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The recent observation of superconductivity in the vicinity of insulating or Fermi surface reconstructed metallic states has established twisted bilayers of WSe$_2$ as an exciting platform to study the interplay of strong electron-electron interactions, broken symmetries and topology. In this work, we study the emergence of electronic ordering in twisted WSe$_2$ driven by gate-screened Coulomb interactions. Our first-principles treatment begins by constructing moir\'e Wannier orbitals that faithfully capture the bandstructure and topology of the system and project the gate-screened Coulomb interaction onto them. Using unbiased functional renormalization group calculations, we find an interplay between intervalley-coherent antiferromagnetic order and chiral, mixed-parity $d/p$-wave superconductivity for carrier concentrations near the displacement field-tunable van-Hove singularity. Our microscopic approach establishes incommensurate intervalley-coherent antiferromagnetic spin fluctuations as the dominant electronic mechanism driving the formation of superconductivity in $\theta = 5.08^{\circ}$ twisted WSe$_2$ and demonstrates that nesting properties of the Fermi surface sheets near the higher-order van-Hove point cause an asymmetric density dependence of the spin ordering as the density is varied across the van-Hove line, in good agreement with experimental observations. We show how the region of superconducting and magnetic order evolves within the two-dimensional phase space of displacement field and electronic density as twist angle is varied between $4^{\circ} \dots 5^{\circ}$., Comment: 11 pages, 6 figures

Graphene, renowned for its exceptional electronic and optical properties as a robust 2D material, traditionally lacks electronic correlation effects. Proximity coupling offers a promising method to endow quantum materials with novel properties. In this study, we achieve such a proximity coupling by intercalating Sn between the buffer layer of graphene on SiC(0001), allowing us to explore the coupling between a correlated 2D electron gas and a Dirac metal. This results in the stabilization of Sn-$\sqrt{3}$ superlattice structures at the interface, which reveal Mott-Hubbard bands, in excellent agreement with both experimental observations and theoretical predictions. Additionally, we found signatures of quasiparticle peaks close to the Fermi energy, in detail depending on the hybridization strength and doping level.

The recent discovery of superconductivity in La$_3$Ni$_2$O$_7$ with $T_\mathrm{c} \simeq 80~\mathrm{K}$ under high pressure opens up a new route to high-$T_\mathrm{c}$ superconductivity. This material realizes a bilayer square lattice model featuring a strong interlayer hybridization unlike many unconventional superconductors. A key question in this regard concerns how electronic correlations driven by the interlayer hybridization affect the low-energy electronic structure and the concomitant superconductivity. Here, we demonstrate using a cluster dynamical mean-field theory that the interlayer electronic correlations (IECs) induce a Lifshitz transition resulting in a change of Fermi surface topology. By solving an appropriate gap equation, we further show that the leading pairing instability, $s \pm$-wave, is enhanced by the IECs. The underlying mechanism is the quenching of a strong ferromagnetic channel, resulting from the Lifshitz transition driven by the IECs. Based on this picture, we provide a possible reason of why superconductivity emerges only under high pressure.

Mott-Hubbard and Hund electron correlations have been realized thus far in separate classes of materials. Here, we show that a single moir\'e homobilayer encompasses both kinds of physics in a controllable manner. We develop a microscopic multiband model that we solve by dynamical mean-field theory to nonperturbatively address the local many-body correlations. We demonstrate how tuning with twist angle, dielectric screening, and hole density allows us to switch between Mott-Hubbard and Hund correlated states in a twisted WSe$_2$ bilayer. The underlying mechanism is based on controlling Coulomb-interaction-driven orbital polarization and the energetics of concomitant local singlet and triplet spin configurations. From a comparison to recent experimental transport data, we find signatures of a filling-controlled transition from a triplet charge-transfer insulator to a Hund-Mott metal. Our finding establishes twisted transition metal dichalcogenides as a tunable platform for exotic phases of quantum matter emerging from large local spin moments.

We propose a way to identify strongly Hund-correlated materials by unveiling a key signature of Hund correlations at the two-particle level. The defining feature is the {\it sign} of the response of the {\it frozen spin ratio} (the long-time local spin-spin correlation function divided by the instantaneous value) under variation of electron density. The underlying physical reason is that the sign is closely related to the strength of charge fluctuations between the dominant atomic multiplets and higher-spin ones in a neighboring charge subspace. It is the predominance of these fluctuations that promotes Hund metallicity. The temperature dependence of the frozen spin ratio can further reveal a non-Fermi-liquid behavior and thus the Hund metal states. We analyze both degenerate and non-degenerate multiorbital Hubbard models and corroborate our argument by taking doped La$_2$CuO$_4$ and LaFeAsO as representative material examples, respectively, of Mott and Hund metals. Our proposal should be applicable to systems with non-half-filled integer electron fillings and their doped cases provided the doping drove the electron density toward the half filling.

Magnetism in two-dimensional (2D) van der Waals (vdW) materials has lately attracted considerable attention from the point of view of both fundamental science and device applications. Obviously, establishing the detailed and solid understanding of their magnetism is the key first step toward various applications. Although $\mathrm{Fe_3GeTe_2}$ is a representative ferromagnetic (FM) metal in this family, many aspects of its magnetic and electronic behaviors still remain elusive. Here, we report our new finding that $\mathrm{Fe_3GeTe_2}$ is a special type of correlated metal known as 'Hund metal'. Furthermore, we demonstrate that Hund metallicity in this material is quite unique by exhibiting remarkable site-dependence of Hund correlation strength, hereby dubbed 'site-differentiated Hund metal'. Within this new picture, many of previous experiments can be clearly understood including the ones that were seemingly contradictory to one another., Comment: 8 pages, 3 figures

Motivated by the recent discovery of superconductivity in infinite-layer nickelates RE$_{1-\delta}$Sr$_\delta$NiO$_2$ (RE$=$Nd, Pr), we study the role of Hund's coupling $J$ in a quarter-filled two-orbital Hubbard model which has been on the periphery of the attention. A region of negative effective Coulomb interaction of this model is revealed to be differentiated from three- and five-orbital models in their typical Hund's metal active fillings. We identify distinctive regimes including four different correlated metals, one of which stems from the proximity to a Mott insulator while the other three, which we call "intermediate" metal, weak Hund's metal, and valence-skipping metal, from the effect of $J$ being away from Mottness. Defining criteria characterizing these metals are suggested, establishing the existence of Hund's metallicity in two-orbital systems.

The recent and exciting discovery of superconductivity in the hole-doped infinite-layer nickelate Nd 1-{\delta} Sr {\delta} NiO 2 draws strong attention to correlated quantum materials. From a theoretical view point, this new class of unconventional superconducting materials provides an opportunity to unveil new physics in correlated quantum materials. Here we study the temperature and doping dependence of the local spectrum as well as the charge, spin and orbital susceptibilities from first principles. By using ab initio LQSGW+DMFT methodology, we show that onsite Hund's coupling in Ni-d orbitals gives rise to multiple signatures of Hund's metallic phase in Ni-eg orbitals. The proposed picture of the nickelates as an eg (two orbital) Hund's metal differs from the picture of the Fe-based superconductors as a five orbital Hund's metal as well as the picture of the cuprates as doped charge transfer insulators. Our finding unveils a new class of the Hunds metals and has potential implications for the broad range of correlated two orbital systems away from half-filling.

To understand the superconductivity recently discovered in Nd$_{0.8}$Sr$_{0.2}$NiO$_2$, we carried out LDA+DMFT (local density approximation plus dynamical mean-field theory) and magnetic force response calculations. The on-site correlation in Ni-$3d$ orbitals causes notable changes in the electronic structure. The calculated temperature-dependent susceptibility exhibits the Curie-Weiss behavior, indicating the localized character of its moment. From the low-frequency behavior of self-energy, we conclude that the undoped phase of this nickelate is Fermi-liquid-like contrary to cuprates. Interestingly, the estimated correlation strength by means of the inverse of quasiparticle weight is found to increase and then decrease as a function of hole concentration, forming a dome-like shape. Another finding is that magnetic interactions in this material become two-dimensional by hole doping. While the undoped NdNiO$_2$ has the sizable out-of-plane interaction, hole dopings strongly suppress it. This two-dimensionality is maximized at the hole concentration $\delta\approx0.25$. Further analysis as well as the implications of our findings are presented.

Multiorbital systems away from global half-filling host intriguing physical properties promoted by Hund's coupling. Despite increasing awareness of this regime dubbed Hund's metal, effect of nonlocal interaction is still elusive. Here we study a three-orbital model with $1/3$ filling (two electrons per site) including the intersite Coulomb interaction ($V$). Using the $GW$ plus extended dynamical mean-field theory, the valence-skipping charge order transition is shown to be driven by $V$. Most interestingly, the instability to this transition is significantly enhanced in the spin-freezing crossover regime, thereby lowering the critical $V$ to the formation of charge order. This behavior is found to be closely related to the population profile of the atomic multiplet states in the spin-freezing regime. In this regime, maximum spin states are dominant in each total charge subspace with substantial amount of one- and three-electron occupations, which leads to almost equal population of one- and the maximum spin three-electron state. Our finding unveils another feature of the Hund's metal, and has potential implications for the broad range of multiorbital systems as well as the recently discovered charge order in iron-pnictides.

To understand the magnetism of VSe$_2$, whose monolayer form has recently been reported to be a room temperature ferromagnet, Here, the combined method of conventional density functional theory with dynamical mean-field theory has been adopted. This higher-level computation method enables us to resolve many of existing controversies and contradictions in between theory and experiment. First of all, this new approach is shown to give the correct magnetic properties of both bulk and two-dimensional limit of VSe$_2$ which demonstrates its superiority to the conventional methods. The results demonstrate that monolayer VSe$_2$ without charge density waves is a ferromagnet with ordering temperature of 250K. From the direct simulation of temperature-dependent magnetic susceptibility and ordered moment, it is shown that its ferromagnetism is clearly two-dimensional in nature. Further, it is shown that this ferromagnetic order is vulnerable to extra charge dopings which provides the important insight to elucidate recent experimental controversies., Comment: 10 pages, 4 figures

To understand the magnetic properties of Fe$_3$GeTe$_2$, we performed the detailed first-principles study. Contrary to the conventional wisdom, it is unambiguously shown that Fe$_3$GeTe$_2$ is not ferromagnetic but antiferromagnetic carrying zero net moment in its stoichiometric phase. Fe defect and hole doping are the keys to make this material ferromagnetic, which are shown by the magnetic force response as well as the total energy calculation with the explicit Fe defects and the varied system charges. Further, we found that the electron doping also induces the antiferro- to ferromagnetic transition. It is a crucial factor to understand the notable recent experiment of gate-controlled ferromagnetism. Our results not only unveil the origin of ferromagnetism of this material but also show how it can be manipulated with defect and doping., Comment: 12 pages, 3 figures

Charge density functional plus $U$ calculations are carried out to examine the validity of molecular $J_\text{eff}$=1/2 and 3/2 state in lacunar spinel GaM$_4$X$_8$ (M = Nb, Mo, Ta, and W). With LDA (spin-unpolarized local density approximation)$+U$, which has recently been suggested as the more desirable choice than LSDA (local spin density approximation)$+U$, we examine the band structure in comparison with the previous prediction based on the spin-polarized version of functional and with the prototypical $J_\text{eff}$=1/2 material Sr$_2$IrO$_4$. It is found that the previously suggested $J_\text{eff}$=1/2 and 3/2 band characters remain valid still in LDA$+U$ calculations while the use of charge-only density causes some minor differences. Our result provides the further support for the novel molecular $J_\text{eff}$ state in this series of materials, which can hopefully motivate the future exploration toward its verification and the further search for new functionalities.

Understanding complex correlated oxides and their phase transitions has long been a challenge. The difficulty largely arises from the intriguing interplay between multiple degrees of freedoms. While degeneracy can play an important role in determining material characteristics, there is no well-defined way to quantify and to unveil its role in real materials having complicated band structures. Here we suggest a way to quantify the `effective degeneracy' relevant to metal-insulator transition by introducing entropy-like terms. This new quantity well describes the electronic behaviors of transition-metal oxides as a function of external and internal parameters. With $3d$ titanates, $4d$ ruthenates, and $5d$ iridates as our examples, we show that this new effective quantity provides useful insights to understand these systems and their phase transitions. For LaTiO$_3$/LaAlO$_3$ superlattice, we suggest a novel `degeneracy control' metal-insulator transition., Comment: First submitted (to other journal) on 13 Jul 2017. Eventually accepted in PRB

We performed the detailed microscopic analysis of the inter-layer magnetic couplings for bilayer CrI$_3$. As the first step toward understanding the recent experimental observations and utilizing them for device applications, we estimated magnetic force response as well as total energy. Various van der Waals functionals equivocally point to the ferromagnetic ground state for the low-temperature structured bilayer CrI$_3$ which is further confirmed independently by magnetic force response calculations. The calculated orbital-dependent magnetic forces clearly show that $e_g$-$t_{2g}$ interaction is the key to stabilize this ferromagnetic order. By suppressing this ferromagnetic interaction and enhancing antiferromagnetic orbital channels of $e_g$-$e_g$ and $t_{2g}$-$t_{2g}$, one can realize the desirable antiferromagnetic order. We showed that high-temperature monoclinic stacking can be the case. Our results provide unique information and insight to understand the magnetism of multi-layer CrI$_3$ paving the way to utilize it for applications., Comment: 15 pages, 3 figures, one-column

We perform charge density functional theory plus $U$ calculation of LaMnO$_3$. While all the previous calculations were based on spin density functionals, our result and analysis show that the use of spin-unpolarized charge-only density is crucial to correctly describe the phase diagram, electronic structure and magnetic property. Using magnetic force linear response calculation, a long-standing issue is clarified regarding the second neighbor out-of-plane interaction strength. We also estimate the orbital-resolved magnetic couplings. Remarkably, the inter-orbital $e_g$-$t_{2g}$ interaction is quite significant due to the Jahn-Teller distortion and orbital ordering., Comment: 7 pages, 4 figures, 1 table

We performed comparative analysis for DFT+$U$ functionals to better understand their applicability to non-collinear magnetism. Taking LiNiPO$_4$ and Sr$_2$IrO$_4$ as examples, we investigated the results out of two formalisms based on charge-only density and spin density functional plus $U$ calculations. Our results show that the ground state spin order in terms of tilting angle is strongly dependent on Hund $J$. In particular, the opposite behavior of canting angles as a function of $J$ is found for LiNiPO$_4$. The dependence on the other physical parameters such as Hubbard $U$ and Slater parameterization $F^4/F^2$ is investigated. We also discuss the formal aspects of these functional dependences as well as parameter dependences. The current study provides useful information and important intuition for the first-principles calculation of non-collinear magnetic materials.

A systematic comparative study has been performed to better understand DFT$+U$ (density functional theory + $U$) method. We examine the effect of choosing different double counting and exchange-correlation functionals. The calculated energy distribution and the Hund-$J$ dependence of potential profile for representative configurations clearly show the different behaviors of each DFT$+U$ formalism. In particular, adopting spin-dependent exchange-correlation functionals likely leads to undesirable magnetic solution. Our analyses are further highlighted by real material examples ranging from insulating oxides (MnO and NiO) to metallic magnetic systems (SrRuO$_3$ and BaFe$_2$As$_2$). The current work sheds new light on understanding DFT$+U$ and provides a guideline to use the related methods., Comment: Accepted for publication in Scientific Reports

A systematic first-principles study has been performed to understand the magnetism of thin film SrRuO$_3$ which lots of research efforts have been devoted to but no clear consensus has been reached about its ground state properties. The relative t$_{2g}$ level difference, lattice distortion as well as the layer thickness play together in determining the spin order. In particular, it is important to understand the difference between two standard approximations, namely LDA and GGA, in describing this metallic magnetism. Landau free energy analysis and the magnetization-energy-ratio plot clearly show the different tendency of favoring the magnetic moment formation, and it is magnified when applied to the thin film limit where the experimental information is severely limited. As a result, LDA gives a qualitatively different prediction from GGA in the experimentally relevant region of strain whereas both approximations give reasonable results for the bulk phase. We discuss the origin of this difference and the applicability of standard methods to the correlated oxide and the metallic magnetic systems., Comment: 5 figures. Accepted for publication in Scientific Reports