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Bilayer nickelate thin film superconductors discovered under ambient pressure enable vast possibilities for investigating electronic structures of the superconducting state. Here, we report angle-resolved photoemission spectroscopy (ARPES) measurements of heterointerfaces between 1, 2, and 3 unit-cell epitaxial La$_{2.85}$Pr$_{0.15}$Ni$_2$O$_7$ films and SrLaAlO$_4$ substates, through pure-oxygen in situ sample transportation. Evidence obtained using photons with distinct probing depths shows that conduction is localized primarily at the first unit cell near the interface. Scanning transmission electron microscopy (STEM), together with energy-dispersive X-ray spectroscopy (EDS) and electron energy loss spectroscopy (EELS), indicates that interfacial Sr diffusion and pronounced oxygen 2p hybridization gradient may collectively account for the interfacial confinement of conduction. Fermi surface maps reveal hole doping compared to non-superconducting ambient-pressure bulk crystals. Measurements of dispersive band structures suggest the contributions from both Ni $d_{x^2-y^2}$ and $d_{z^2}$ orbitals at the Fermi level. Density functional theory (DFT) + U calculations capture qualitative features of the ARPES results, consistent with a hole-doped scenario. These findings constrain theoretical models of the superconducting mechanism and suggest pathways for enhancing superconductivity in nickelates under ambient pressure., Comment: under review

The recent discovery of ambient-pressure superconductivity in thin-film bilayer nickelates opens new possibilities for investigating electronic structures in this new class of high-transition temperature $T_C$ superconductors. Here, we construct a realistic multi-orbital Hubbard model for the thin-film system, by integrating ab initio calculations with scanning transmission electron microscopy (STEM) measurements, which reveal a higher-symmetry lattice. The interaction parameters are calculated with the constrained random phase approximation (cRPA). Density functional theory (DFT) plus cluster dynamical mean-field theory (CDMFT) calculations, with cRPA calculated on-site Coulomb repulsive $U$ and experimentally measured electron filling $n$, quantitatively reproduces Fermi surfaces from angle-resolved photoemission spectroscopy (ARPES) experiments. The distinct Fermi surface topology from simple DFT+$U$ results features the indispensable role of correlation effects. Based upon the correlated electronic structures, A modified random-phase-approximation (RPA) approach yields a pronounced $s^{\pm}$-wave pairing instability, due to the strong spin fluctuations originated from Fermi surface nesting between bands with predominantly $d_{z^{2}}$ characters. Our findings highlight the quantitative effectiveness of the DFT+cRPA+CDMFT approach that precisely determines correlated electronic structure parameters without fine-tuning. The revealed intermediate correlation effect may explain the same order-of-magnitude onset $T_C$ observed both in pressured bulk and strained thin film bilayer nickelates., Comment: 4 figures and 3 tables in main manuscript. 9 figures and 2 tables in supplementary material

Analytic continuation is a critical step in quantum many-body computations, connecting imaginary-time or Matsubara Green's functions with real-frequency spectral functions, which can be directly compared to experimental results. However, due to the ill-posed nature of the analytic continuation problems, they have not been completely solved so far. In this paper, we suggest a simple, yet highly efficient method for analytic continuations of Matsubara Green's functions. This method takes advantage of barycentric rational functions to directly interpolate Matsubara Green's functions. At first, the nodes and weights of the barycentric rational functions are determined by the adaptive Antoulas-Anderson algorithm, avoiding reliance on the non-convex optimization. Next, the retarded Green's functions and the relatively spectral functions are evaluated by the resulting interpolants. We systematically explore the performance of this method through a series of toy models and realistic examples, comparing its accuracy and efficiency with other popular methods, such as the maximum entropy method. The benchmark results demonstrate that the new method can accurately reproduce not only continuous but also discrete spectral functions, irrespective of their positive definiteness. It works well even in the presence of intermediate noise, and outperforms traditional analytic continuation methods in computational speed. We believe that this method should stand out for its robustness against noise, broad applicability, high precision, and ultra efficiency, offering a promising alternative to the maximum entropy method., Comment: 18 pages, 16 figures, and 2 tables. The repository of source codes is https://github.com/huangli712/ACFlow

In designing material functionalities for transition metal oxides, lattice structure and d-orbital occupancy are key determinants. However, the modulation of these two factors is inherently limited by the need to balance thermodynamic stability, growth kinetics, and stoichiometry precision, particularly for metastable phases. We introduce a methodology, namely the gigantic-oxidative atomic-layer-by-layer epitaxy (GOALL-Epitaxy), enhancing oxidation power 3-4 orders of magnitude beyond conventional pulsed laser deposition (PLD) and oxide molecular beam epitaxy (OMBE), while ensuring atomic-layer-by-layer growth of designed complex structures. Thermodynamic stability is markedly augmented with stronger oxidation at elevated temperatures, whereas growth kinetics is sustained by laser ablation at lower temperatures. We demonstrate the accurate growth of complex nickelates and cuprates, especially an artificially designed structure with alternating single and double NiO2 layers possessing distinct nominal d-orbital occupancy, as a parent of high-temperature superconductor. The GOALL-Epitaxy enables material discovery within the vastly broadened growth parameter space.

Recently, above-room temperature superconductivity was reported in the Cu doped lead apatite Pb$_{10-x}$Cu$_x$(PO4)$_6$O, dubbed LK-99. By relaxing the structure with Cu substitution, we derive a four-band low-energy model with two 3/4 filled bands of predominantly Cu $d_{xz}$ and $d_{yz}$ character and two filled O $p_x$ and $p_y$ bands. This model is further downfolded to a two-band Cu-$d_{xz/yz}$ model. Using {\it ab-initio} derived interaction parameters, we perform dynamical mean field theory calculations to determine the correlated electronic structure in the normal state. These calculations yield a Mott insulator at $x=1$ and a strongly correlated non-Fermi liquid metal upon doping. The very large interaction versus bandwidth ratio $U/W\approx 30$-$50$ and the local moment paramagnetic behavior in the relevant filling regime are hard to reconcile with diamagnetism and high-temperature superconductivity. Hence, our calculations suggest that this behavior should come from a component with a different stoichiometry.

The alkali-doped fulleride Cs$_{3}$C$_{60}$, crystallized in the space group Fm$\overline 3$m or Pm$\overline 3$n, exhibits unconventional $s$-wave superconductivity under pressure with a maximum $T_c\sim 38$ K. Recently, a new primitive-cubic-structured Cs$_{3}$C$_{60}$ phase corresponding to the space group Pa$\overline 3$ has been reported (arXiv:2208.09429) and the authors observed superconductivity at ambient pressure. Using density-functional theory (DFT) calculations, we show that the proposed Pa$\overline 3$ structure is not stable under ionic relaxation, but transforms into the FCC structure. We study the normal and superconducting state of the stable FCC phase at different temperatures and volumes using DFT plus dynamical mean-field theory (DFT+DMFT) in the Nambu formalism. As temperature increases, the transition between superconductor and normal metal (Mott insulator) at small (big) volume is found to be second (first) order. The recently developed maximum entropy analytic continuation method for the anomalous-self-energy is used to study the momentum-resolved spectra and optical conductivity., Comment: 6 pages + 4 pages, 1 Table

Sr$_2$IrO$_4$ has attracted a lot of attention due to its structural and electronic similarities to La$_2$CuO$_4$ which is the parent compound of high-T$_c$ superconducting cuprates. It was proposed to be a strong spin-orbit coupled J$_{eff}$ = 1/2 Mott insulator, but the Mott nature of its insulating ground state and the origin of the gap have not been conclusively established. Here, we use ultrafast laser pulses to realize an insulator-metal transition in Sr$_2$IrO$_4$ and probe the resulting dynamics using time- and angle-resolved photoemission spectroscopy. We observe a closing of the gap and the formation of weakly-renormalized electronic bands in the gap region. Comparing these observations to the expected temperature and doping evolution of Mott gaps and Hubbard bands provides clear evidence that the insulating state does not originate from Mott correlations. We instead propose a correlated band insulator picture, where antiferromagnetic correlations play a key role in the opening of the gap. More broadly, our results demonstrate that energy-momentum resolved nonequilibrium dynamics can be used to clarify the nature of equilibrium states in correlated materials.

The anomalous self-energy plays an important role in the analysis of superconducting states. Its spectral weight provides information on the pairing glue of superconductors, but it can change in sign. In many numerical approaches, for example Monte Carlo methods based on the Nambu formalism, the anomalous self-energy is obtained on the Matsubara axis, and nonpositive spectral weight cannot be directly obtained using the standard maximum entropy analytic continuation method. Here, we introduce an auxiliary self-energy corresponding to a linear combination of the normal and anomalous self-energies. We analytically and numerically prove that this auxiliary function has non-negative spectral weight independent of the pairing symmetry, which allows to compute the sign-changing spectrum of the original self-energy using the maximum entropy approach. As an application, we calculate the momentum-resolved spectral function of K$_3$C$_{60}$ in the superconducting state., Comment: 6+3 pages

The quadratic band crossing points (QBCPs) at Fermi level in two-dimension have been proposed to be unstable under electron-electron interaction. The possible interaction driven states include quantum anomalous Hall (QAH) state and various nematic ordered states. In this work, motivated by the discovery of ferromagnetic van der Waals layered metal-organic framework CrCl$_2$(pyrazine)$_2$, we theoretically propose that the single layer of CrCl$_2$(pyrazine)$_2$ might realize one or some of these interaction driven states based on the QBCP protected by $C_4$ symmetry. By introducing the short-range density-density type repulsion interactions into this system, we have found the phase diagram depending on different interaction range and strength. The exotic phases include the staggered chiral flux state manifesting QAH effect, the site-nematic insulator and the site-nematic Dirac semimetal state. The QAH state is robust against perturbations breaking the QBCP but it is weakened by increasing temperature. The metal-organic framework is tunable by changing the transition-metal elements, which might improve the gap size and stability of this interaction induced QAH state.

Full or empty narrow bands near the Fermi level are known to enhance superconductivity by promoting scattering processes and spin fluctuations. Here, we demonstrate that doublon-holon fluctuations in systems with half-filled narrow bands can similarly boost the superconducting $T_c$. We study the half-filled attractive bilayer Hubbard model on the square lattice using dynamical mean-field theory. The band structure of the noninteracting system contains a wide band formed by bonding orbitals and a narrow band formed by antibonding orbitals, with bandwidths tunable by the inter-layer hopping. The shrinking of the narrow band can lead to a substantial increase in the superconducting order parameter and phase stiffness in the wide band. At the same time, the coupling to the wide band allows the narrow band to remain superconducting -- and to reach the largest order parameter -- in the flat band limit. We develop an anomalous worm sampling method to study superconductivity in the limit of vanishing effective hopping. By analyzing the histogram of the local eigenstates, we clarify how the interplay between different interaction terms in the bonding/antibonding basis promotes pair fluctuations and superconductivity., Comment: 7+12 pages, 4+7 figures

Rashba materials have appeared as an ideal playground for spin-to-charge conversion in prototype spintronics devices. Among them, $\alpha$-GeTe(111) is a non-centrosymmetric ferroelectric (FE) semiconductor for which a strong spin-orbit interaction gives rise to giant Rashba coupling. Its room temperature ferroelectricity was recently demonstrated as a route towards a new type of highly energy-efficient non-volatile memory device based on switchable polarization. Currently based on the application of an electric field, the writing and reading processes could be outperformed by the use of femtosecond (fs) light pulses requiring exploration of the possible control of ferroelectricity on this timescale. Here, we probe the room temperature transient dynamics of the electronic band structure of $\alpha$-GeTe(111) using time and angle-resolved photoemission spectroscopy (tr-ARPES). Our experiments reveal an ultrafast modulation of the Rashba coupling mediated on the fs timescale by a surface photovoltage (SPV), namely an increase corresponding to a 13 % enhancement of the lattice distortion. This opens the route for the control of the FE polarization in $\alpha$-GeTe(111) and FE semiconducting materials in quantum heterostructures., Comment: 31 pages, 12 figures

Bulk-boundary correspondence has achieved a great success in the identification of topological states. However, this elegant strategy doesn't apply to the Dirac semimetals (DSMs). Here, we propose that kagome lattices Pd$_3$Pb$_2$X$_2$ (X = S, Se) are unique type-I DSMs without surface Fermi arc states, which are different from the previous well-known DSMs, such as Na$_3$Bi and Cd$_3$As$_2$. Pd$_3$Pb$_2$X$_2$ are characterized by nontrivial topological invariant Z$_3$, guaranteeing a higher-order bulk-hinge correspondence and the existence of higher-order Fermi arcs, as well as fractional corner charges on the hinges. The type-I DSMs are located at the phase boundaries of several topological phases, including type-II DSMs and three-dimensional weak topological insulators. The phase transitions can be easily manipulated by external strain. Our results provide feasible platforms for the study of these unique DSMs and the related phase transitions., Comment: 15 pages, 10 figures and 4 tables

Based on the first-principles calculations within local density approximation and model analysis, we propose that the iso-structural compounds Cu2SnS3 and Cu2SnSe3 are both the simplest nodal line semimetals with only one nodal line in their crystal momentum space when spin-orbit coupling (SOC) is ignored. The including of SOC drives Cu2SnS3 into a Weyl semimetal (WSM) state with only two pairs of Weyl nodes, the minimum number required for WSM with time reversal symmetry. In contrast, SOC leads Cu2SnSe3 to strong topological insulator (TI) state. This difference can be well understood as there is a topological phase transition (TPT). In it, the Weyl nodes are driven by tunable SOC and annihilate in a mirror plane, resulting in a TI. This TPT, together with the evolution of Weyl nodes, the changing of mirror Chern numbers of mirror plane and the Z2 indices protected by time-reversal symmetry has been demonstrated by the calculation of Cu2SnS3-xSex within virtual crystal approximation and an effective k $\cdot$ p model analysis. Though our first-principles calculations have overestimated the topological states in both compounds, we believe that the theoretical demonstration of controlling TPT and evolution of Weyl nodes will stimulate further efforts in exploring them.

Recently, square-net materials have attracted lots of attention for the Dirac semimetal phase with negligible spin-orbit coupling (SOC) gap, e.g. ZrSiS/LaSbTe and CaMnSb$_2$. In this paper, we demonstrate that the Jahn-Teller effect enlarges the nontrivial SOC gap in the distorted structure, e.g. LaAsS and SrZnSb$_2$. Its distorted $X$ square-net layer ($X=$ P, As, Sb, Bi) resembles a quantum spin Hall (QSH) insulator. Since these QSH layers are simply stacked in the $\hat{x}$ direction and weakly coupled, three-dimensional QSH effect can be expected in these distorted materials, such as insulating compounds CeAs$_{1+x}$Se$_{1-y}$ and EuCdSb$_2$. Our detailed calculations show that it hosts two twisted nodal wires without SOC [each consists of two noncontractible time-reversal symmetry- and inversion symmetry-protected nodal lines touching at a fourfold degenerate point], while with SOC it becomes a topological crystalline insulator with symmetry indicators $(000; 2)$ and mirror Chern numbers $(0, 0)$. The nontrivial band topology is characterized by a generalized spin Chern number $C_{s+}=2$ when there is a gap between two sets of $\hat{s}_{x}$ eigenvalues. The nontrivial topology of these materials can be well reproduced by our tight-binding model and the calculated spin Hall conductivity is quantized to $\sigma^{x}_{yz} = (\frac{\hbar}{e})\frac{G_xe^2}{\pi h}$ with $G_x$ a reciprocal lattice vector.

Magnetic Weyl semimetal (WSM) is of great importance both for fundamental physics and potential applications due to its spontaneous magnetism, robust band topology, and enhanced Berry curvature. It possesses many unique quantum effects, including large intrinsic anomalous Hall effect, Fermi arcs, and chiral anomaly. In this work, using ab initio calculations, we propose that Ni doped pyrochlore Tl$_2$Nb$_2$O$_7$ is a magnetic WSM caused by exchange field splitting on bands around its quadratic band crossing point. The exchange field tuned by Ni 3d on-site Coulomb interaction parameter $U$ drives the evolution of Weyl nodes and the resulting topological phase transition. Since Weyl nodes can exist at generic point in Brillouin zone and are hard to be exactly identified, the creation and annihilation of them, i.e., the change in their number, chirality and distribution, have been consistently confirmed with a combined theoretical approach, which employs parity criterion, symmetry indicator analysis and the Wilson loop of Wannier center. We find that Weyl nodes remain in a quite large range of $U$ and are close to Fermi level, which makes the experimental observation very possible. We think this method and our proposal of magnetic WSM will be useful in finding more WSMs and adding our understanding on the topological phase transition.

The pairing mechanism in different classes of correlated materials, including iron based superconductors, is still under debate. For FeSe monolayers, uniform nematic fluctuations have been shown in a lattice Monte Carlo study to play a potentially important role. Here, using dynamical mean field theory calculations for the same model system, we obtain a similar phase diagram and provide an alternative interpretation of the superconductivity in terms of local orbital fluctuations and phase rigidity. Our study clarifies the relation between the superconducting order parameter, superfluid stiffness and orbital fluctuations, and provides a link between the spin/orbital freezing theory of unconventional superconductivity and theoretical works considering the role of nematic fluctuations., Comment: 11 pages, 7 figures

Thin films provide a versatile platform to tune electron correlations and explore new physics in strongly correlated materials. Epitaxially grown thin films of the alkali-doped fulleride K$_{3+x}$C$_{60}$, for example, exhibit %various intriguing phenomena, including Mott transitions and superconductivity, depending on dimensionality and doping. Surprisingly, in the trilayer case, a strong electron-hole doping asymmetry has been observed in the superconducting phase, which is absent in the three-dimensional bulk limit. Using density-functional theory plus dynamical mean-field theory, we show that this doping asymmetry results from a substantial charge reshuffling from the top layer to the middle layer. While the nominal filling per fullerene is close to $n=3$, the top layer rapidly switches to an $n=2$ insulating state upon hole doping, which \textcolor{black}{implies a} doping asymmetry of the superconducting gap. The interlayer charge transfer and layer-selective metal-insulator transition result from the interplay between crystal field splittings, strong Coulomb interactions, and an effectively negative Hund coupling. This peculiar charge reshuffling is absent in the monolayer system, which is an $n=3$ Mott insulator, as expected from the nominal filling., Comment: 5+3 pages, 4+3 figures

The pairing mechanism in A$_3$C$_{60}$ is investigated by studying the properties of a three-orbital Hubbard model with antiferromagnetic Hund coupling in the normal and superconducting phase. Local orbital fluctuations are shown to be substantially enhanced in the superconducting state, with a fluctuation energy scale that matches the low-energy peak in the spectral weight of the order parameter. Our results demonstrate that local orbital fluctuations provide the pairing glue in strongly correlated fulleride superconductors and support the spin/orbital freezing theory of unconventional superconductivity. They are also consistent with the experimentally observed universal relation between the gap energy and local susceptibility in a broad range of unconventional superconductors., Comment: 5+3 pages, 5+7 figures

An antiferromagnetic Hund coupling in multiorbital Hubbard systems induces orbital freezing and an associated superconducting instability, as well as unique composite orders in the case of an odd number of orbitals. While the rich phase diagram of the half-filled three-orbital model has recently been explored in detail, the properties of the doped system remain to be clarified. Here, we complement the previous studies by computing the entropy of the half-filled model, which exhibits an increase in the orbital-frozen region, and a suppression in the composite ordered phase. The doping dependent phase diagram shows that the composite ordered state can be stabilized in the doped Mott regime, if conventional electronic orders are suppressed by frustration. While antiferro orbital order dominates the filling range $2\lesssim n \le 3$, and ferro orbital order the strongly interacting region for $1\lesssim n < 2$, we find superconductivity with a remarkably high $T_c$ around $n=1.5$ (quarter filling). Also in the doped system, there is a close connection between the orbital freezing crossover and superconductivity., Comment: 10 pages, 10 figures

The Hund coupling in multiorbital Hubbard systems induces spin freezing and associated Hund metal behavior. Using dynamical mean field theory, we explore the effect of local moment formation, spin and charge excitations on the entropy and specific heat of the three-orbital model. In particular, we demonstrate a substantial enhancement of the entropy in the spin-frozen metal phase at low temperatures, and peaks in the specific heat associated with the activation of spin and charge fluctuations at high temperature. We also clarify how these temperature scales depend on the interaction parameters and filling., Comment: 19 pages, 11 figures

Based on first-principles calculations and symmetry-based indicator analysis, we find a class of topological crystalline insulators (TCIs) with $C_2$ rotation anomaly in a family of Zintl compounds, including $\mathrm{Ba}_{3}\mathrm{Cd}_{2}\mathrm{As}_{4}$, $\mathrm{Ba}_{3}\mathrm{Zn}_{2}\mathrm{As}_{4}$ and $\mathrm{Ba}_{3}\mathrm{Cd}_{2}\mathrm{Sb}_{4}$. The nontrivial band topology protected by coexistence of $C_2$ rotation symmetry and time-reversal symmetry $T$ leads to two surface Dirac cones at generic momenta on both top and bottom surfaces perpendicular to the rotation axis. In addition, ($d-2$)-dimensional helical hinge states are also protected along the hinge formed by two side surfaces parallel with the rotation axis. We develop a method based on Wilson loop technique to prove the existence of these surface Dirac cones due to $C_2$ anomaly and precisely locate them as demonstrated in studying these TCIs. The helical hinge states are also calculated. Finally, we show that external strain can be used to tune topological phase transitions among TCIs, strong Z$_2$ topological insulators and trivial insulators., Comment: 10 pages, 10 figures

A universal mechanism to generate chiral hinge states in the ferromagnetic axion insulator phase is proposed, which leads to an exotic transport phenomena, the quantum anomalous Hall effect (QAHE) on some particular surfaces determined by both the crystalline symmetry and the magnetization direction. A realistic material system Sm doped $\text{Bi}_2\text{Se}_3$ is then proposed to realize such exotic hinge states by combing the first principle calculations and the Green's function techniques. A physically accessible way to manipulate the surface QAHE is also proposed, which makes it very different from the QAHE in ordinary 2D systems., Comment: 8 pages, 5 figures

Predicting a new Dirac semimetal (DSM), as well as other topological materials, is quite challenging, since the relationship between crystal structure, composing atoms and the band topology is complex and elusive. Here, we demonstrate an approach to design DSMs via exploring the chemical degree of freedom. Based on the understanding of the well-known DSM Na$_3$Bi, three compounds in one family, namely Na$_2$MgSn, Na$_2$MgPb and Na$_2$CdSn, have been exactly located. Further hybrid-functional calculations with improved estimation of band inversion show that two of them, Na$_2$MgPb and Na$_2$CdSn, have band topology of DSMs. The nontrivial surface states with Fermi arcs on the (010) and (100) side surfaces are shown to connect the projection of bulk Dirac nodes. Most importantly, the candidate compounds are dynamically stable and have been experimentally synthesized. The ideas in this work would stimulate more designs on locating topological materials based on the understanding of existing ones., Comment: 14 pages, 4 figures

Recently published discoveries of acoustic and optical mode inversion in the phonon spectrum of certain metals became the first realistic example of non-interacting topological bosonic excitations in existing materials. However, the observable physical and technological use of such topological phonon phases remained unclear. In this work we provide a strong theoretical and numerical evidence that for a class of metallic compounds (known as triple point topological metals), the points in the phonon spectrum, at which three (two optical and one acoustic) phonon modes (bands) cross, represent a well-defined topological material phase, in which the hosting metals have very strong thermoelectric response. The triple point bosonic collective excitations appearing due to these topological phonon band-crossing points significantly suppress the lattice thermal conductivity, making such metals phonon-glass like. At the same time, the topological triple-point and Weyl fermionic quasiparticle excitations present in these metals yield good electrical transport (electron-crystal) and cause a local enhancement in the electronic density of states near the Fermi level, which considerably improves the thermopower. This combination of "phonon-glass" and "electron-crystal" is the key for high thermoelectric performance in metals. We call these materials topological thermoelectric metals and propose several newly predicted compounds for this phase (TaSb and TaBi). We hope that this work will lead researchers in physics and materials science to the detailed study of topological phonon phases in electronic materials, and the possibility of these phases to introduce novel and more efficient use of thermoelectric materials in many everyday technological applications.

In the present paper, we present an efficient continuous-time quantum Monte Carlo impurity solver with high acceptance rate at low temperature for multi-orbital quantum impurity models with general interaction. In this hybridization expansion impurity solver, the imaginary time evolution operator for the high energy multiplets, which decays very rapidly with the imaginary time, is approximated by a probability normalized $\delta$-function. As the result, the virtual charge fluctuations of $f^{n}\rightarrow f^{n\pm1}$ are well included on the same footing without applying Schrieffer-Wolff transformation explicitly. As benchmarks, our algorithm perfectly reproduces the results for both Coqblin-Schriffeer and Kondo lattice models obtained by CT-J method developed by Otsuki {\it et al}. Furthermore, it allows capturing low energy physics of heavy-fermion materials directly without fitting the exchange coupling $J$ in the Kondo model., Comment: 14 pages, 9 figures

Based on first-principles calculations and effective model analysis, a Dirac nodal-net semimetal state is recognized in AlB$_2$-type TiB$_2$ and ZrB$_2$ when spin-orbit coupling (SOC) is ignored. Taking TiB$_2$ as an example, there are several topological excitations in this nodal-net structure including triple point, nexus, and nodal link, which are protected by coexistence of spatial-inversion symmetry and time reversal symmetry. This nodal-net state is remarkably different from that of IrF$_4$, which requires sublattice chiral symmetry. In addition, linearly and quadratically dispersed two-dimensional surface Dirac points are identified as having emerged on the B-terminated and Ti-terminated (001) surfaces of TiB$_2$ respectively, which are analogous to those of monolayer and bilayer graphene., Comment: 12 pages, 13 figures, Corrected some citations

A new type of topological state in strongly corrected condensed matter systems, heavy Weyl fermion state, has been found in a heavy fermion material CeRu$_4$Sn$_6$, which has no inversion symmetry. Both two different types of Weyl points, type I and II, can be found in the quasi-particle band structure obtained by the LDA+Guztwiller calculations, which can treat the strong correlation effects among the f-electrons from Cerium atoms. The surface calculations indicate that the topologically protected Fermi arc states exist on the (010) but not on the (001) surfaces., Comment: 5 pages, 6 figures