We report the cumulative reaction probabilities (CRP) of the three-dimensional Cl+H₂ → H+HCl calculated on the Stern-Persky-Klein potential energy surface, using the generalized Newton variational principle, for total angular momentum J =0, over a total reaction energy range from 9 to 19 kcal/mol. The relation between CRP and reaction rate constants, as well as the calculation for complete reaction rates (summed over all J), bypassing the direct calculation of the CRP's for J>0, are also discussed.

Large longitudinal magnetoresistance (LMR) was observed in nonmagnetic silver telluride films. The magnitude of the LMR is not simply dependent on T and H, for example, multi-peaks of ρ at low field and low temperature appear in the Ag-Te film. Because both of -Δρ/ρ and a transition from -Δρ/ρ to +Δρ/ρ exist in Ag-Te films, the magnetoresistance (MR) behavior of the Ag-Te film does not like the bulk Ag-Te, but likes the doped semiconductors. About -27% of LMR was observed at low field in the Ag-Te films, while it could be negligible in the doped semiconductors. The MR behavior in Ag-Te films is discussed by means of a formation of impurity bands in the films.

Distribution of the parallel momentum of ²⁸Si fragments from the breakup of 30.7MeV/nucleon ²⁹P has been measured on C targets. The distribution has the FWHM with the value of 110.5±23.5MeV/c, which is quantitatively consistent with the Galuber model calculation assuming by a valence proton in ²⁹P. The density distribution is also predicted by the Skyrme--Hartree--Fock calculation. The results show that the proton-skin structure may exist in ²⁹P.

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.

The chiral $2\times 2$ charge order has been reported and confirmed in the kagome superconductor RbV$_{3}$Sb$_{5}$, while its interplay with superconductivity remains elusive owing to its lowest superconducting transition temperature $T_{\scriptscriptstyle{\rm C}}$ of about 0.85 K in the AV$_{3}$Sb$_{5}$ family (A = K, Rb, Cs) that severely challenges electronic spectroscopic probes. Here, utilizing dilution-refrigerator-based scanning tunneling microscopy down to 30 mK, we observe chiral $2\times 2$ pair density waves with residual Fermi arcs in RbV$_{3}$Sb$_{5}$. We find a superconducting gap of 150 µeV with substantial residual in-gap states. The spatial distribution of this gap exhibits chiral $2\times 2$ modulations, signaling a chiral pair density wave (PDW). Our quasi-particle interference imaging of the zero-energy residual states further reveals arc-like patterns. We discuss the relation of the gap modulations with the residual Fermi arcs under the space-momentum correspondence between PDW and Bogoliubov Fermi states.

Single-layer superconductors are ideal materials for fabricating superconducting nano devices. However, up to date, very few single-layer elemental superconductors have been predicted and especially no one has been successfully synthesized yet. Here, using crystal structure search techniques and ab initio calculations, we predict that a single-layer planar carbon sheet with 4- and 8-membered rings called T-graphene is a new intrinsic elemental superconductor with superconducting critical temperature ($T_{\rm c}$) up to around 20.8 K. More importantly, we propose a synthesis route to obtain such a single-layer T-graphene, that is, a T-graphene potassium intercalation compound (C$_4$K with $P4/mmm$ symmetry) is firstly synthesized at high pressure ($>$11.5 GPa) and then quenched to ambient condition; and finally, the single-layer T-graphene can be either exfoliated using the electrochemical method from the bulk C$_4$K, or peeled off from bulk T-graphite C$_4$, where C$_4$ can be obtained from C$_4$K by evaporating the K atoms. Interestingly, we find that the calculated $T_{\rm c}$ of C$_4$K is about 30.4 K at 0 GPa, which sets a new record for layered carbon-based superconductors. The present findings add a new class of carbon-based superconductors. In particular, once the single-layer T-graphene is synthesized, it can pave the way for fabricating superconducting devices together with other 2D materials using the layer-by-layer growth techniques.

Frustrated quantum magnets are expected to host many exotic quantum spin states like quantum spin liquid (QSL), and have attracted numerous interest in modern condensed matter physics. The discovery of the triangular lattice spin liquid candidate YbMgGaO$_4$ stimulated an increasing attention on the rare-earth-based frustrated magnets with strong spin-orbit coupling. Here we report the synthesis and characterization of a large family of rare-earth chalcogenides AReCh$_2$ (A = alkali or monovalent ions, Re = rare earth, Ch = O, S, Se). The family compounds share the same structure ($R\bar{3}m$) as YbMgGaO$_4$, and antiferromagnetically coupled rare-earth ions form perfect triangular layers that are well separated along the $c$-axis. Specific heat and magnetic susceptibility measurements on NaYbO$_2$, NaYbS$_2$ and NaYbSe$_2$ single crystals and polycrystals, reveal no structural or magnetic transition down to 50 mK. The family, having the simplest structure and chemical formula among the known QSL candidates, removes the issue on possible exchange disorders in YbMgGaO$_4$. More excitingly, the rich diversity of the family members allows tunable charge gaps, variable exchange coupling, and many other advantages. This makes the family an ideal platform for fundamental research of QSLs and its promising applications.

Transition metal dichalcogenides, featuring layered structures, have aroused enormous interest as a platform for novel physical phenomena and a wide range of potential applications. Among them, special interest has been placed upon WTe$_{2}$ and MoTe$_{2}$, which exhibit non-trivial topology both in single layer and bulk as well as pressure induced or enhanced superconductivity. We study another distorted 1T material NbTe$_{2}$ through systematic electrical transport measurements. Intrinsic superconductivity with onset transition temperature ($T_{\rm c}^{\rm onset}$) up to 0.72 K is detected where the upper critical field ($H_{\rm c}$) shows unconventional quasi-linear behavior, indicating spin-orbit coupling induced p-wave paring. Furthermore, a general model is proposed to fit the angle-dependent magnetoresistance, which reveals the Fermi surface anisotropy of NbTe$_{2}$. Finally, non-saturating linear magnetoresistance up to 50 T is observed and attributed to the quantum limit transport.

High-temperature superconductivity (HTSC) remains one of the most challenging and fascinating mysteries in condensed matter physics. Recently, superconductivity with transition temperature exceeding liquid-nitrogen temperature is discovered in La$_{3}$Ni$_{2}$O$_{7}$ at high pressure, which provides a new platform to explore the unconventional HTSC. In this work, using high-resolution angle-resolved photoemission spectroscopy and ab initio calculation, we systematically investigate the electronic structures of La$_{3}$Ni$_{2}$O$_{7}$ at ambient pressure. Our experiments are in nice agreement with ab initio calculations after considering an orbital-dependent band renormalization effect. The strong electron correlation effect pushes a flat band of $d_{z^{2}}$ orbital component below the Fermi level ($E_{\rm F}$), which is predicted to locate right at $E_{\rm F}$ under high pressure. Moreover, the $d_{x^{2}-y^{2}}$ band shows pseudogap-like behavior with suppressed spectral weight and diminished quasiparticle peak near $E_{\rm F}$. Our findings provide important insights into the electronic structure of La$_{3}$Ni$_{2}$O$_{7}$, which will shed light on understanding of the unconventional superconductivity in nickelates.

Orthogonal metal is a new quantum metallic state that conducts electricity but acquires no Fermi surface (FS) or quasiparticles, and hence orthogonal to the established paradigm of Landau's Fermi-liquid (FL). Such a state may hold the key of understanding the perplexing experimental observations of quantum metals that are beyond FL, i.e., dubbed non-Fermi-liquid (nFL), ranging from the Cu- and Fe-based oxides, heavy fermion compounds to the recently discovered twisted graphene heterostructures. However, to fully understand such an exotic state of matter, at least theoretically, one would like to construct a lattice model and to solve it with unbiased quantum many-body machinery. Here we achieve this goal by designing a 2D lattice model comprised of fermionic and bosonic matter fields coupled with dynamic $\mathbb{Z}_2$ gauge fields, and obtain its exact properties with sign-free quantum Monte Carlo simulations. We find that as the bosonic matter fields become disordered, with the help of deconfinement of the $\mathbb{Z}_2$ gauge fields, the system reacts with changing its nature from the conventional normal metal with an FS to an orthogonal metal of nFL without FS and quasiparticles and yet still responds to magnetic probe like an FL. Such a quantum phase transition from a normal metal to an orthogonal metal, with its electronic and magnetic spectral properties revealed, is calling for the establishment of new paradigm of quantum metals and their transition with conventional ones.

High resolution laser-based angle-resolved photoemission measurements are carried out on an overdoped superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ with a $T_{\rm c}$ of 75 K. Two Fermi surface sheets caused by bilayer splitting are clearly identified with rather different doping levels: the bonding sheet corresponds to a doping level of 0.14, which is slightly underdoped while the antibonding sheet has a doping of 0.27 that is heavily overdoped, giving an overall doping level of 0.20 for the sample. Different superconducting gap sizes on the two Fermi surface sheets are revealed. The superconducting gap on the antibonding Fermi surface sheet follows a standard d-wave form while it deviates from the standard d-wave form for the bonding Fermi surface sheet. The maximum gap difference between the two Fermi surface sheets near the antinodal region is $\sim$2 meV. These observations provide important information for studying the relationship between the Fermi surface topology and superconductivity, and the layer-dependent superconductivity in high temperature cuprate superconductors.

The parent compounds of the high-temperature cuprate superconductors are Mott insulators. It has been generally agreed that understanding the physics of the doped Mott insulators is essential to understanding the mechanism of high temperature superconductivity. A natural starting point is to elucidate the basic electronic structure of the parent compound. Here we report comprehensive high resolution angle-resolved photoemission measurements on Ca$_2$CuO$_2$Cl$_2$, a Mott insulator and a prototypical parent compound of the cuprates. Multiple underlying Fermi surface sheets are revealed for the first time. The high energy waterfall-like band dispersions exhibit different behaviors near the nodal and antinodal regions. Two distinct energy scales are identified: a d-wave-like low energy peak dispersion and a nearly isotropic lower Hubbard band gap. These observations provide new information of the electronic structure of the cuprate parent compound, which is important for understanding the anomalous physical properties and superconductivity mechanism of the high temperature cuprate superconductors.

We report high-resolution scanning tunneling microscopy (STM) study of nano-sized Pb islands grown on SrTiO$_{3}$, where three distinct types of gaps with different energy scales are revealed. At low temperature, we find that the superconducting gap (${\it\Delta}_{\rm s}$) in nano-sized Pb islands is significantly enhanced from the one in bulk Pb, while there is no essential change in superconducting transition temperature $T_{\rm c}$, giving rise to a larger BCS ratio 2${\it\Delta}_{\rm s}/k_{_{\rm B}}T_{\rm c} \sim 8.31$ and implying stronger electron-phonon coupling. The stronger coupling can originate from the interface electron-phonon interactions between Pb islands and SrTiO$_{3}$. As the superconducting gap is totally suppressed under applied magnetic field, the Coulomb gap with apparent V-shape emerges. Moreover, the size of Coulomb gap (${\it\Delta}_{\rm C}$) depends on the lateral size of Pb islands ($R$) with ${\it\Delta}_{\rm C}\sim 1/R^{0.35}$, indicating that quantum size effect can significantly influence electronic correlations. Our experimental results shall shed important light on the interplay among superconductivity, quantum size effect and correlations in nano-sized strong-coupling superconductors.

In this paper the coherent and the squeezed state of the bose field is written as a universal form by means of a projector which transforms the old vacuum state to the new vacuum state. The transformed vacuum state is the coherent state or the squeed state. Our result is equivalent to the original definations.

High-order quantum coherence reveals the statistical correlation of quantum particles. Manipulation of quantum coherence of light in the temporal domain enables the production of the single-photon source, which has become one of the most important quantum resources. High-order quantum coherence in the spatial domain plays a crucial role in a variety of applications, such as quantum imaging, holography, and microscopy. However, the active control of second-order spatial quantum coherence remains a challenging task. Here we predict theoretically and demonstrate experimentally the first active manipulation of second-order spatial quantum coherence, which exhibits the capability of switching between bunching and anti-bunching, by mapping the entanglement of spatially structured photons. We also show that signal processing based on quantum coherence exhibits robust resistance to intensity disturbance. Our findings not only enhance existing applications but also pave the way for broader utilization of higher-order spatial quantum coherence.

Devices of electric double-layer transistors (EDLTs) with ionic liquid have been employed as an effective way to dope carriers over a wide range. However, the induced electronic states can hardly survive in the materials after releasing the gate voltage $V_{\rm G}$ at temperatures higher than the melting point of the selected ionic liquid. Here we show that a permanent superconductivity with transition temperature $T_{\rm c}$ of 24 and 15 K is realized in single crystals and polycrystalline samples of HfNCl and ZrNCl upon applying proper $V_{\rm G}$'s at different temperatures. Reversible change between insulating and superconducting states can be obtained by applying positive and negative $V_{\rm G}$ at low temperature such as 220 K, whereas $V_{\rm G}$'s applied at 250 K induce the irreversible superconducting transition. The upper critical field $H_{\rm c2}$ of the superconducting states obtained at different gating temperatures shows similar temperature dependence. We propose a reasonable scenario that partial vacancy of Cl ions could be caused by applying proper $V_{\rm G}$'s at slightly higher processing temperatures, which consequently results in a permanent electron doping in the system. Such a technique shows great potential to systematically tune the bulk electronic state in the similar two-dimensional systems.

Layer-structured oxides Y_1−xBi_xBaCo₄O₇(0.00 ≤ x ≤ 0.05) were successfully synthesized and their structural and oxygen absorption properties were investigated by x−ray diffraction and thermogravimetry. Though Bi solubility was limited to about 5%, corresponding to Y_0.95Bi_0.05BaCo₄O₇, it is found that the structure and oxygen absorption properties of Y_1−xBi_xBaCo₄O₇ are affected significantly as the Bi content x increases. Rietveld refinement results show that Y_1−xBi_xBaCo₄O₇(x ≤ 0.05) is single phase with a hexagonal crystal structure (space group P6₃mc). Unit cell parameters and volume are changed and CoO₄ tetrahedra are distorted along the c−axis in Bi doped YBaCo₄O₇. The TG results show that Y_1−xBi_xBaCo₄O₇ undergoes two oxygen absorption processes in oxygen from room temperature to 1000°C and the maximum mass increase of the doped samples is less than that of YBaCo₄O₇. Bi doping effects on the structure and oxygen absorption properties are discussed on the basis of average radius and disorder of the Y site, the valence of Bi and the oxygen activation energy.

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.

We investigate in underdoped cuprates possible coexistence of the superconducting order at zero momentum and pair density wave (PDW) at momentum ${\boldsymbol Q}=(\pi, \pi)$ in the presence of a Néel order. By symmetry, the d-wave uniform singlet pairing $dS_0$ can coexist with the d-wave triplet PDW $dT_{\boldsymbol Q}$, and the p-wave singlet PDW $pS_{\boldsymbol Q}$ can coexist with the p-wave uniform triplet $pT_0$. At half filling, we find that the novel $pS_{\boldsymbol Q}+pT_0$ state is energetically more favorable than the $dS_0+dT_{\boldsymbol Q}$ state. At finite doping, however, the $dS_0+dT_{\boldsymbol Q}$ state is more favorable. In both types of states, the variational triplet parameters $dT_{\boldsymbol Q}$ and $pT_0$ are of secondary significance. Our results point to a fully symmetric $Z_2$ quantum spin liquid with spinon Fermi surface in proximity to the Néel order at zero doping, which may not be adiabatically connected to the d-wave singlet superconductivity at finite doping with intertwining d-wave triplet PDW fluctuations and spin moment fluctuations. The results are obtained by variational quantum Monte Carlo simulations.

Topological phase transition in a single material usually refers to transitions between a trivial band insulator and a topological Dirac phase, and the transition may also occur between different classes of topological Dirac phases. It is a fundamental challenge to realize quantum transition between $Z_{2}$ nontrivial topological insulator (TI) and topological crystalline insulator (TCI) in one material because $Z_{2}$ TI and TCI have different requirements on the number of band inversions. The $Z_{2}$ TIs must have an odd number of band inversions over all the time-reversal invariant momenta, whereas the newly discovered TCIs, as a distinct class of the topological Dirac materials protected by the underlying crystalline symmetry, owns an even number of band inversions. Taking PbSnTe$_{2}$ alloy as an example, here we demonstrate that the atomic-ordering is an effective way to tune the symmetry of the alloy so that we can electrically switch between TCI phase and $Z_{2}$ TI phase in a single material. Our results suggest that the atomic-ordering provides a new platform towards the realization of reversibly switching between different topological phases to explore novel applications.

The Majorana zero mode (MZM), which manifests as an exotic neutral excitation in superconductors, is the building block of topological quantum computing. It has recently been found in the vortices of several iron-based superconductors as a zero-bias conductance peak in tunneling spectroscopy. In particular, a clean and robust MZM has been observed in the cores of free vortices in (Li$_{0.84}$Fe$_{0.16}$)OHFeSe. Here using scanning tunneling spectroscopy, we demonstrate that Majorana-induced resonant Andreev reflection occurs between the STM tip and this zero-bias bound state, and consequently, the conductance at zero bias is quantized as $2e^{2}/h$. Our results present a hallmark signature of the MZM in the vortex of an intrinsic topological superconductor, together with its intriguing behavior.

The phenomenon of phase separation into antiferromagnetic (AFM) and superconducting (SC) or normal-state regions has great implication for the origin of high-temperature (high-$T_{\rm c}$) superconductivity. However, the occurrence of an intrinsic antiferromagnetism above the $T_{\rm c}$ of (Li,Fe)OHFeSe superconductor is questioned. Here we report a systematic study on a series of (Li,Fe)OHFeSe single crystal samples with $T_{\rm c}$ up to $\sim$41 K. We observe an evident drop in the static magnetization at $T_{\rm afm} \sim 125$ K, in some of the SC ($T_{\rm c} \lesssim 38$ K, cell parameter $c \lesssim 9.27$ Å) and non-SC samples. We verify that this AFM signal is intrinsic to (Li,Fe)OHFeSe. Thus, our observations indicate mesoscopic-to-macroscopic coexistence of an AFM state with the normal (below $T_{\rm afm}$) or SC (below $T_{\rm c}$) state in (Li,Fe)OHFeSe. We explain such coexistence by electronic phase separation, similar to that in high-$T_{\rm c}$ cuprates and iron arsenides. However, such an AFM signal can be absent in some other samples of (Li,Fe)OHFeSe, particularly it is never observed in the SC samples of $T_{\rm c} \gtrsim 38$ K, owing to a spatial scale of the phase separation too small for the macroscopic magnetic probe. For this case, we propose a microscopic electronic phase separation. The occurrence of two-dimensional AFM spin fluctuations below nearly the same temperature as $T_{\rm afm}$, reported previously for a (Li,Fe)OHFeSe ($T_{\rm c} \sim 42$ K) single crystal, suggests that the microscopic static phase separation reaches vanishing point in high-$T_{\rm c}$ (Li,Fe)OHFeSe. A complete phase diagram is thus established. Our study provides key information of the underlying physics for high-$T_{\rm c}$ superconductivity.

We propose a simple quantum voting machine using microwave photon qubit encoding, based on a setup comprising multiple microwave cavities and a coupled superconducting flux qutrit. This approach primarily relies on a multi-control single-target quantum phase gate. The scheme offers operational simplicity, requiring only a single step, while ensuring verifiability through the measurement of a single qubit phase information to obtain the voting results. It provides voter anonymity, as the voting outcome is solely tied to the total number of affirmative votes. Our quantum voting machine also has scalability in terms of the number of voters. Additionally, the physical realization of the quantum voting machine is general and not limited to circuit quantum electrodynamics. Quantum voting machine can be implemented as long as the multi-control single-phase quantum phase gate is realized in other physical systems. Numerical simulations indicate the feasibility of this quantum voting machine within the current quantum technology.

The outstanding issue to overcoming atmospheric turbulence on distant imaging is a fundamental interest and technological challenge. We propose a novel scenario and technique to restore the optical image in turbulent environmental by referring to Cyclopean image with binocular vision. With human visual intelligence, image distortion resulting from the turbulence is shown to be substantially suppressed. Numerical simulation results taking into account of the atmospheric turbulence, optical image system, image sensors, display and binocular vision perception are presented to demonstrate the robustness of the image restoration, which is compared with a single channel planar optical imaging and sensing. Experiment involving binocular telescope, image recording and the stereo-image display is conducted and good agreement is obtained between the simulation with perceptive experience. A natural extension of the scenario is to enhance the capability of anti-vibration or anti-shaking for general optical imaging with Cyclopean image.

While density functional theory (DFT) serves as a prevalent computational approach in electronic structure calculations, its computational demands and scalability limitations persist. Recently, leveraging neural networks to parameterize the Kohn–Sham DFT Hamiltonian has emerged as a promising avenue for accelerating electronic structure computations. Despite advancements, challenges such as the necessity for computing extensive DFT training data to explore each new system and the complexity of establishing accurate machine learning models for multi-elemental materials still exist. Addressing these hurdles, this study introduces a universal electronic Hamiltonian model trained on Hamiltonian matrices obtained from first-principles DFT calculations of nearly all crystal structures on the Materials Project. We demonstrate its generality in predicting electronic structures across the whole periodic table, including complex multi-elemental systems, solid-state electrolytes, Moiré twisted bilayer heterostructure, and metal-organic frameworks. Moreover, we utilize the universal model to conduct high-throughput calculations of electronic structures for crystals in GNoME datasets, identifying 3940 crystals with direct band gaps and 5109 crystals with flat bands. By offering a reliable efficient framework for computing electronic properties, this universal Hamiltonian model lays the groundwork for advancements in diverse fields, such as easily providing a huge data set of electronic structures and also making the materials design across the whole periodic table possible.

The search for quantum spin liquid (QSL) materials has attracted significant attention in the field of condensed matter physics in recent years, however so far only a handful of them are considered as candidates hosting QSL ground state. Owning to their geometrically frustrated structures, Kagome materials are ideal systems to realize QSL. We synthesize the kagome structured material claringbullite (Cu$_4$(OH)$_6$FCl) and then replace inter-layer Cu with Zn to form Cu$_3$Zn(OH)$_6$FCl. Comprehensive measurements reveal that doping Zn$^{2+}$ ions transforms magnetically ordered Cu$_4$(OH)$_6$FCl into a non-magnetic QSL candidate Cu$_3$Zn(OH)$_6$FCl. Therefore, the successful syntheses of Cu$_4$(OH)$_6$FCl and Cu$_3$Zn(OH)$_6$FCl provide not only a new platform for the study of QSL but also a novel pathway of investigating the transition between QSL and magnetically ordered systems.

We report a comprehensive high-pressure study on the monoclinic TlFeSe$_{2}$ single crystal, which is an antiferromagnetic insulator with quasi-one-dimensional crystal structure at ambient pressure. It is found that TlFeSe$_{2}$ undergoes a pressure-induced structural transformation from the monoclinic phase to an orthorhombic structure above $P_{\rm c} \approx 13$ GPa, accompanied with a large volume collapse of $\Delta V/V_{0}=8.3{\%}$. In the low-pressure monoclinic phase, the insulating state is easily metallized at pressures above 2 GPa; while possible superconductivity with $T_{\rm c}^{\rm onset} \sim 2$ K is found to emerge above 30 GPa in the high-pressure phase. Such a great tunability of TlFeSe$_{2}$ under pressure indicates that the ternary $A$FeSe$_{2}$ system ($A$ = Tl, K, Cs, Rb) should be taken as an important platform for explorations of interesting phenomena such as insulator-metal transition, dimensionality crossover, and superconductivity.

Quantum anomalous Hall (QAH) effect is a quantum Hall effect that occurs without the need of external magnetic field. A system composed of multiple parallel QAH layers is an effective high Chern number QAH insulator and the key to the applications of the dissipationless chiral edge channels in low energy consumption electronics. Such a QAH multilayer can also be engineered into other exotic topological phases such as a magnetic Weyl semimetal with only one pair of Weyl points. This work reports the first experimental realization of QAH multilayers in the superlattices composed of magnetically doped (Bi,Sb)$_{2}$Te$_{3}$ topological insulator and CdSe normal insulator layers grown by molecular beam epitaxy. The obtained multilayer samples show quantized Hall resistance $h/Ne^{2}$, where $h$ is Planck's constant, $e$ is the elementary charge and $N$ is the number of the magnetic topological insulator layers, resembling a high Chern number QAH insulator. The QAH multilayers provide an excellent platform to study various topological states of matter.

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.

Using the natural orbitals renormalization group (NORG) method, we investigate the screening of the local spin of an Anderson impurity interacting with the helical edge states in a quantum spin Hall insulator. It is found that there is a local spin formed at the impurity site and the local spin is completely screened by electrons in the quantum spin Hall insulator. Meanwhile, the local spin is screened dominantly by a single active natural orbital. We then show that the Kondo screening mechanism becomes transparent and simple in the framework of the natural orbitals formalism. We project the active natural orbital respectively into real space and momentum space to characterize its structure. We confirm the spin-momentum locking property of the edge states based on the occupancy of a Bloch state on the edge to which the impurity couples. Furthermore, we study the dynamical property of the active natural orbital represented by the local density of states, from which we observe the Kondo resonance peak.