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We use the topological heavy fermion (THF) model and its Kondo Lattice (KL) formulation to study the symmetric Kondo state in twisted bilayer graphene. Via a large-N approximation, we find a symmetric Kondo (SK) state in KL mode at fillings $\nu=0,\pm 1,\pm 2$. In the SK state, all symmetries are preserved and the local moments are Kondo screened by the conduction electrons. At the mean-field level of the THF model at $\nu=0,\pm 1, \pm 2, \pm 3$, we also find a similar symmetric state. We study the stability of the symmetric state by comparing its energy with the ordered states and find the ordered states to have lower energy. However, moving away from integer fillings by doping holes to the light bands, we find the energy difference is reduced, which suggests the loss of ordering and a tendency towards Kondo screening. In order to include many-body effects beyond the mean-field approximation, we perform dynamical mean-field theory (DMFT) calculations on the THF model. We find the spin susceptibility follows a Curie behavior at $\nu=0, \pm 1,\pm 2$ down to $\sim 2\text{K}$ where the onset of screening of the local moment becomes visible. This hints to very low Kondo temperatures at these fillings, in agreement with the outcome of our mean-field calculations. At non-integer filling $\nu=\pm 0.5,\pm 0.8,\pm 1.2$ DMFT shows deviations from a $1/T$-susceptibility at much higher temperatures, suggesting a more effective screening of local moments with doping. Finally, we study the effect of a $C_{3z}$-rotational-symmetry-breaking strain via mean-field approaches and find that a symmetric phase (that only breaks $C_{3z}$ symmetry) can be stabilized at sufficiently large strain at $\nu=0,\pm 1, \pm 2$. Our results suggest that a symmetric Kondo phase is strongly suppressed at integer fillings, but could be stabilized either at non-integer fillings or by applying strain., Comment: 40 pages, 15 figures

Exotic ordered ground states driven by electronic correlations are expected to be induced in monolayer graphene when doped to the Van Hove singularity. Such doping levels are reached by intercalating Gd in graphene on SiC(0001), resulting in a strong homogeneity and stability. The electronic spectrum now exhibits severe renormalizations. Flat bands develop which is driven by electronic correlations according to our theoretical studies. Due to strong electron-phonon coupling in this regime, polaron replica bands develop. Thus, interesting ordered ground states should be made accessible.

Magic-angle twisted bilayer graphene (MA-tBLG) has appeared as a tunable testing ground to investigate the conspiracy of electronic interactions, band structure, and lattice degrees of freedom to yield exotic quantum many-body ground states in a two-dimensional Dirac material framework. While the impact of external parameters such as doping or magnetic field can be conveniently modified and analyzed, the all-surface nature of the quasi-2D electron gas combined with its intricate internal properties pose a challenging task to characterize the quintessential nature of the different insulating and superconducting states found in experiments. We analyze the interplay of internal screening and dielectric environment on the intrinsic electronic interaction profile of MA-tBLG. We find that interlayer coupling generically enhances the internal screening. The influence of the dielectric environment on the effective interaction strength depends decisively on the electronic state of MA-tBLG. Thus, we propose the experimental tailoring of the dielectric environment, e.g. by varying the capping layer composition and thickness, as a promising pursuit to provide further evidence for resolving the hidden nature of the quantum many-body states in MA-tBLG., Comment: 9 pages, 3 figures, supplemental material included (8 figures)

In contrast to the Hubbard model, the extended Hubbard model, which additionally accounts for non-local interactions, lacks systemic studies of thermodynamic properties especially across the metal-insulator transition. Using a variational principle, we perform such a systematic study and describe how non-local interactions screen local correlations differently in the Fermi-liquid and in the insulator. The thermodynamics reveal that non-local interactions are at least in parts responsible for first-order metal-insulator transitions in real materials., Comment: 19 pages, 9 figures. Resubmission to SciPost

Monolayers of transition metal dichalcogenides (TMDCs) exhibit an exceptionally strong Coulomb interaction between charge carriers due to the two-dimensional carrier confinement in connection with weak dielectric screening. High densities of excited charge carriers in the various band-structure valleys cause strong many-body renormalizations that influence both the electronic properties and the optical response of the material. We investigate electronic and optical properties of the typical monolayer TMDCs MoS$_2$, MoSe$_2$, WS$_2$ and WSe$_2$ in the presence of excited carriers by solving semiconductor Bloch equations on the full Brillouin zone. With increasing carrier density, we systematically find a reduction of the exciton binding energies due to Coulomb screening and Pauli blocking. Together with excitation-induced band-gap shrinkage this leads to redshifts of excitonic resonances up to the dissociation of excitons. As a central result, we predict for all investigated monolayer TMDCs that the $\Sigma$-valley shifts stronger than the K-valley. Two of the materials undergo a transition from direct to indirect band gaps under carrier excitation similar to well-known strain-induced effects. Our findings have strong implications for the filling of conduction-band valleys with excited carriers and are relevant to transport and optical applications as well as the emergence of phonon-driven superconductivity.

Using ab-initio calculations we reveal the nature of the insulating phase recently found experimentally in monolayer 1T-NbSe$_2$. We find soft phonon modes in a large parts of the Brillouin zone indicating the strong-coupling nature of a charge-density-wave instability. Structural relaxation of a $\sqrt{13}\times\sqrt{13}$ supercell reveals a Star-of-David reconstruction with an energy gain of 60 meV per primitive unit cell. The band structure of the distorted phase exhibits a half-filled flat band which is associated with orbitals that are delocalized over several atoms in each Star of David. By including many-body corrections through a combined GW, hybrid-functional, and DMFT treatment, we find the flat band to split into narrow Hubbard bands. The lowest energy excitation across the gap turns out to be between itinerant Se-$p$ states and the upper Hubbard band, determining the system to be a charge-transfer insulator. Combined hybrid-functional and GW calculations show that long-range interactions shift the Se-$p$ states to lower energies. Thus, a delicate interplay of local and long-range correlations determines the gap nature and its size in this distorted phase of the monolayer 1T-NbSe$_2$., Comment: 10 pages, 11 figures

Atomically thin layers of transition metal dichalcogenides (TMDCs) exhibit exceptionally strong Coulomb interaction between charge carriers due to the two-dimensional carrier confinement in connection with weak dielectric screening. The van der Waals nature of interlayer coupling makes it easy to integrate TMDC layers into heterostructures with different dielectric or metallic substrates. This allows to tailor electronic and optical properties of these materials, as Coulomb interaction inside atomically thin layers is very susceptible to screening by the environment. Here we theoretically investigate dynamical screening effects in TMDCs due to bulk substrates doped with carriers over a large density range, thereby offering three-dimensional plasmons as tunable degree of freedom. We report a wide compensation of renormalization effects leading to a spectrally more stable exciton than predicted for static substrate screening, even if plasmons and excitons are in resonance. We also find a nontrivial dependence of the single-particle band gap on substrate doping density due to dynamical screening. Our investigation provides microscopic insight into the mechanisms that allow for manipulations of TMDC excitons by means of arbitrary plasmonic environments on the nanoscale.

Plasmonic excitations behave fundamentally different in layered materials in comparison to bulk systems. They form gapless modes, which in turn couple at low energies to the electrons. Thereby they can strongly influence superconducting instabilities. Here, we show how these excitations can be controlled from the outside via changes in the dielectric environment or in the doping level, which allows for external tuning of the superconducting transition temperature. By solving the gap equation for an effective system, we find that the plasmonic influence can both strongly enhance or reduce the transition temperature, depending on the details of the plasmon-phonon interplay. We formulate simple experimental guidelines to find plasmon- induced elevated transition temperatures in layered materials., Comment: 13 pages, 10 figures

The electronic and optical properties of monolayer transition-metal dichalcogenides (TMDs) and van der Waals heterostructures are strongly subject to their dielectric environment. In each layer the field lines of the Coulomb interaction are screened by the adjacent material, which reduces the single-particle band gap as well as exciton and trion binding energies. By combining an electrostatic model for a dielectric hetero-multi-layered environment with semiconductor many-particle methods, we demonstrate that the electronic and optical properties are sensitive to the interlayer distances on the atomic scale. Spectroscopical measurements in combination with a direct solution of a three-particle Schr\"odinger equation reveal trion binding energies that correctly predict recently measured interlayer distances.

Nanostructures with open shell transition metal or molecular constituents host often strong electronic correlations and are highly sensitive to atomistic material details. This tutorial review discusses method developments and applications of theoretical approaches for the realistic description of the electronic and magnetic properties of nanostructures with correlated electrons. First, the implementation of a flexible interface between density functional theory and a variant of dynamical mean field theory (DMFT) highly suitable for the simulation of complex correlated structures is explained and illustrated. On the DMFT side, this interface is largely based on recent developments of quantum Monte Carlo and exact diagonalization techniques allowing for efficient descriptions of general four fermion Coulomb interactions, reduced symmetries and spin-orbit coupling, which are explained here. With the examples of the Cr (001) surfaces, magnetic adatoms, and molecular systems it is shown how the interplay of Hubbard U and Hund's J determines charge and spin fluctuations and how these interactions drive different sorts of correlation effects in nanosystems. Non-local interactions and correlations present a particular challenge for the theory of low dimensional systems. We present our method developments addressing these two challenges, i.e., advancements of the dynamical vertex approximation and a combination of the constrained random phase approximation with continuum medium theories. We demonstrate how non-local interaction and correlation phenomena are controlled not only by dimensionality but also by coupling to the environment which is typically important for determining the physics of nanosystems., Comment: tutorial review submitted to EPJ-ST (scientific report of research unit FOR 1346); 14 figures, 26 pages

The interplay of Coulomb and electron-phonon interactions with thermal and quantum fluctuations facilitates rich phase diagrams in two-dimensional electron systems. Layered transition metal dichalcogenides hosting charge, excitonic, spin and superconducting order form an epitomic material class in this respect. Theoretical studies of materials like NbS$_2$ have focused on the electron-phonon coupling whereas the Coulomb interaction, particularly strong in the monolayer limit, remained essentially untouched. Here, we analyze the interplay of short- and long-range Coulomb as well as electron-phonon interactions in NbS$_2$ monolayers. The combination of these interactions causes electronic correlations that are fundamentally different to what would be expected from the interaction terms separately. The fully interacting electronic spectral function resembles the non-interacting band structure but with appreciable broadening. An unexpected coexistence of strong charge and spin fluctuations puts NbS$_2$ close to spin and charge order, suggesting monolayer NbS$_2$ as a platform for atomic scale engineering of electronic quantum phases.

While the Hubbard model is the standard model to study Mott metal-insulator transitions, it is still unclear to which extent it can describe metal-insulator transitions in real solids, where non-local Coulomb interactions are always present. By using a variational principle, we clarify this issue for short- and long-ranged non-local Coulomb interactions for half-filled systems on bipartite lattices. We find that repulsive non-local interactions generally stabilize the Fermi-liquid regime. The metal-insulator phase boundary is shifted to larger interaction strengths to leading order linearly with non-local interactions. Importantly, non-local interactions can raise the order of the metal-insulator transition. We present a detailed analysis of how the dimension and geometry of the lattice as well as the temperature determine the critical non-local interaction leading to a first-order transition: for systems in more than two dimensions with non-zero density of states at the Fermi energy the critical non-local interaction is arbitrarily small; otherwise it is finite., Comment: 10 pages, 11 figures

The role of defects in van der Waals heterostructures made of graphene and hexagonal boron nitride (h-BN) is studied by a combination of ab initio and model calculations. Despite the weak van der Waals interaction between layers, defects residing in h-BN, such as carbon impurities and antisite defects, reveal a hybridization with graphene p$_{\rm z}$ states, leading to midgap state formation. The induced midgap states modify the transport properties of graphene and can be reproduced by means of a simple effective tight-binding model. In contrast to carbon defects, it is found that oxygen defects do not strongly hybridize with graphene's low-energy states. Instead, oxygen drastically modifies the band gap of graphene, which emerges in a commensurate stacking on h-BN lattices., Comment: 5 pages, 4 figures

We demonstrate how weak hybridization can lead to apparent heavy doping of 2d materials even in case of physisorptive binding. Combining ab-intio calculations and a generic model we show that strong reshaping of Fermi surfaces and changes in Fermi volumes on the order of several 10$\%$ can arise without actual charge transfer. This pseudodoping mechanism is very generically effective in metallic 2d materials either weakly absored to metallic substrates or embedded in vertical heterostructures. It can explain strong apparent doping of TaS2 on Au (111) observed in recent experiments. Consequences of pseudodoping for many-body instabilities are discussed., Comment: 5 pages, 2 figures

We investigate the Peierls-Feynman-Bogoliubov variational principle to map Hubbard models with nonlocal interactions to effective models with only local interactions. We study the renormalization of the local interaction induced by nearest-neighbor interaction and assess the quality of the effective Hubbard models in reproducing observables of the corresponding extended Hubbard models. We compare the renormalization of the local interactions as obtained from numerically exact determinant Quantum Monte Carlo to approximate but more generally applicable calculations using dual boson, dynamical mean field theory, and the random phase approximation. These more approximate approaches are crucial for any application with real materials in mind. Furthermore, we use the dual boson method to calculate observables of the extended Hubbard models directly and benchmark these against determinant Quantum Monte Carlo simulations of the effective Hubbard model., Comment: 12 pages, 10 figures

A quantitative description of Coulomb interactions is developed for two-dimensional superconducting materials, enabling us to compare intrinsic with external screening effects, such as those due to substrates. Using the example of a doped monolayer of MoS2 embedded in a tunable dielectric environment, we demonstrate that the influence of external screening is limited to a length scale, bounded from below by the effective thickness of the quasi-two-dimensional material and from above by its intrinsic screening length. As a consequence, it is found that unconventional Coulomb-driven superconductivity cannot be induced in MoS2 by tuning the substrate properties alone. Our calculations of the retarded Morel-Anderson Coulomb potential {\mu *} reveal that the Coulomb interactions, renormalized by the reduced layer thickness and the substrate properties, can shift the onset of the electron-phonon driven superconducting phase in monolayer MoS2 but do not significantly affect the critical temperature at optimal doping., Comment: 8 pages, 5 figures

The recently proposed theoretical concept of a Hund's metal is regarded as a key to explain the exotic magnetic and electronic behavior occuring in the strongly correlated electron systems of multiorbital metallic materials. However, a tuning of the abundance of parameters, that determine these systems, is experimentally challenging. Here, we investigate the smallest possible realization of a Hund's metal, a Hund's impurity, realized by a single magnetic impurity strongly hybridized to a metallic substrate. We experimentally control all relevant parameters including magnetic anisotropy and hybridization by hydrogenation with the tip of a scanning tunneling microscope and thereby tune it through a regime from emergent magnetic moments into a multi-orbital Kondo state. Our comparison of the measured temperature and magnetic field dependent spectral functions to advanced many-body theories will give relevant input for their application to non-Fermi liquid transport, complex magnetic order, or unconventional superconductivity.

We report on the quenching of single Ni adatom moments on Te-terminated Bi2Te2Se and Bi2Te3 topological insulator surfaces. The effect becomes manifested as a missing X-ray magnetic circular dichroism for resonant L3,2 transitions into partially filled Ni 3d states of occupancy n_d = 9.2. On the basis of a comparative study of Ni and Fe using scanning tunneling microscopy and ab initio calculations we are able to relate the element specific moment formation to a local Stoner criterion. While Fe adatoms form large spin moments of m_s = 2.54 mu_B with out-of-plane anisotropy due to a sufficiently large density of states at the Fermi energy, Ni remains well below an effective Stoner threshold for local moment formation. With the Fermi level remaining in the bulk band gap after adatom deposition, non-magnetic Ni and preferentially out-of-plane oriented magnetic Fe with similar structural properties on Bi2Te2Se surfaces constitute a perfect platform to study off-on effects of time-reversal symmetry breaking on topological surface states.

The rich phenomenology of plasmonic excitations in the dichalcogenides is analyzed as a function of doping. The many-body polarization, the dielectric response function and electron energy loss spectra are calculated using an ab initio based model involving material-realistic Coulomb interactions, band structure and spin-orbit coupling. Focusing on the representative case of MoS$_2$, a plethora of plasmon bands are observed, originating from scattering processes within and between the conduction or valence band valleys. We discuss the resulting square-root and linear collective modes, arising from long-range versus short-range screening of the Coulomb potential. We show that the multi-orbital nature of the bands and spin-orbit coupling strongly affects inter-valley scattering processes by gapping certain two-particle modes at large momentum transfer.

The electronic structure of the Cr(001) surface with its sharp resonance at the Fermi level is a subject of controversial debate of many experimental and theoretical works. To date, it is unclear whether the origin of this resonance is an orbital Kondo or an electron-phonon coupling effect. We have combined ab initio density functional calculations with dynamical mean-field simulations to calculate the orbitally resolved spectral function of the Cr(001) surface. The calculated orbital character and shape of the spectrum is in agreement with data from (inverse) photoemission experiments. We find that dynamic electron correlations crucially influence the surface electronic structure and lead to a low energy resonance in the $d_{z^2}$ and $d_{xz/yz}$ orbitals. Our results help to reconvene controversial experimental results from (I)PES and STM measurements., Comment: 8 pages, 5 figures

We introduce an approach to derive realistic Coulomb interaction terms in free standing layered materials and vertical heterostructures from ab-initio modelling of the corresponding bulk materials. To this end, we establish a combination of calculations within the framework of the constrained random phase approximation, Wannier function representation of Coulomb matrix elements within some low energy Hilbert space and continuum medium electrostatics, which we call Wannier function continuum electrostatics (WFCE). For monolayer and bilayer graphene we reproduce full ab-initio calculations of the Coulomb matrix elements within an accuracy of $0.2$eV or better. We show that realistic Coulomb interactions in bilayer graphene can be manipulated on the eV scale by different dielectric and metallic environments. A comparison to electronic phase diagrams derived in [M. M. Scherer et al., Phys. Rev. B 85, 235408 (2012)] suggests that the electronic ground state of bilayer graphene is a layered antiferromagnet and remains surprisingly unaffected by these strong changes in the Coulomb interaction., Comment: 12 pages, 8 figures

We describe a variational approach to solving Anderson impurity models by means of exact diagonalization. Optimized parameters of a discretized auxiliary model are obtained on the basis of the Peierls-Feynman-Bogoliubov principle. Thereby, the variational approach resolves ambiguities related with the bath discretization, which is generally necessary to make Anderson impurity models tractable by exact diagonalization. The choice of variational degrees of freedom made here allows systematic improvements of total energies over mean field decouplings like Hartree-Fock. Furthermore, our approach allows us to embed arbitrary bath discretization schemes in total energy calculations and to systematically optimize and improve on traditional routes to the discretization problem such as fitting of hybridization functions on Matsubara frequencies. Benchmarks in terms of a single orbital Anderson model demonstrate that the variational exact diagonalization method accurately reproduces free energies as well as several single- and two-particle observables obtained from an exact solution. Finally, we demonstrate the applicability of the variational exact diagonalization approach to realistic five orbital problems with the example system of Co impurities in bulk Cu and compare to continuous-time Monte Carlo calculations. The accuracy of established bath discretization schemes is assessed in the framework of the variational approach introduced here., Comment: 10 pages, 4 figures, accepted in PRB, v2: Added section on spectral information

Ultrafast magnetization dynamics in metallic heterostructures consists of a combination of local demagnetization in the ferromagnetic constituent and spin-dependent transport contributions within and in between the constituents. Separation of these local and non-local contributions is essential to obtain microscopic understanding and for potential applications of the underlying microscopic processes. By comparing the ultrafast changes of the polarization rotation and ellipticity in the magneto-optical Kerr effect (MOKE) we observe a time-dependent magnetization profile M(z,t) in Co/Cu(001) films by exploiting the effective depth sensitivity of the method. By analyzing the spatio-temporal correlation of these profiles we find that on time scales before hot electron thermalization (<100 fs) the transient magnetization of Co films is governed by spin-dependent transport effects, while after hot electron thermalization (>200 fs) local spin-flip processes dominate., Comment: 9 pages, 6 figures; revised version (title/abstract changed, text/figures from former ancillary file now included in main text, one additional figure, slightly expanded discussion); conclusions remain the same as in previous version