The first digit law, also known as Benford's law or the significant digit law, is an empirical phenomenon that the leading digit of numbers from real world sources favors small ones in a form $\log(1+{1}/{d})$, where $d=1, 2,\ldots, 9$. Such a law has been elusive for over 100 years because it has been obscure whether this law is due to the logical consequence of the number system or some mysterious mechanism of nature. We provide a simple and elegant proof of this law from the application of the Laplace transform, which is an important tool of mathematical methods in physics. It is revealed that the first digit law originates from the basic property of the number system, thus it should be attributed as a basic mathematical knowledge for wide applications.

Measurement-device-independent quantum key distribution (MDI-QKD) offers a practical way to realize a star-type quantum network. Previous experiments on MDI-QKD networks can only support the point-to-point communication. We experimentally demonstrate a plug-and-play MDI-QKD network which can support the point-to-multipoint communication among three users. Benefiting from the plug-and-play MDI-QKD architecture, the whole network is automatically stabilized in spectrum, polarization, arrival time, and phase reference. The users only need the encoding devices, which means that the hardware requirements are greatly reduced. Our experiment shows that it is feasible to establish a point-to-multipoint MDI-QKD network.

The realization of controllable couplings between any two qubits and among any multiple qubits is the critical problem in building a programmable quantum processor (PQP). We present a design to implement these types of couplings in a double-dot molecule system, where all the qubits are connected directly with capacitors and the couplings between them are controlled via the voltage on the double-dot molecules. A general interaction Hamiltonian of $n$ qubits is presented, from which we can derive the Hamiltonians for performing operations needed in building a PQP, such as gate operations between arbitrary two qubits and parallel coupling operations for multigroup qubits. The scheme is realizable with current technology.

Due to the obvious deviations of the existing theoretical models from the experimental results of ferroelectric phase transition, a new model is proposed on the basis of the coupling between spontaneous polarization and spontaneous strain in ferroelectrics. The spontaneous polarization and specific heat of ferroelectric phase transition predicted by the model are in better agreement with the corresponding data of triglyceride sulfate, a typical ferroelectric. In addition, the model predicts a new type of ferroelectric in which a phase transition and a phase-like transition coexist.

We demonstrate a simple scheme of 6.835 GHz microwave source based on the sub-sampling phase lock loop (PLL). A dielectric resonant oscillator of 6.8 GHz is directly phase locked to an ultra-low phase noise 100 MHz oven controlled crystal oscillator (OCXO) utilizing the sub-sampling PLL. Then the 6.8 GHz is mixed with 35 MHz from an direct digital synthesizer (DDS) which is also referenced to the 100 MHZ OCXO to generate the final 6.835 GHz signal. Benefiting from the sub-sampling PLL, the processes of frequency multiplication, which are usually necessary in the development of a microwave source, are greatly simplified. The architecture of the microwave source is pretty simple. Correspondingly, its power consumption and cost are low. The absolute phase noises of the 6.835 GHz output signal are $-$47 dBc/Hz, $-$77 dBc/Hz, $-$104 dBc/Hz and $-$121 dBc/Hz at 1 Hz, 10 Hz, 100 Hz and 1 kHz offset frequencies, respectively. The frequency stability limited by the phase noise through the Dick effect is theoretically estimated to be better than $5.0 \times 10^{-14}\tau^{1/2}$ when it is used as the local oscillator of the Rb atomic clocks. This low phase noise microwave source can also be used in other experiments of precision measurement physics.

We analyze the effect of electrode diameter and thickness on the mass sensitivity. Through the theoretical approximate calculation, we find that the mass sensitivity does not change monotonically with electrode diameter and there is a maximum point. The optimum electrode diameter corresponding to the maximum mass sensitivity varies with the electrode thickness. For a particular electrode diameter, a quartz crystal microbalance (QCM) with thick electrode has a higher mass sensitivity. A proper plating experiment using 35 QCMs with different electrode diameters and thicknesses verifies this finding. The present study further reveals how electrode size affects mass sensitivity and is helpful for QCM design.

We report the creation of the first mixture of $^6$Li and $^{88}$Sr atoms in an optical dipole trap. Using this mixture, a measurement of the interspecies thermalization process is carried out and the previously unknown interspecies s-wave scattering length between $^6$Li and $^{88}$Sr atoms is extracted to be $|a_{\rm ^6Li-^{88}Sr}|=(380^{+160}_{-100})a_0$ with $a_0$ being the Bohr radius from the rate of interspecies thermalization.

We obtain bi-component Coulomb crystals using laser-cooled $^{40}$Ca$^{+}$ ions to sympathetically cool $^{9}$Be$^{+}$ ions in a linear Paul trap. The shell structures of the bi-component Coulomb crystals are investigated. The secular motion frequencies of the two different ions are determined and compared with those in the single-component Coulomb crystals. In the radial direction, the resonant motion frequencies of the two ionic species shift toward each other due to the strong motion coupling in the ion trap. In the axial direction, the motion frequency of the laser-cooled $^{40}$Ca$^{+}$ is impervious to the sympathetically cooled $^{9}$Be$^{+}$ ions because the spatially separation of the two different ionic species leads to the weak motion coupling in the axial direction.

Spatial characteristics of Thomson scattering spectra are studied for an electron moving in the circularly polarized laser field in the presence of a strong uniform magnetic field. The results show that the angular distributions of the spectra with respect to the azimuthal and polar angles exhibit different symmetries, respectively, which depend on the fields and electron parameters sensitively and significantly. Moreover, for relatively large parameters such as high laser intensity, high magnetic resonance parameter as well as large initial momentum of electron, the two lobes in spectra tend to the laser-propagating direction so that the radiation can be collimated in the forward direction. Furthermore, an important finding is that by choosing the appropriate fields and initial momentum of electron, the high frequency part of the Thomson scattering spectra can reach the frequency range of soft x-ray, in which a high radiation power per solid angle as $\sim$$10^{11}$ a.u. can be obtained.

We demonstrate a Fe:ZnSe laser gain-switched by a 2.9 μm ZnGeP$_{2}$ optical parametric oscillator under pulse repetition frequency of 1 kHz at liquid nitrogen temperature of 77 K. The maximum output power is 63 mW with pulse duration of 34.4 ns. The wavelength covers 3686.6–4088.6 nm and centers at 3897.7 nm. The output power decreases with increasing the temperature of the crystal in 77–222 K.

We report the generation of heralded single photons with Gaussian-shape temporal waveforms through the spatial light modulation technique in an atomic ensemble. Both the full width at half maximum and the peak position of the Gaussian waveform can be controlled while the single photon nature holds well. We also analyze the bandwidth of the generated single photons in frequency domain and show how the sidebands of the frequency spectrum are modified by the shape of the temporal waveform. The generated single photons are especially suited for the realization of high efficiency quantum storage based on electromagnetically induced transparency.

Nanosecond pulse generation is demonstrated in a mode-locked erbium-doped fiber laser (EDFL) utilizing a samarium oxide (Sm$_{2}$O$_{3}$) film. The Sm$_{2}$O$_{3}$ film exhibits a modulation depth of 33%, which is suitable for mode-locking operation. The passively pulsed EDFL operates stably at 1569.8 nm within a pumping power from 109 to 146 mW. The train of generated output pulses has a pulse width of 356 nm repeated at a fundamental frequency of 0.97 MHz. The average output power of 3.91 mW is obtained at a pump power of 146 mW, corresponding to 4.0 nJ pulse energy. The experimental result indicates that the proposed Sm$_{2}$O$_{3}$ saturable absorber is viable for the construction of a flexible and reliably stable mode-locked pulsed fiber laser operating in the 1.5 μm region.

We propose and demonstrate a new approach for a high power pulse laser reflection sequence combination with a fast steering mirror (FSM). This approach possesses significant advantages for lasers combining with a variety of output power, wavelength, pulse duration, repetition rates and polarization. The maximum number of laser routes participating in combination principally depends on the FSM's adjustment time of the step response, lasers' repetition rates and pulse duration. A proof-of-principle experiment is performed with two 2-kW level pulsed beams. The results indicate that the combined beam has an excellent pointing stability with rms pointing jitter $\sim $8.5 $\mu$rad. Meanwhile, a high combining efficiency of 98.6% is achieved with maintaining good beam quality.

For an electron-electron collision with characteristic scale length larger than the relative gyro-radius of the two colliding electrons, when the initial relative parallel kinetic energy cannot surmount the Coulomb repulsive potential, reflection will occur with interchange of the parallel velocities of the two electrons after the collision. The Fokker–Planck approach is employed to derive the electron collision term $\mathcal{C}_{\rm R}$ describing parallel velocity scattering due to the reflections for a magnetized plasma where the average electron gyro-radius is much smaller than the Debye length but much larger than the Landau length. The electron parallel velocity friction and diffusion coefficients due to the reflections are evaluated, which are found not to depend on the electron perpendicular velocity. By studying the temporal evolution of the $H$ quantity due to $\mathcal{C}_{\rm R}$, it is found that $\mathcal{C}_{\rm R}$ eventually makes the system relax to a state in which the electron parallel velocity distribution is decoupled from the perpendicular velocity distribution.

Structural, electronic and magnetic properties of La-, Ce-, Pr-, Nd-, Pm-, Sm- and Eu-doped $\beta$-graphyne are investigated by comprehensive ab initio calculation based on density functional theory. The adsorption energies indicate that the dopings are suitable. The doped $\beta$-graphyne undergoes transition from semiconductor to metal. Furthermore, the doping of Nd, Pm, Sm and Eu atoms can induce magnetization. The results are useful for spintronics and the design of future electronic devices.

An intrinsic magnetic topological insulator (TI) is a stoichiometric magnetic compound possessing both inherent magnetic order and topological electronic states. Such a material can provide a shortcut to various novel topological quantum effects but remained elusive experimentally for a long time. Here we report the experimental realization of thin films of an intrinsic magnetic TI, MnBi$_{2}$Te$_{4}$, by alternate growth of a Bi$_{2}$Te$_{3}$ quintuple layer and a MnTe bilayer with molecular beam epitaxy. The material shows the archetypical Dirac surface states in angle-resolved photoemission spectroscopy and is demonstrated to be an antiferromagnetic topological insulator with ferromagnetic surfaces by magnetic and transport measurements as well as first-principles calculations. The unique magnetic and topological electronic structures and their interplays enable the material to embody rich quantum phases such as quantum anomalous Hall insulators and axion insulators at higher temperature and in a well-controlled way.

We report on magnetoresistance, Hall effect, and quantum Shubnikov–de Haas oscillation (SdH) experiments in NbIrTe$_4$ single crystals, which was recently predicted to be a type-II Weyl semimetal. NbIrTe$_4$ manifests a non-saturating and parabolic magnetoresistance at low temperatures. The magneto-transport measurements show that NbIrTe$_4$ is a multiband system. The analysis of the SdH oscillations reveals four distinct oscillation frequencies. Combined with the density-functional theory calculations, we show that they come from two types of Fermi surfaces: electron pocket E$_1$ and hole pocket H$_2$.

We report single crystal growth of CoSi, which has recently been recognized as a new type of topological semimetal hosting fourfold and sixfold degenerate nodes. The Shubnikov–de Haas quantum oscillation (QO) is observed on our crystals. There are two frequencies originating from almost isotropic bulk electron Fermi surfaces, in accordance with band structure calculations. The effective mass, scattering rate, and QO phase difference of the two frequencies are extracted and discussed.

The spin-polarized photocurrent is used to study the in-plane electric field dependent spin transport in undoped InGaAs/AlGaAs multiple quantum wells. In the temperature range of 77–297 K, the spin-polarized photocurrent shows an anisotropic spin transport under different oriented in-plane electric fields. We ascribe this characteristic to two dominant mechanisms: the hot phonon effect and the Rashba spin-orbit effect which is influenced by the in-plane electric fields with different orientations. The formulas are proposed to fit our experiments, suggesting a guide of potential applications and devices.

Electrical transport properties of bismuth vanadate (BiVO$_{4}$) are studied under high pressures with electrochemical impedance spectroscopy. A pressure-induced ionic-electronic transition is found in BiVO$_{4}$. Below 3.0 GPa, BiVO$_{4}$ has ionic conduction behavior. The ionic resistance decreases under high pressures due to the increasing migration rate of O$^{2-}$ ions. Above 3.0 GPa the channels for ion migration are closed. Transport mechanism changes from the ionic to the electronic behavior. First-principles calculations show that bandgap width narrows under high pressures, causing the continuous decrease of electrical resistance of BiVO$_{4}$.

We report protonation in several compounds by an ionic-liquid-gating method, under optimized gating conditions. This leads to single superconducting phases for several compounds. Non-volatility of protons allows post-gating magnetization and transport measurements. The superconducting transition temperature $T_{\rm c}$ is enhanced to 43.5 K for FeSe$_{0.93}$S$_{0.07}$, and 41 K for FeSe after protonation. Superconducting transitions with $T_{\rm c} \sim 15$ K for ZrNCl, $\sim$7.2 K for 1$T$-TaS$_2$, and $\sim$3.8 K for Bi$_2$Se$_3$ are induced after protonation. Electric transport in protonated FeSe$_{0.93}$S$_{0.07}$ confirms high-temperature superconductivity. Our $^{1}$H nuclear magnetic resonance (NMR) measurements on protonated FeSe$_{1-x}$S$_{x}$ reveal enhanced spin-lattice relaxation rate $1/^{1}T_1$ with increasing $x$, which is consistent with the LDA calculations that H$^{+}$ is located in the interstitial sites close to the anions.

FeTe, a non-superconducting parent compound in the iron-chalcogenide family, becomes superconducting after annealing in oxygen. Under the presence of magnetism, spin-orbit coupling, inhomogeneity and lattice distortion, the nature of its superconductivity is not well understood. Here we combine the mutual inductance technique with magneto transport to study the magnetization and superconductivity of FeTe thin films. It is found that the films with the highest $T_{\rm C}$ show non-saturating superfluid density and a strong magnetic hysteresis distinct from that in a homogeneous superconductor. Such a hysteresis can be well explained by a two-level critical state model and suggests the importance of granularity to superconductivity in this compound.

The recently synthesized first $4d$ transition-metal oxide-hydride LaSr$_{3}$NiRuO$_{4}$H$_{4}$ with the unusual high H:O ratio surprisingly displays no magnetic order down to 1.8 K. This is in sharp contrast to the similar unusual low-valent Ni$^{+}$-Ru$^{2+}$ layered oxide LaSrNiRuO$_{4}$ which has a rather high ferromagnetic (FM) ordering Curie temperature $T_{\rm C}\sim 250$ K. Using density functional calculations with the aid of crystal field level diagrams and superexchange pictures, we find that the contrasting magnetism is due to the distinct spin-orbital states of the Ru$^{2+}$ ions (in addition to the common Ni$^{+}$ $S=1/2$ state but with a different orbital state): the Ru$^{2+}$ $S=0$ state in LaSr$_{3}$NiRuO$_{4}$H$_{4}$, but the Ru$^{2+}$ $S=1$ state in LaSrNiRuO$_{4}$. The Ru$^{2+}$ $S=0$ state has the $(xy)^2(xz,yz)^4$ occupation due to the RuH$_4$O$_2$ octahedral coordination, and then the nonmagnetic Ru$^{2+}$ ions dilute the $S=1/2$ Ni$^+$ sublattice which consequently has a very weak antiferromagnetic superexchange and thus accounts for the presence of no magnetic order down to 1.8 K in LaSr$_{3}$NiRuO$_{4}$H$_{4}$. In strong contrast, the Ru$^{2+}$ $S=1$ state in LaSrNiRuO$_{4}$ has the $(3z^2-r^2)^2(xz,yz)^3(xy)^1$ occupation due to the planar square RuO$_4$ coordination, and then the multi-orbital FM superexchange between the $S=1/2$ Ni$^+$ and $S=1$ Ru$^{2+}$ ions gives rise to the high $T_{\rm C}$ in LaSrNiRuO$_{4}$. This work highlights the importance of spin-orbital states in determining the distinct magnetism.

An amorphous magnetic material system (Co$_{20}$Fe$_{47}$Ta$_{20}$B$_{13})_{1-x}$O$_{x}$ is fabricated by magneto sputtering. Three stages of magnetization behavior exist when oxygen content changes in the system. As the oxygen increases, the absence of percolation effect of magnetic nano-particles makes the multi-domain structure broken so that high coercivity appears in the samples with proper oxygen content. A temperature-dependent Stoner–Wohlfarth model is used to explain the magnetization properties at relatively high temperature. Magnetizations with magnetic field in and out of the sample plane are also investigated to prove the mechanisms. This work provides a systematic study of a new kind ofv amorphous magnetic system and is helpful for us to know more about this type of material.

MICAtronics, based on the functional oxide/mica heterostructures, has recently attracted much attention due to its potential applications in transparent, flexible electronics and devices. However, the weak van der Waals interaction decreases the tolerable lattice mismatch and thus limits the species of function oxides that are able to be epitaxially grown on mica. We successfully fabricate relatively high-quality epitaxial anatase TiO$_{2}$ thin films on mica substrates. Structural analyses reveal that the carefully chosen growth temperature (650$^\circ\!$C) and suitable crystalline phase (anatase phase) of TiO$_{2}$ are the key issues for this van der Waals epitaxy. Moreover, as a buffer layer, the TiO$_{2}$ layer successfully suppresses the decomposition of BiFeO$_{3}$ and the difficulty of epitaxial growth of BiFeO$_{3}$ is decreased. Therefore, relatively high-quality anatase TiO$_{2}$ is proved to be an effective buffer layer for fabricating more functional oxides on mica.

The mechanism for the self-assembly of hollow micelles from rod-coil diblock copolymers is proposed. In a coil-selective solvent, the diblock copolymers self-assemble into a layered structure. It is assumed that the rigid rods form an elastic shell whose properties are dictated by a bending energy. For a hollow micelle, the coils outside the micelle form a brush, while the coils inside the micelle can be in two different states, a brush or an adsorption layer, corresponding to symmetric or asymmetric configurations, respectively. The total energy density of a hollow micelle is calculated by combining the interfacial energy, elastic bending energy and the stretching energy of the brushes. For the asymmetric configuration with a polymer brush on one side, the competition between the elastic bending energy and the brush stretching energy leads to a finite spontaneous curvature, stabilizing hollow spherical micelles. Comparison of the free energy density for different geometries demonstrates that transitions for the different geometry micelles are controlled by the degree of polymerization of the coils and the length of the rods. These results are in agreement with the experimental results.

Plasma treatment is a powerful tool to tune the properties of two-dimensional materials. Previous studies have utilized various plasma treatments on two-dimensional materials. We find a new effect of plasma treatment. After controlled oxygen-plasma treatment on field-effect transistors based on two-dimensional SnSe$_{2}$, the capacitive coupling between the silicon back gate and the channel through the 300 nm SiO$_{2}$ dielectric can be dramatically enhanced by about two orders of magnitude (from 11 nF/cm$^{2}$ to 880 nF/cm$^{2}$), reaching good efficiency of ion-liquid gating. At the same time, plasma treated devices show large hysteresis in the gate sweep demonstrating memory behavior. We reveal that this spontaneous ion gating and hysteresis are achieved with the assistance of a thin layer of water film automatically formed on the sample surface with water molecules from the ambient air, due to the change in hydrophilicity of the plasma treated samples. The water film acts as the ion liquid to couple the back gate and the channel. Thanks to the rich carrier dynamics in plasma-treated two-dimensional transistors, synaptic functions are realized to demonstrate short- and long-term memories in a single device. This work provides a new perspective on the effects of plasma treatment and a facile route for realizing neuromorphic devices.