One of the most important multipartite entangled states, Greenberger–Horne–Zeilinger state (GHZ), serves as a fundamental resource for quantum foundation test, quantum communication and quantum computation. To increase the number of entangled particles, significant experimental efforts should been invested due to the complexity of optical setup and the difficulty in maintaining the coherence condition for high-fidelity GHZ state. Here, we propose an ultra-integrated scalable on-chip GHZ state generation scheme based on frequency combs. By designing several microrings pumped by different lasers, multiple partially overlapped quantum frequency combs are generated to supply as the basis for on-chip polarization-encoded GHZ state with each qubit occupying a certain spectral mode. Both even and odd numbers of GHZ states can be engineered with constant small number of integrated components and easily scaled up on the same chip by only adjusting one of the pump wavelengths. In addition, we give the on-chip design of projection measurement for characterizing GHZ states and show the reconfigurability of the state. Our proposal is rather simple and feasible within the existing fabrication technologies and we believe it will boost the development of multiphoton technologies.

Plasmon-free surface-enhanced Raman scattering (SERS) substrates have attracted tremendous attention for their abundant sources, excellent chemical stability, superior biocompatibility, good signal uniformity, and unique selectivity to target molecules. Recently, researchers have made great progress in fabricating novel plasmon-free SERS substrates and exploring new enhancement strategies to improve their sensitivity. This review summarizes the recent developments of plasmon-free SERS substrates and specially focuses on the enhancement mechanisms and strategies. Furthermore, the promising applications of plasmon-free SERS substrates in biomedical diagnosis, metal ions and organic pollutants sensing, chemical and biochemical reactions monitoring, and photoelectric characterization are introduced. Finally, current challenges and future research opportunities in plasmon-free SERS substrates are briefly discussed.

Two-dimensional Janus van der Waals (vdW) heterojunctions, referring to the junction containing at least one Janus material, are found to exhibit tuneable electronic structures, wide light adsorption spectra, controllable contact resistance, and sufficient redox potential due to the intrinsic polarization and unique interlayer coupling. These novel structures and properties are promising for the potential applications in electronics and energy conversion devices. To provide a comprehensive picture about the research progress and guide the following investigations, here we summarize their fundamental properties of different types of two-dimensional Janus vdW heterostructures including electronic structure, interface contact and optical properties, and discuss the potential applications in electronics and energy conversion devices. The further challenges and possible research directions of the novel heterojunctions are discussed at the end of this review.

Laser-induced breakdown spectroscopy (LIBS) has been widely studied due to its unique advantages such as remote sensing, real-time multi-elemental detection and none-to-little damage. With the efforts of researchers around the world, LIBS has been developed by leaps and bounds. Moreover, in recent years, more and more Chinese LIBS researchers have put tremendous energy in promoting LIBS applications. It is worth mentioning that the application of LIBS in a specific field has its special application background and technical difficulties, therefore it may develop in different stages. A review summarizing the current development status of LIBS in various fields would be helpful for the development of LIBS technology as well as its applications especially for Chinese LIBS community since most of the researchers in this field work in application. In the present work, we summarized the research status and latest progress of main research groups in coal, metallurgy, and water, etc. Based on the current research status, the challenges and opportunities of LIBS were evaluated, and suggestions were made to further promote LIBS applications.

Copper indium thiophosphate, CuInP₂S₆, has attracted much attention in recent years due to its van der Waals layered structure and robust ferroelectricity at room temperature. In this review, we aim to give an overview of the various properties of CuInP₂S₆, covering structural, ferroelectric, dielectric, piezoelectric and transport properties, as well as its potential applications. We also highlight the remaining questions and possible research directions related to this fascinating material and other compounds of the same family.

Relatively large measurement uncertainty severely hindered wide application for laser-induced breakdown spectroscopy (LIBS), therefore it is of great importance to understand the mechanism of signal uncertainty generation, including initiation and propagation. It has been found that the fluctuation of plasma morphology was the main reason for signal uncertainty. However, it still remains unclear what mechanism leads to laser-induced plasma morphology fluctuation. In the present work, we employed three fast-imaging cameras to capture three successive plasma images from a same laser-induced Titanium alloy plasma, which enables us to understand more clearly of the plasma evolution process especially for the early plasma evolution stage when plasma and surrounding gases interact drastically. Seen from the images, the plasma experienced an increasing morphological fluctuation as delay time increased, transforming from a “stable plasma” before the delay time of 100 ns to a “fluctuating plasma” after the delay time of 300 ns. Notably, the frontier part of plasma showed a significant downward motion from the delay time of 150 ns to 200 ns and crashed with the lower part of the plasma, making the plasma flatter and later even splitting the plasma into two parts, which was considered as a critical process for the transformation of “stable plasma” to “unstable plasma”. By calculating the correlation coefficient of plasma image pairs at successive delay times, it was found that the higher the similarity between two plasma at early stage, the more similar at later stage; this implied that the tiny plasma fluctuation earlier than the critical delay time (150–200 ns) was amplified, causing a large plasma fluctuation at the later stage as well as LIBS measurement uncertainty. The initiation of slight fluctuation was linked with Rayleigh–Taylor Instability (RTI) due to the drastic material interpenetration at the plasma-ambient gas interface at earlier stage (before 50 ns). That is, the uncertainty generation of LIBS was proposed as: plasma morphology fluctuation was inevitably trigged by RTI at the early stage and the tiny fluctuation was amplified by the back pressed downward process of plasma frontier material, leading to severe morphology fluctuation as well as LIBS signal uncertainty.

We demonstrate experimentally the simultaneous generation and detection of two types of continuous variable nonclassical states from one type-0 phase-matching optical parametric amplification (OPA) and subsequent two ring filter cavities (RFCs). The output field of the OPA includes the baseband ω₀ and sideband modes ω₀±nω_fsubjects to the cavity resonance condition, which are separated by two cascaded RFCs. The first RFC resonates with half the pump wavelength ω₀ and the transmitted baseband component is a squeezed state. The reflected fields of the first RFC, including the sideband modes ω₀±ω_f, are separated by the second RFC, construct Einstein–Podolsky–Rosen entangled state. All freedoms, including the filter cavities for sideband separation and relative phases for the measurements of these sidebands, are actively stabilized. The noise variance of squeezed states is 10.2 dB below the shot noise limit (SNL), the correlation variances of both quadrature amplitude-sum and quadrature phase-difference for the entanglement state are 10.0 dB below the corresponding SNL.

In the past two decades, the revolutionary technologies of creating cold and ultracold molecules have provided cutting-edge experiments for studying the fundamental phenomena of collision physics. To a large degree, the recent explosion of interest in the molecular collisions has been sparked by dramatic progress of experimental capabilities and theoretical methods, which permit molecular collisions to be explored deep in the quantum mechanical limit. Tremendous experimental advances in the field have already been achieved, and the authors, from an experimental perspective, provide a review of these studies for exploring the nature of molecular collisions occurring at temperatures ranging from the Kelvin to the nanoKelvin regime, as well as for applications of producing ultracold molecules.

In view of wide applications of structured light fields and plasmonic vortices, we propose the concept of compound plasmonic vortex and design several structured plasmonic vortex generators. This kind of structured plasmonic vortex generators consists of multiple spiral nanoslits and they can generate two or more concentric plasmonic vortices. Different from Laguerre–Gaussian beam, the topological charge of the plasmonic vortex in different region is different. Theoretical analysis lays the basis for the design of radially structured plasmonic vortex generators and numerical simulations for several examples confirm the effectiveness of the design principle. The discussions about the interference of vortex fields definite the generation condition for the structured vortex. This work provides a design methodology for generating new vortices using spiral nanoslits and the advanced radially structured plasmonic vortices is helpful for broadening the applications of vortex fields.

Traditional simulation methods have made prominent progress in aiding experiments for understanding thermal transport properties of materials, and in predicting thermal conductivity of novel materials. However, huge challenges are also encountered when exploring complex material systems, such as formidable computational costs. As a rising computational method, machine learning has a lot to offer in this regard, not only in speeding up the searching and optimization process, but also in providing novel perspectives. In this work, we review the state-of-the-art studies on material’s thermal properties based on machine learning technique. First, the basic principles of machine learning method are introduced. We then review applications of machine learning technique in the prediction and optimization of material’s thermal properties, including thermal conductivity and interfacial thermal resistance. Finally, an outlook is provided for the future studies.

Van der Waals (vdW) heterobilayers formed by two-dimensional (2D) transition metal dichalcogenides (TMDCs) created a promising platform for various electronic and optical properties. ab initio band results indicate that the band offset of type-II band alignment in TMDCs vdW heterobilayer could be tuned by introducing Janus WSSe monolayer, instead of an external electric field. On the basis of symmetry analysis, the allowed interlayer hopping channels of TMDCs vdW heterobilayer were determined, and a four-level k·p model was developed to obtain the interlayer hopping. Results indicate that the interlayer coupling strength could be tuned by interlayer electric polarization featured by various band offsets. Moreover, the difference in the formation mechanism of interlayer valley excitons in different TMDCs vdW heterobilayers with various interlayer hopping strength was also clarified.

This brief review summarizes recent theoretical and experimental results which predict and establish the existence of quantum droplets (QDs), i.e., robust two- and three-dimensional (2D and 3D) selftrapped states in Bose–Einstein condensates (BECs), which are stabilized by effective self-repulsion induced by quantum fluctuations around the mean-field (MF) states [alias the Lee–Huang–Yang (LHY) effect]. The basic models are presented, taking special care of the dimension crossover, 2D→3D. Recently reported experimental results, which exhibit stable 3D and quasi-2D QDs in binary BECs, with the inter-component attraction slightly exceeding the MF self-repulsion in each component, and in single-component condensates of atoms carrying permanent magnetic moments, are presented in some detail. The summary of theoretical results is focused, chiefly, on 3D and quasi-2D QDs with embedded vorticity, as the possibility to stabilize such states is a remarkable prediction. Stable vortex states are presented both for QDs in free space, and for singular but physically relevant 2D modes pulled to the center by the inverse-square potential, with the quantum collapse suppressed by the LHY effect.

Explosive astrophysical transients at cosmological distances can be used to place precision tests of the basic assumptions of relativity theory, such as Lorentz invariance, the photon zero-mass hypothesis, and the weak equivalence principle (WEP). Signatures of Lorentz invariance violations (LIV) include vacuum dispersion and vacuum birefringence. Sensitive searches for LIV using astrophysical sources such as gamma-ray bursts, active galactic nuclei, and pulsars are discussed. The most direct consequence of a nonzero photon rest mass is a frequency dependence in the velocity of light propagating in vacuum. A detailed representation of how to obtain a combined severe limit on the photon mass using fast radio bursts at different redshifts through the dispersion method is presented. The accuracy of the WEP has been well tested based on the Shapiro time delay of astrophysical messengers traveling through a gravitational field. Some caveats of Shapiro delay tests are discussed. In this article, we review and update the status of astrophysical tests of fundamental physics.

The variability in multi-pulse gamma-ray bursts (GRBs) may help to reveal the mechanism of underlying processes from the central engine. To investigate whether the self-organized criticality (SOC) phenomena exist in the prompt phase of GRBs, we statistically study the properties of GRBs with more than 3 pulses in each burst by fitting the distributions of several observed physical variables with a Markov Chain Monte Carlo approach, including the isotropic energy E_iso, the duration time T, and the peak count rate P of each pulse. Our sample consists of 454 pulses in 93 GRBs observed by the CGRO/BATSE satellite. The best-fitting values and uncertainties for these power-law indices of the differential frequency distributions are: {\alpha }_E^d=1.54\pm 0.09, {\alpha }_T^d={1.82}_{-0.15}^{+0.14} and {\alpha }_P^d={2.09}_{-0.19}^{+0.18}, while the power-law indices in the cumulative frequency distributions are: {\alpha }_E^c={1.44}_{-0.10}^{+0.08}, {\alpha }_T^c={1.75}_{-0.13}^{+0.11} and {\alpha }_P^c={1.99}_{-0.19}^{+0.16}. We find that these distributions are roughly consistent with the physical framework of a Fractal-Diffusive, Self-Organized Criticality (FD-SOC) system with the spatial dimension S = 3 and the classical diffusion β=1. Our results support that the jet responsible for the GRBs should be magnetically dominated and magnetic instabilities (e.g., kink model, or tearing-model instability) lead the GRB emission region into the SOC state.

We study the stability of zero-vorticity and vortex lattice quantum droplets (LQDs), which are described by a two-dimensional (2D) Gross–Pitaevskii (GP) equation with a periodic potential and Lee– Huang–Yang (LHY) term. The LQDs are divided in two types: onsite-centered and offsite-centered LQDs, the centers of which are located at the minimum and the maximum of the potential, respectively. The stability areas of these two types of LQDs with different number of sites for zero-vorticity and vorticity with S = 1 are given. We found that the μ–N relationship of the stable LQDs with a fixed number of sites can violate the Vakhitov–Kolokolov (VK) criterion, which is a necessary stability condition for nonlinear modes with an attractive interaction. Moreover, the μ–N relationship shows that two types of vortex LQDs with the same number of sites are degenerated, while the zero-vorticity LQDs are not degenerated. It is worth mentioning that the offsite-centered LQDs with zero-vorticity and vortex LQDs with S = 1 are heterogeneous.

Alkaline-earth-like (AEL) atoms with two valence electrons and a nonzero nuclear spin can be excited to Rydberg state for quantum computing. Typical AEL ground states possess no hyperfine splitting, but unfortunately a GHz-scale splitting seems necessary for Rydberg excitation. Though strong magnetic fields can induce a GHz-scale splitting, weak fields are desirable to avoid noise in experiments. Here, we provide two solutions to this outstanding challenge with realistic data of well-studied AEL isotopes. In the first theory, the two nuclear spin qubit states |0〉 and |1〉 are excited to Rydberg states |r〉 with detuning Δ and 0, respectively, where a MHz-scale detuning Δ arises from a weak magnetic field on the order of 1 G. With a proper ratio between Δ and Ω, the qubit state |1〉 can be fully excited to the Rydberg state while |0〉 remains there. In the second theory, we show that by choosing appropriate intermediate states a two-photon Rydberg excitation can proceed with only one nuclear spin qubit state. The second theory is applicable whatever the magnitude of the magnetic field is. These theories bring a versatile means for quantum computation by combining the broad applicability of Rydberg blockade and the incomparable advantages of nuclear-spin quantum memory in two-electron neutral atoms.

Simulation of open quantum dynamics for various Hamiltonians and spectral densities are ubiquitous for studying various quantum systems. On a quantum computer, only log₂N qubits are required for the simulation of an N-dimensional quantum system, hence simulation in a quantum computer can greatly reduce the computational complexity compared with classical methods. Recently, a quantum simulation approach was proposed for studying photosynthetic light harvesting [npj Quantum Inf. 4, 52 (2018)]. In this paper, we apply the approach to simulate the open quantum dynamics of various photosynthetic systems. We show that for Drude–Lorentz spectral density, the dimerized geometries with strong couplings within the donor and acceptor clusters respectively exhibit significantly improved efficiency. We also demonstrate that the overall energy transfer can be optimized when the energy gap between the donor and acceptor clusters matches the optimum of the spectral density. The effects of different types of baths, e.g., Ohmic, sub-Ohmic, and super-Ohmic spectral densities are also studied. The present investigations demonstrate that the proposed approach is universal for simulating the exact quantum dynamics of photosynthetic systems.

The three lowest-lying \mathrm{\Upsilon } states, i.e., \mathrm{\Upsilon }(1S), \mathrm{\Upsilon }(2S), and \mathrm{\Upsilon }(3S), composed of bb¯ pairs and below the BB ¯ threshold, provide a good platform for the researches of hadronic physics and physics beyond the Standard Model. They can be produced directly in e⁺e⁻ colliding experiments, such as CLEO, Babar, and Belle, with low continuum backgrounds. In these experiments, many measurements of the exclusive \mathrm{\Upsilon }(1S) and \mathrm{\Upsilon }(2S) decays into light hadrons, which shed light on the “80% rule” for the Okubo–Zweig–Iizuka suppressed decays in the bottomonium sector, were carried out. Meanwhile, many studies of the charmonium and bottomonium productions in \mathrm{\Upsilon }(1S, 2S, 3S) decays were performed, to distinguish different Quantum Chromodynamics (QCD) models. Besides, exotic states and new physics were also extensively explored in \mathrm{\Upsilon }(1S, 2S, 3S) decays at CLEO, BaBar, and Belle. The \mathrm{\Upsilon }(1S, 2S, 3S) states can also be produced in pp collisions and in collisions involving heavy ions. The precision measurements of their cross sections and polarizations at the large hadron collider (LHC), especially in the CMS, ATLAS, and LHCb experiments, help to understandΥproduction mechanisms in pp collisions. The observation of the sequentialΥsuppression in heavy ion collisions at CMS, LHCb, and ALICE is of great importance for verifying the quark–gluon plasma predicted by QCD. In this article, we review the experimental results on \mathrm{\Upsilon }(1S, 2S, 3S) at e⁺e⁻ colliders and the LHC, and summarize their prospects at Belle II and the LHC.

MoS₂ is a promising candidate for hydrogen evolution reaction (HER), while its active sites are mainly distributed on the edge sites rather than the basal plane sites. Herein, a strategy to overcome the inertness of the MoS₂ basal surface and achieve high HER activity by combining single-boron catalyst and compressive strain was reported through density functional theory (DFT) computations. The ab initio molecular dynamics (AIMD) simulation on B@MoS₂ suggests high thermodynamic and kinetic stability. We found that the rather strong adsorption of hydrogen by B@MoS₂ can be alleviated by stress engineering. The optimal stress of −7% can achieve a nearly zero value of ΔG_H (~ −0.084 eV), which is close to that of the ideal Pt–SACs for HER. The novel HER activity is attributed to (i) the B– doping brings the active site to the basal plane of MoS₂ and reduces the band-gap, thereby increasing the conductivity; (ii) the compressive stress regulates the number of charge transfer between (H)–(B)–(MoS₂), weakening the adsorption energy of hydrogen on B@MoS₂. Moreover, we constructed a SiN/B@MoS₂ heterojunction, which introduces an 8.6% compressive stress for B@MoS₂ and yields an ideal ΔGH. This work provides an effective means to achieve high intrinsic HER activity for MoS₂.

A recent review [19] provides detailed information on the synthesis, optical properties, applications and potential development of all-inorganic metal halide nanostructured perovskites.

Carbon has three hybridization forms of sp⁻, sp²⁻ and sp³⁻, and the combination of different forms can obtain different kinds of carbon allotropes, such as diamond, carbon nanotubes, fullerene, graphynes (GYs) and graphdiyne (GDY). Among them, the GDY molecule is a single-layer two-dimensional (2D) planar structure material with highly π-conjugation formed by sp⁻ and sp²⁻ hybridization. GDY has a carbon atom ring composed of benzene ring and acetylene, which makes GDY have a uniformly distributed pore structure. In addition, GDY planar material have some slight wrinkles, which makes GDY have better self-stability than other 2D planar materials. The excellent properties of GDY make it attract the attention of researchers. Therefore, GDY is widely used in chemical catalysis, electronics, communications, clean energy and composite materials. This paper summarizes the recent progress of GDY research, including structure, preparation, properties and application of GDY in the field of catalysts.

Chemistry in the ultracold regime enables fully quantum-controlled interactions between atoms and molecules, leading to the discovery of the hidden mechanisms in chemical reactions which are usually curtained by thermal averaging in the high temperature. Recently a couple of diatomic molecules have been cooled to ultracold regime based on laser cooling techniques, but the chemistry associated with these simple molecules is highly limited. In comparison, free radicals play a major role in many important chemical reactions, but yet to be cooled to submillikelvin temperature. Here we propose a novel method of decelerating CH₃, the simplest polyatomic free radical, with lithium atoms simultaneously by travelling wave magnetic decelerator. This scheme paves the way towards co-trapping CH₃ and lithium, so that sympathetical cooling can be used to preparing ultracold free radical sample.

Low-dimensional all-inorganic metal halide perovskite (AIMHP) materials, as a new class of nanomaterials, hold great promise for various optoelectronic devices. In the past few years, tremendous progress has been achieved in the development of efficient and stable AIMHP nanomaterials for optical property studies and related applications. Here, we offer a critical overview on the unique merits and the state-of-the-art design of AIMHP using different composition strategies. Then, the effects of material compositions, dimensionality, morphologies and structures on optical properties are summarized. We also comprehensively present recent advances in the development AIMHP nanomaterials for practical applications including solar cells, light-emitting diodes, lasers and photodetectors. Lastly, the critical challenges and future opportunities in this emerging field are highlighted.

We extend the idea of laser cooling with adiabatic passage to multi-level type-II transitions. We find the cooling force can be significantly enhanced when a proper magnetic field is applied. That is because the magnetic field decomposes the multi-level system into several two-level sub-systems, hence the stimulated absorption and stimulated emission can occur in order, allowing for the multiple photon momentum transfer. We show that this scheme also works on the laser-coolable molecules with a better cooling effect compared to the conventional Doppler cooling. A reduced dependence on spontaneous emission based on our scheme is observed as well. Our results suggest this scheme is very feasible for laser cooling of polar molecules.

Carbon-rich materials are the key.

Pyrochlore magnets can be a unique platform to demonstrate numerous important concepts and applications of frustrated magnetic physics in modern condensed matter physics. Most works on pyrochlore magnets deal with the interacting spin-1/2 local moments, while much less works have studied the spin-1 systems. We here review the physics with interacting spin-1 local moments on the pyrochlore lattice to illustrate the potentially interesting physics associated with spin-1 magnets. The generic pyrochlore spin-1 model includes the antiferromagnetic Heisenberg interaction, the Dzyaloshinskii– Moriya interaction and the single-ion spin anisotropy. The global phase diagram of this generic spin model is reviewed, and the relation between different quantum phases in the phase diagram is clarified. The critical properties of the transition from the parent quantum paramagnet to the proximate orders are discussed. The presence of quantum order by disorder in the parts of the ordered phases is analyzed. The elementary excitations with respect to the ground states are further reviewed, and the topological natures of these excitations are carefully addressed. The materials’ relevance of the spin-1 pyrochlore magnets are finally reviewed. This review may provide insights about the interesting spin-1 local moments on frustrated systems.

Favourable band alignment and excellent visible light response are vital for photochemical water splitting. In this work, we have theoretically investigated how ferroelectric polarization and its reversibility in direction can be utilized to modulate the band alignment and optical absorption properties. For this objective, 2D van der Waals heterostructures (HTSs) are constructed by interfacing monolayer MoS₂ with ferroelectric In2Se3. We find the switch of polarization direction has dramatically changed the band alignment, thus facilitating different type of reactions. In In₂Se₃/MoS₂/In₂Se₃ heterostructures, one polarization direction supports hydrogen evolution reaction and another polarization direction can favour oxygen evolution reaction. These can be used to create tuneable photocatalyst materials where water reduction reactions can be selectively controlled by polarization switching. The modulation of band alignment is attributed to the shift of reaction potential caused by spontaneous polarization. Additionally, the formed type-II van der Waals HTSs also significantly improve charge separation and enhance the optical absorption in the visible and infrared regions. Our results pave a way in the design of van der Waals HTSs for water splitting using ferroelectric materials.

The interlayer bonding in two-dimensional (2D) materials is particularly important because it is not only related to their physical and chemical stability but also affects their mechanical, thermal, electronic, optical, and other properties. To address this issue, we report the direct characterization of the interlayer bonding in 2D SnSe using contact-resonance atomic force microscopy (CR-AFM) in this study. Site-specific CR spectroscopy and CR force spectroscopy measurements are performed on both SnSe and its supporting SiO₂/Si substrate comparatively. Based on the cantilever and contact mechanic models, the contact stiffness and vertical Young’s modulus are evaluated in comparison with SiO₂/Si as a reference material. The interlayer bonding of SnSe is further analyzed in combination with the semi-analytical model and density functional theory calculations. The direct characterization of interlayer interactions using this non-destructive methodology of CR-AFM would facilitate a better understanding of the physical and chemical properties of 2D layered materials, specifically for interlayer intercalation and vertical heterostructures.

The magnetic and electronic properties of strontium titanate with different carbon dopant configurations are explored using first-principles calculations with a generalized gradient approximation (GGA) and the GGA+U approach. Our results show that the structural stability, electronic properties and magnetic properties of C-doped SrTiO₃ strongly depend on the distance between carbon dopants. In both GGA and GGA+U calculations, the doping structure is mostly stable with a nonmagnetic feature when the carbon dopants are nearest neighbors, which can be ascribed to the formation of a C–C dimer pair accompanied by stronger C–C and weaker C–Ti hybridizations as the C–C distance becomes smaller. As the C–C distance increases, C-doped SrTiO₃ changes from an n-type nonmagnetic metal to ferromagnetic/antiferromagnetic half-metal and to an antiferromagnetic/ferromagnetic semiconductor in GGA calculations, while it changes from a nonmagnetic semiconductor to ferromagnetic half-metal and to an antiferromagnetic semiconductor using the GGA+U method. Our work demonstrates the possibility of tailoring the magnetic and electronic properties of C-doped SrTiO₃, which might provide some guidance to extend the applications of strontium titanate as a magnetic or optoelectronic material.