We study the quantum-droplet state in a three-dimensional (3D) Bose gas in the presence of 1D spin-orbit coupling and Raman coupling, especially the stripe phase with density modulation, by numerically computing the ground state energy including the mean-field energy and Lee–Huang–Yang correction. In this droplet state, the stripe can exist in a wider range of Raman coupling, compared with the BEC-gas state. More intriguingly, both spin-orbit coupling and Raman coupling strengths can be used to tune the droplet density.

We apply supervised machine learning to study the topological states of one-dimensional non-Hermitian systems. Unlike Hermitian systems, the winding number of such non-Hermitian systems can take half integers. We focus on a non-Hermitian model, an extension of the Su–Schrieffer–Heeger model. The non-Hermitian model maintains the chiral symmetry. We find that trained neuron networks can reproduce the topological phase diagram of our model with high accuracy. This successful reproduction goes beyond the parameter space used in the training process. Through analyzing the intermediate output of the networks, we attribute the success of the networks to their mastery of computation of the winding number. Our work may motivate further investigation on the machine learning of non-Hermitian systems.

As a foundation of quantum physics, uncertainty relations describe ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertainty relations are formulated by mathematical bounds for a specific state. Here we present a method for geometrically characterizing uncertainty relations as an entire area of variances of the observables, ranging over all possible input states. We find that for the pair of position and momentum operators, Heisenberg's uncertainty principle points exactly to the attainable area of the variances of position and momentum. Moreover, for finite-dimensional systems, we prove that the corresponding area is necessarily semialgebraic; in other words, this set can be represented via finite polynomial equations and inequalities, or any finite union of such sets. In particular, we give the analytical characterization of the areas of variances of (a) a pair of one-qubit observables and (b) a pair of projective observables for arbitrary dimension, and give the first experimental observation of such areas in a photonic system.

A novel method for constructing a kernel for the meson bound-state problem is described. It produces a closed form that is symmetry-consistent (discrete and continuous) with the gap equation defined by any admissible gluon-quark vertex, $\varGamma$. Applicable even when the diagrammatic content of $\varGamma$ is unknown, the scheme can foster new synergies between continuum and lattice approaches to strong interactions. The framework is illustrated by showing that the presence of a dressed-quark anomalous magnetic moment in $\varGamma$, an emergent feature of strong interactions, can remedy many defects of widely used meson bound-state kernels, including the mass splittings between vector and axial-vector mesons and the level ordering of pseudoscalar and vector meson radial excitations.

Inspired by the $P_{cs}(4459)$ reported by the LHCb collaboration recently, we investigate the $P_{cs}(4459)$ production from $\varXi_b$ decay in a molecular scenario using an effective Lagrangian approach. With different $J^P$ assignments to $P_{cs}(4459)$, the magnitude of branching fractions of $\varXi_b \to P_{cs}(4459) K$ is estimated, which is of the order of $10^{-4}$. Together with the decay properties of $P_{cs}(4459)$, the present estimations could be further testified by precise measurements and contribute to a better understanding of the molecular interpretations and the exploration of $J^P$ quantum numbers of $P_{cs}(4459)$.

We periodically modulate the lattice trapping potential of a $^{87}$Sr optical clock to Floquet engineer the clock transition. In the context of atomic gases in lattices, Floquet engineering has been used to shape the dispersion and topology of Bloch quasi-energy bands. Differently from these previous works manipulating the external (spatial) quasi-energies, we target the internal atomic degrees of freedom. We shape Floquet spin quasi-energies and measure their resonance profiles with Rabi spectroscopy. We provide the spectroscopic sensitivity of each band by measuring the Fisher information and show that this is not depleted by the Floquet dynamical modulation. The demonstration that the internal degrees of freedom can be selectively engineered by manipulating the external degrees of freedom inaugurates a novel device with potential applications in metrology, sensing and quantum simulations.

FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS)

Above-band-gap optical excitation of electron-hole pairs screens the doping-induced surface electric field and generates terahertz (THz) pulses via free-carrier transport. THz emission from a heavily doped silicon surface is much weaker than that of lightly doped samples. A polarity reversal of the THz electric field is observed in heavily doped p-type silicon, indicating that the doping related and carrier induced surface electric fields oppose each other. By comparing the penetration depth of the excitation laser with the thickness of the depletion layer for the doped silicon, it is shown that competition between diffusion and drift current causes the polarity reversal.

We demonstrated a nonlinear temporal filter based on the self-diffraction (SD) process. Temporal contrast enhancement, angular dispersion and spectrum broadening properties of the SD process are investigated in experiment and simulation. Driven by spectral phase well compensated laser pulses with bandwidth of 28 nm, the filter produced clean pulses with a temporal contrast higher than $10^{10}$ and excellent spatial profile, the spectrum of which was smoothed and broadened to 64 nm. After implementing this filter into a home-made 30 TW Ti:sapphire amplifier, temporal contrast of the amplified pulses was enhanced to $10^{10}$ within the time scale of $-400$ ps.

Two-dimensional surface-enhanced Raman scattering (SERS) substrates have drawn intense attention due to their excellent spectral reproducibility, high uniformity and perfect anti-interference ability. However, the inferior detection sensitivity and low enhancement have limited the practical application of two-dimensional SERS substrates. To address this issue, we propose that the interaction between the MoTe$_{2}$ substrate and the analyte rhodamine 6G molecules could be remarkably enhanced by the introduced p-doping effect and lattice distortion of MoTe$_{2}$ via hydrogen plasma treatment. After the treatment, the SERS is greatly improved, the enhancement factor of probe molecules reaches $1.83 \times 10^{6}$ as well as the limit of detection concentration reaches $10^{-13}$ M. This method is anticipated to afford new enhancement probability for other 2D materials, even non-metal oxide semiconductor SERS substrates.

CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMAL PROPERTIES

Searching for new carbon allotropes with superior properties has been a longstanding interest in material sciences and condensed matter physics. Here we identify a novel superhard carbon phase with an 18-atom trigonal unit cell in a full-$sp^{3}$ bonding network, termed tri-C$_{18}$ carbon, by first-principles calculations. Its structural stability has been verified by total energy, phonon spectra, elastic constants, and molecular dynamics simulations. Furthermore, tri-C$_{18}$ carbon has a high bulk modulus of 400 GPa and Vickers hardness of 79.0 GPa, comparable to those of diamond. Meanwhile, the simulated x-ray diffraction pattern of tri-C$_{18}$ carbon matches well with the previously unexplained diffraction peaks found in chimney soot, indicating the possible presence of tri-C$_{18}$ carbon. Remarkably, electronic band structure calculations reveal that tri-C$_{18}$ carbon has a wide indirect bandgap of 6.32 eV, larger than that of cubic diamond, indicating its great potential in electronic or optoelectronic devices working in the deep ultraviolet region.

Strategies to prolong operational life are highly pursued to strengthen the advantage of cost-effectiveness on sodium-ion batteries (SIBs). We demonstrate the crucial influence of particles' internal mechanical strains on durability of cathode, which does not attract enough attentions from the community. Among the investigated samples, 2% Ti-modified-Na$_{0.67}$Ni$_{0.1}$Co$_{0.1}$Mn$_{0.8}$O$_{2}$ suppresses the $c$-axis lattice variation by 38%, attains the reversible capacity 86% higher after 200 cycles, and still keeps intact morphology. This approach indicates that the mechanical properties could tailor cyclic stability of cathode, which is particular important to further improve competitiveness for SIBs.

As a new electrochemical power system, safety (especially thermal safety) of Na-ion batteries (NIBs) is the key towards large-scale industrialization and market application. Thus, research on the thermal stability of NIBs is helpful to evaluate the safety properties and to provide effective strategies to prevent the occurrence of battery safety failure. Thermal stability of the high-power 26650 cylindrical NIBs using Cu-based layered oxide cathode and hard carbon anode is studied. The high power NIBs can achieve fast charge and discharge at 5–10 C rate and maintain 80% capacity after 4729 cycles at 2 C/2 C rate, where the unit C denotes a measure of the rate at which a battery is charge-discharged relative to its maximum capacity. The results of accelerating rate calorimeter and differential scanning calorimetry (ARC-DSC) test results show that NIBs have a higher initial decomposition temperature ($\ge$110 ℃) and a lower maximum thermal runaway temperature ($\le $350 ℃) than those of Li-ion batteries (LIBs), exhibiting a favorable thermal stability. It should be noted that the heat generation of cathode accounts for a large proportion of the total heat generation while the thermal stability of the anode determines the initial thermal runaway temperature, which is similar to LIBs. Finally, the whole temperature characteristics of the NIBs in the range of $-60 $ ℃–1000 ℃ are summarized, which provide guidance for the safety design and applications of NIBs.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

Based on first-principles calculations and symmetry arguments, we reveal that the non-centrosymmetric ternary tetradymite BiSbTe$_{3}$ possesses exotic dual topological features of Weyl semimetallic phases with $Z_{2}$ index (1:000). The results show that the helical Dirac-type surface states protected by the time-reversal symmetry are present in the vicinity of the Brillouin zone center, which is consistent with the experimental report. Furthermore, we show that four pairs of Weyl points reside exactly at the Fermi level, which are guaranteed to be located on high-symmetry planes due to mirror symmetries. The helical surface states and the projected Weyl nodes are well separated in the momentum space, facilitating their observations in experiments. This work not only uncovers a unique quantum phenomenon with dual topological features in the tetradymite family but also paves a fascinating avenue for exploring the coexistence of multi-topological states with wide applications.

GdTe$_{3}$ is a layered antiferromagnetic (AFM) metal with charge density wave (CDW). We grew monolayer (ML) GdTe$_{3}$ on graphene/6H-SiC(0001) substrates by molecular beam epitaxy. The electronic and magnetic structures are studied by scanning tunneling microscopy/spectroscopy, quasi-particle interference (QPI) and first-principles calculations. Strong evidence of CDW persisting at the two-dimensional (2D) limit is found. Band dispersions and partially gapped energy bands near the Fermi surface are revealed by the QPI patterns. By density functional theory $+ U$ calculations, AFM order with stripe pattern is found to be the magnetic ground state for ML GdTe$_{3}$. These results provide fundamental understanding and pave the way for further investigation of GdTe$_{3}$ at the 2D limit.

The relationship between structural and electronic phase transitions in V$_2$O$_3$ thin films is of critical importance for understanding of the mechanism behind metal–insulator transition (MIT) and related technological applications. Despite being extensively studied, there are currently no clear consensus and picture of the relation between structural and electronic phase transitions so far. Using V$_2$O$_3$ thin films grown on $r$-plane Al$_2$O$_3$ substrates, which exhibit abrupt MIT and structural phase transition, we show that the electronic phase transition occurs concurrently with the structural phase transition as revealed by the electrical transport and Raman spectra measurements. Our result provides experimental evidence for clarifying this issue, which could form the basis of theoretical studies as well as technological applications in V$_2$O$_3$.

A $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ effective Hamiltonian is important for theoretical analysis in condensed matter physics. Based on the kdotp-symmetry package, we develop an upgraded package named as kdotp-generator. This generator takes in arbitrary magnetic symmetries with their representations and returns symmetry-allowed $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ Hamiltonians. Using this package, we calculate $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ Hamiltonians for irreducible co-representations in 1651 magnetic space groups up to the third order, and their linear coupling to external fields including the electromagnetic field and the strain tensor. We hope that the package will facilitate related research in the future.

In the band theory, first-principles calculations, the tight-binding method and the effective $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ model are usually employed to investigate electronic structures of condensed matters. The effective $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ model has a compact form with a clear physical picture, and first-principles calculations can give more accurate results. Nowadays, it has been widely recognized to combine the $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ model and first-principles calculations to explore topological materials. However, the traditional method to derive the $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ Hamiltonian is complicated and time-consuming by hand. We independently developed a programmable algorithm to construct effective $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ Hamiltonians for condensed matters. Symmetries and orbitals are used as the input information to produce the one-/two-/three-dimensional $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ Hamiltonian in our method, and the open-source code can be directly downloaded online. At last, we also demonstrated the application to MnBi$_2$Te$_4$-family magnetic topological materials.

Magnetic topological materials have attracted much attention due to the correlation between topology and magnetism. Recent studies suggest that EuCd$_2$As$_2$ is an antiferromagnetic topological material. Here by carrying out thorough magnetic, electrical and thermodynamic property measurements, we discover a long-time relaxation of the magnetic susceptibility in EuCd$_2$As$_2$. The (001) in-plane magnetic susceptibility at 5 K is found to continuously increase up to $\sim$10% over the time of $\sim$14 hours. The magnetic relaxation is anisotropic and strongly depends on the temperature and the applied magnetic field. These results will stimulate further theoretical and experimental studies to understand the origin of the relaxation process and its effect on the electronic structure and physical properties of the magnetic topological materials.

Ultra-thin topological insulators provide a platform for realizing many exotic phenomena such as the quantum spin Hall effect, and quantum anomalous Hall effect. These effects or states are characterized by quantized transport behavior of edge states. Experimentally, although these states have been realized in various systems, the temperature for the edge states to be the dominating channel in transport is extremely low, contrary to the fact that the bulk gap is usually in the order of a few tens of milli-electron volts. There must be other in-gap conduction channels that do not freeze out until a much lower temperature. Here we grow ultra-thin topological insulator Bi$_{2}$Te$_{3}$ and Sb$_{2}$Te$_{3}$ films by molecular beam epitaxy and investigate the structures of domain boundaries in these films. By scanning tunneling microscopy and spectroscopy we find that the domain boundaries with large rotation angles have pronounced in-gap bound states, through which one-dimensional conduction channels are suggested to form, as visualized by spatially resolved spectroscopy. Our work indicates the critical role played by domain boundaries in degrading the transport properties.

Topological superconductors (TSCs) have been widely investigated in recent years due to their novel physics and ability to host Majorana fermions (MFs) which are key to topological quantum computation. Despite the great interest, only a few compounds have been proposed as candidates of intrinsic TSCs, such as iron-based superconductor FeSe$_{0.55}$Te$_{0.45}$ and 2M-WS$_{2}$. Among them, quasi-one-dimensional superconductor TaSe$_{3}$ possesses fascinating properties such as its simple stoichiometry, layered nature and chemical stability. Here, using scanning tunneling microscope/spectroscopy (STM/STS), we systematically investigate the topography and electronic structure of TaSe$_{3}$. Our STM/STS measurement reveals large atomically flat, defect-free surfaces suitable for the search of MF; electronic density of states consistent with our angle-resolved photoemission result and band-structure calculations, and a uniform superconducting gap with a typical size of $\sim $0.25 meV. Remarkably, additional edge states are observed in the vicinity of the terrace edge, suggesting they may have a topological origin. Our result proves the coexistence of superconductivity and topological electronic structure in TaSe$_{3}$, making it an intriguing platform to investigate topological superconductivity.

We propose a new method to construct low-dimensional quantum devices consisting of the magnetic topological insulators. Unlike previous systems based on locally depleting two-dimensional electron gas in semiconductor heterojunctions, magnetization provides a simpler and rewriteable fabrication way. The motion of electrons can be manipulated through the domain wall formed by the boundary between different magnetic domains. Here, three devices designed by local magnetization are presented. For the quantum point contact, conductance exhibits quantized plateaus with the increasing silt width between two magnetic domains. For the quantum dot, conductance shows pronounced peaks as the change of gate voltage. Finally, for the Aharonov–Bohm ring, conductance oscillates periodically with the external magnetic field. Numerical results show that the transport of these local magnetization systems is identical to that of the previous systems based on depleting two-dimensional electron gas, and the only difference is the approach of construction. These findings may pave the way for realization of low-power-consumption devices based on magnetic domain walls.

We introduce a generalized Rashba coupling approximation to analytically solve confined two-dimensional electron systems with both the Rashba and Dresselhaus spin–orbit couplings in an external magnetic field. A solvable Hamiltonian is obtained by performing a simple change of basis, which has the same form as that with only Rashba coupling. Each Landau state becomes a new displaced-Fock state instead of the original Harmonic oscillator Fock state. Analytical energies are consistent with the numerical ones in a wide range of coupling strength even for a strong Zeeman splitting, exhibiting the validity of the analytical approximation. By using the eigenstates, spin polarization correctly displays a jump at the energy-level crossing point, where the corresponding spin conductance exhibits a pronounced resonant peak. As the component of the Dresselhaus coupling increases, the resonant point shifts to a smaller value of the magnetic field. In contrast to pure Rashba couplings, we find that the Dresselhaus coupling and Zeeman splittings tend to suppress the resonant spin Hall effect. Our method provides an easy-to-implement analytical treatment to two-dimensional electron gas systems with both types of spin–orbit couplings by applying a magnetic field.

We report an implementation of the momentum space quantum Monte Carlo (QMC) method on the interaction model for the twisted bilayer graphene (TBG). The long-range Coulomb repulsion is treated exactly with the flat bands, spin and valley degrees of freedom of electrons taking into account. We prove the absence of the minus sign problem for QMC simulation when either the two valleys or the two spin degrees of freedom are considered. By taking the realistic parameters of the twist angle and interlayer tunnelings into the simulation, we benchmark the QMC data with the exact band gap obtained at the chiral limit, to reveal the insulating ground states at the charge neutrality point (CNP). Then, with the exact Green's functions from QMC, we perform stochastic analytic continuation to obtain the first set of single-particle spectral function for the TBG model at CNP. Our momentum space QMC scheme therefore offers the controlled computation pathway for systematic investigation of the electronic states in realistic TBG model at various electron fillings.

The recent observation of superconductivity in thin films of infinite-layer nickelate Nd$ _{0.8}$Sr$ _{0.2}$NiO$ _{2}$ has received considerable attention. Despite the many efforts to understand the superconductivity in infinite-layer nickelates, a consensus on the underlying mechanism for the superconductivity has yet to be reached, partly owing to the challenges with the material synthesis. Here, we report the successful growth of superconducting infinite-layer Nd$ _{0.8}$Sr$ _{0.2}$NiO$ _{2}$ films by pulsed laser deposition and soft chemical reduction. The details on the growth process are discussed.

We report $^{121/123}$Sb nuclear quadrupole resonance (NQR) and $^{51}$V nuclear magnetic resonance (NMR) measurements on kagome metal CsV$_3$Sb$_5$ with $T_{\rm c}=2.5$ K. Both $^{51}$V NMR spectra and $^{121/123}$Sb NQR spectra split after a charge density wave (CDW) transition, which demonstrates a commensurate CDW state. The coexistence of the high temperature phase and the CDW phase between $91$ K and $94$ K manifests that it is a first-order phase transition. At low temperature, electric-field-gradient fluctuations diminish and magnetic fluctuations become dominant. Superconductivity emerges in the charge order state. Knight shift decreases and $1/T_{1}T$ shows a Hebel–Slichter coherence peak just below $T_{\rm c}$, indicating that CsV$_3$Sb$_5$ is an s-wave superconductor.

The coupling between electric ordering and magnetic ordering in two-dimensional (2D) materials is important for both fundamental research of 2D multiferroics and future development of magnetism-based information storage and operation. Here, we introduce a scheme for realizing a magnetic phase transition through the transition of electric ordering. We take CuMoP$_{2}$S$_{6}$ monolayer as an example, which is a member of the large 2D transition-metal chalcogen-phosphates family. Based on first-principles calculations, we find that it is a multiferroic with unprecedented characters, namely, it exhibits two different phases: an antiferroelectric-antiferromagnetic phase and a ferroelectric-ferromagnetic phase, in which the electric and magnetic orderings are strongly coupled. Importantly, the electric polarization is out-of-plane, so the magnetism can be readily switched by using the gate electric field. Our finding reveals a series of 2D multiferroics with special magnetoelectric coupling, which hold great promise for experimental realization and practical applications.