearly with the superconducting transition temperature $T_c$, down to the extremely underdoped case. On the same batch of ultrathin flakes, we measure the Nernst effect via on-chip thermometry. Together, we obtain the vortex entropy and find that it decays exponentially with $T_c$ or $\rho_s$. We further analyze the Nernst signal above $T_c$ in the framework of Gaussian superconducting fluctuations. The combination of electrical and thermoelectric measurements in the two-dimensional limit provides fresh insight into high temperature superconductivity.

Light-matter interaction in quantum materials presents a new paradigm as light can tip the balance between many competing quantum many-body phases to result in new phenomena. Describing the optical response of such materials requires complex models. Here, we develop a non-local model to describe the optical response of a quantum material, 1T-TaS$_2$. 1T-TaS$_2$ is a nearly commensurate charge-density-wave material at room temperature. The competing stacking configurations of the charge domains in this layered material result in significant optical inhomogeneity that necessitates a non-local dielectric function. We experimentally measure the non-local optical response of 1T-TaS$_2$ films under various illumination intensities and validate our model. The non-local parameter extracted from our measurements sheds light on the competition between the two stacking configurations of 1T-TaS$_2$. Our technique of measuring non-local optical response serves as a quick, simple, and non-invasive method to probe the energy landscape of strong correlations in many such quantum materials., Comment: 7 pages, 4 figures

Superconductivity and long-range ferromagnetism hardly coexist in a uniform manner. The counter-example has been observed, in uranium-based superconductors for instance, with a coexisting temperature limited to about 1 K. Here, we report the coexistence of high temperature superconductivity and itinerant ferromagnetism in lithium intercalated FeSe flakes. In superconducting samples with transition temperature around 40 K, we observe the anomalous Hall effect with a hysteresis loop in transverse resistivity and a butterfly-like pattern of magneto-resistance. Intriguingly, such ferromagnetism persists down to a temperature at which the zero-field resistance fully vanishes. Furthermore, the superconductivity is enhanced under an in-plane magnetic field, suggestive of the participation of spin-polarized Cooper pairs. The surprising finding underscores a uniform coexistence of the two antagonistic phenomena on a record-high energy scale.

Exploration of new dielectrics with large capacitive coupling is an essential topic in modern electronics when conventional dielectrics suffer from the leakage issue near breakdown limit. To address this looming challenge, we demonstrate that rare-earth-metal fluorides with extremely-low ion migration barriers can generally exhibit an excellent capacitive coupling over 20 $\mu$F cm$^{-2}$ (with an equivalent oxide thickness of ~0.15 nm and a large effective dielectric constant near 30) and great compatibility with scalable device manufacturing processes. Such static dielectric capability of superionic fluorides is exemplified by MoS$_2$ transistors exhibiting high on/off current ratios over 10$^8$, ultralow subthreshold swing of 65 mV dec$^{-1}$, and ultralow leakage current density of ~10$^{-6}$ A cm$^{-2}$. Therefore, the fluoride-gated logic inverters can achieve significantly higher static voltage gain values, surpassing ~167, compared to conventional dielectric. Furthermore, the application of fluoride gating enables the demonstration of NAND, NOR, AND, and OR logic circuits with low static energy consumption. Notably, the superconductor-to-insulator transition at the clean-limit Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ can also be realized through fluoride gating. Our findings highlight fluoride dielectrics as a pioneering platform for advanced electronics applications and for tailoring emergent electronic states in condensed matters., Comment: 33 pages, 5 figures

Exceptional point (EP)-based optical sensors exhibit exceptional sensitivity but poor detectivity due to their acute sensitivity to perturbations such as noise. When the optical budget is limited as in applications on mobile platforms, high detectivity might be equally important as high sensitivity. In such scenarios, off-EP sensing is advantageous where a slight loss in sensitivity can lead to a significant gain in detectivity. Here, we show that a passive parity-time symmetric plasmonic-photonic hybrid shows a peak in its detectivity off EP where the sensitivity is still very high-surpassing the sensitivities of equivalent fully-plasmonic and fully-photonic systems. We demonstrate the high detectivity of off-EP sensing of anti-mouse IgG protein using this plasmonic-photonic hybrid system. We report a sensitivity of 1.2 nm/nM while requiring a minimum optical budget of 1.3 nJ. Thus, non-Hermitian plasmonic-photonic hybrids could be the best class of nanophotonic sensors for real-world applications., Comment: 17 pages, 4 figures, under review by ACS Photonics

Josephson tunneling in twisted cuprate junctions provides a litmus test for the pairing symmetry, which is fundamental for understanding the microscopic mechanism of high temperature superconductivity. This issue is rekindled by experimental advances in van der Waals stacking and the proposal of an emergent d+id-wave. So far, all experiments have been carried out on Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi-2212) with double CuO$_2$ planes but show controversial results. Here, we investigate junctions made of Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+y}$ (Bi-2201) with single CuO$_2$ planes. Our on-site cold stacking technique ensures uncompromised crystalline quality and stoichiometry at the interface. Junctions with carefully calibrated twist angles around 45{\deg} show strong Josephson tunneling and conventional temperature dependence. Furthermore, we observe standard Fraunhofer diffraction patterns and integer Fiske steps in a junction with a twist angle of 45.0$\pm$0.2{\deg}. Together, these results pose strong constraints on the d or d+id-wave pairing and suggest an indispensable isotropic pairing component., Comment: 32 pages, 5 figures

In recent years, particular physical phenomena enabled by non-Hermitian metamaterial systems have attracted significant research interests. In this paper, a non-Hermitian three-dimensional metamaterial near the exceptional point (EP) is proposed to demonstrate extremely asymmetric absorption and reflection. Unlike its conventional counterparts, this proposed metamaterial is constructed with a loss-assisted design. Localized losses are introduced into the structure by combining our technique of graphene-based resistive inks with conventional printed circuit board (PCB) process. Extremely asymmetric absorption and reflection near the EP are experimentally observed by tuning the loss between split ring resonators (SRRs) in the meta-atoms. Simultaneously, by linking the equivalent circuit model (ECM) with the Hamiltonian quantum physical model, the equivalent non-Hermitian Hamiltonian is obtained and a non-Hermitian transmission matrix is constructed. We show that tuning the structure and circuit parameters of the ECM produces a metamaterial system with EP response. Our system can be used in the design of asymmetric metamaterial absorbers. Our work lays down the way for the manipulation of EP to develop perfect absorption, sensing and other applications in the 3D metamaterial platform.

The application of sodium laser guide star is the key difference between modern adaptive optics system and traditional adaptive optics system. Especially in system like multi-conjugate adaptive optics, sodium laser guide star asterism which is formed by several laser guide stars in certain pattern is required to probe more atmospheric turbulence in different directions. To achieve this, a sodium laser guide star asterism launching platform is required. In this paper, we will introduce the sodium laser guide star asterism launching platform built and tested on the 1.8m telescope of the Gaomeigu Observatory. The platform has two functions: one is to compare the performance of sodium laser guide stars generated by different lasers at the same place; the other is to generate sodium laser guide star asterism with adjustable shape. The field test results at the beginning of 2021 verify the important role of the platform, which is also the first time to realize sodium laser guide star asterism in China.

There is a heated debate on the Josephson effect in twisted Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ flakes. Recent experimental results suggest the presence of either anomalously isotropic pairing or exotic $d$+i$d$-wave pairing, in addition to the commonly believed $d$-wave one. Here, we address this controversy by fabricating ultraclean junctions with uncompromised crystalline quality and stoichiometry at the junction interfaces. In the optimally doped regime, we obtain prominent Josephson coupling (2-4 mV) in multiple junctions with the twist angle of 45$^\circ$, in sharp contrast to a recent report that shows two orders of magnitude suppression around 45$^\circ$ from the value at 0$^\circ$. We further extend this study to the previously unexplored overdoped regime and observe pronounced Josephson tunneling at 45$^\circ$ together with Josephson diode effect up to 50 K. Our work helps establish the persistent presence of an isotropic pairing component across the entire superconducting phase diagram., Comment: 6 pages, 5 figures

Existing solutions to network scheduling typically assume that the instantaneous link rates are completely known before a scheduling decision is made or consider a bandit setting where the accurate link quality is discovered only after it has been used for data transmission. In practice, the decision maker can obtain (relatively accurate) channel information, e.g., through beamforming in mmWave networks, right before data transmission. However, frequent beamforming incurs a formidable overhead in densely deployed mmWave WLANs. In this paper, we consider the important problem of throughput optimization with joint link probing and scheduling. The problem is challenging even when the link rate distributions are pre-known (the offline setting) due to the necessity of balancing the information gains from probing and the cost of reducing the data transmission opportunity. We develop an approximation algorithm with guaranteed performance when the probing decision is non-adaptive, and a dynamic programming based solution for the more challenging adaptive setting. We further extend our solutions to the online setting with unknown link rate distributions and develop a contextual-bandit based algorithm and derive its regret bound. Numerical results using data traces collected from real-world mmWave deployments demonstrate the efficiency of our solutions.

Chinese Grammatical Error Correction (CGEC) is both a challenging NLP task and a common application in human daily life. Recently, many data-driven approaches are proposed for the development of CGEC research. However, there are two major limitations in the CGEC field: First, the lack of high-quality annotated training corpora prevents the performance of existing CGEC models from being significantly improved. Second, the grammatical errors in widely used test sets are not made by native Chinese speakers, resulting in a significant gap between the CGEC models and the real application. In this paper, we propose a linguistic rules-based approach to construct large-scale CGEC training corpora with automatically generated grammatical errors. Additionally, we present a challenging CGEC benchmark derived entirely from errors made by native Chinese speakers in real-world scenarios. Extensive experiments and detailed analyses not only demonstrate that the training data constructed by our method effectively improves the performance of CGEC models, but also reflect that our benchmark is an excellent resource for further development of the CGEC field., Comment: Long paper, accepted at the Findings of EMNLP 2022

Chinese Spell Checking (CSC) task aims to detect and correct Chinese spelling errors. Recently, related researches focus on introducing character similarity from confusion set to enhance the CSC models, ignoring the context of characters that contain richer information. To make better use of contextual information, we propose a simple yet effective Curriculum Learning (CL) framework for the CSC task. With the help of our model-agnostic CL framework, existing CSC models will be trained from easy to difficult as humans learn Chinese characters and achieve further performance improvements. Extensive experiments and detailed analyses on widely used SIGHAN datasets show that our method outperforms previous state-of-the-art methods. More instructively, our study empirically suggests that contextual similarity is more valuable than character similarity for the CSC task., Comment: Accepted by ICASSP2023

The microscopic understanding of high-temperature superconductivity in cuprates has been hindered by the apparent complexity of crystal structures in these materials. We used scanning tunneling microscopy and spectroscopy to study an electron-doped copper oxide compound Sr$_{1-x}$Nd$_x$CuO$_2$ that has only bare cations separating the CuO$_2$ planes and thus the simplest infinite-layer structure among all cuprate superconductors. Tunneling conductance spectra of the major CuO$_2$ planes in the superconducting state revealed direct evidence for a nodeless pairing gap, regardless of variation of its magnitude with the local doping of trivalent neodymium. Furthermore, three distinct bosonic modes are observed as multiple peak-dip-hump features outside the superconducting gaps and their respective energies depend little on the spatially varying gaps. Along with the bosonic modes with energies identical to those of the external, bending and stretching phonons of copper oxides, our findings indicate their origin from lattice vibrations rather than spin excitations., Comment: 16 Pages, 4 figures, 5 supplemental figures

Understanding the rich and competing electronic orders in cuprate superconductors may provide important insight into the mechanism of high-temperature superconductivity. Here, by measuring Bi2Sr2CaCu2O8+x in the extremely underdoped regime, we obtain evidence for a distinct type of ordering, which manifests itself as resistance oscillations at low magnetic fields (<10 T) and at temperatures around the superconducting transition. By tuning the doping level p continuously, we reveal that these low-field oscillations occur only when p<0.1. The oscillation amplitude increases with decreasing p but the oscillation period stays almost constant. We show that these low-field oscillations can be well described by assuming a periodic superconducting structure with a mesh size of about 50 nm. Such a charge order, which is distinctly different from the well-established charge density wave and pair density wave, seems to be an unexpected piece of the puzzle on the correlated physics in cuprates.