On-site Coulomb Repulsion Research Articles

First-principles calculations of local structure and electronic properties of Er<sup>3+</sup>-doped TiO<sub>2</sub>

Trivalent rare earth erbium ion (Er<sup>3+</sup>) doped titanium oxide (TiO<sub>2</sub>) can possess a very wide range of applications due to its excellent optoelectronic properties, thus standing out among many rare-earth-doped luminescent crystals. However, the issues regarding local structure and electronic properties have not been finalized. To address these problems, the CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) method combined with the first-principles calculations is employed, and many converged structures of Er<sup>3+</sup>-doped TiO<sub>2</sub> are successfully obtained. Further structural optimization is performed by using the VASP (Vienna <i>ab initio</i> simulation package) software package, and we report for the first time that the lowest energy structure of Er<sup>3+</sup>-doped TiO<sub>2</sub> has the <inline-formula><tex-math id="M2">\begin{document}$ P\overline 4 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20221847_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20221847_M2.png"/></alternatives></inline-formula><i>m</i>2 symmetry. It can be observed that the doped Er<sup>3+</sup> ions enter into the host crystal and occupy the positions of Ti<sup>4+</sup> ions, resulting in structural distortion, which eventually leads the local Er<sup>3+</sup> coordination site symmetry to reduce from <i>D</i><sub>2<i>d</i></sub> into <i>C</i><sub>2<i>v</i></sub>. We speculate that there are two reasons: 1) the difference in charge between Er<sup>3+</sup> ions and Ti<sup>4+</sup> ions leads to charge compensation; 2) the difference between their electron radii is obvious: the radius is 0.0881 for Er<sup>3+</sup> ion and 0.0881 for Ti<sup>4+</sup> ion. In addition, during the structural search, we also find many metastable structures that may exist at a special temperature or pressure, which play an important role in the studying of structural evolution. When the electronic band structure of the Er<sup>3+</sup>-doped TiO<sub>2</sub> system is calculated, we adopt the method of local density approximation (LDA) combined with the on-site Coulomb repulsion parameter <i>U</i> to accurately describe the strongly correlated system. For the specific value of <i>U</i>, we adopt 3.5 eV and 7.6 eV to describe the strong correlation of 3d electrons of Ti<sup>4+</sup> ions and 4f electrons of Er<sup>3+</sup> ions, respectively. According to the calculation of electronic properties, the band gap value of Er<sup>3+</sup> doped TiO<sub>2</sub> is about 2.27 eV, which is lower than that of the host crystal (<i>E</i><sub>g</sub> = 2.40 eV). The results show that the reduction in the band gap is mainly caused by the f state of Er<sup>3+</sup> ions. The doping of Er ion does reduce the band gap value, but it does not change the conductivity of the system, which have great application prospect in diode-pumped laser. These findings not only provide the data for further exploring the properties and applications of Er<sup>3+</sup>:TiO<sub>2</sub> crystals, but also present an approach to studying other rare-earth-doped crystalline materials.

Synthesis and n-Type Semiconducting Properties of Bis(dioxaborin) Compounds Containing a π-Extended 2,2'-Bithiophene Structure.

Bis(dioxaborin) compounds containing π-conjugated systems have been studied as n-type semiconductors for organic field-effect transistors (OFETs). In this study, with the aim of investigating the effect of the extension of the π-conjugation on the n-type semiconducting properties and stability of bis(dioxaborin) compounds, we synthesized new compounds containing 2,2'-bithiophene derivatives extended with an olefin or an acetylene spacer. The absorption maxima of the compounds containing olefin spacers were greatly red-shifted compared with those of the original compound without a π-spacer. The newly synthesized compounds exhibited high electron affinity, and the olefin spacers effectively reduced the on-site Coulomb repulsion in the two-electron reduction of the compounds. An OFET fabricated using one of these compounds having a layer-by-layer crystal structure exhibited n-type semiconductor behavior with a low threshold voltage, most likely due to the small on-site Coulomb repulsion. The electron-transporting properties were investigated by theoretical calculations based on the Marcus theory.

Induction of large magnetic anisotropy energy and formation of multiple Dirac states in SrIrO3 films: Role of correlation and spin–orbit coupling

The 5d transition metal oxides, in particular iridates, host novel electronic and magnetic phases due to the interplay between onsite Coulomb repulsion (U) and spin–orbit coupling (SOC). The reduced dimensionality brings another degree of freedom to increase the functionality of these systems. By taking the example of ultrathin films of SrIrO3, theoretically we demonstrate that confinement led localization can introduce large magnetic anisotropy energy (MAE) in the range of 2–7 meV/Ir, which is one to two order higher than that of the traditional MAE compounds formed out of transition metals and their multilayers. Furthermore, in the weak correlation limit, tailored terminations can yield multiple Dirac states across a large energy window of 2 eV around the Fermi energy, which is rare phenomena in correlated oxides and upon experimental realization it will give rise to unique transport properties with excitation and doping.

Multipolar ordering in the three-orbital Hubbard model

The ground-state phase diagrams of the three-orbital t2g Hubbard model are studied using a Hartree-Fock approximation. First, a complete set of multipolar order parameters for t2g models defined in terms of the effective total angular momentum jeff are theoretically derived. These order parameters can classify off-diagonal orders between jeff = 1/2 and jeff = 3/2 manifolds. Second, through extensive Hartree-Fock calculations, the ground-state phase diagrams in the space of (1) the onsite Coulomb repulsion U, (2) the spin-orbit coupling (SOC), and (3) the number of electrons are mapped out. A variety of nontrivial quantum phases with jeff-diagonal and jeff-off-diagonal multipole orders are found. Finally, future studies using more numerically expensive methods, such as dynamical mean-field theory are discussed.

Temperature-independent localization of Ce 4f electrons in cerium monoarsenide

In order to reveal the valence state of Ce ions and the occupancy number of Ce 4f electrons versus temperature in cerium monoarsenide (CeAs), we perform an ab initio calculation by using a many-body scheme combing density functional theory (DFT) with dynamical mean field theory (DMFT), taking into account the spin-orbit coupling (SOC) interaction and on-site Coulomb repulsion between Ce 4f electrons. Results demonstrate that Ce 4f j=5/2 and j=7/2 manifolds exhibit the metallic and insulating characters, respectively, irrespective of temperature. Ce 4f-4f correlation, Ce 4f-conduction electrons hybridization, SOC interaction and final state effects yield a complicated spectrum function for CeAs. Coupling of 4f atomic configuration transition, hybridization and temperature does not change the localized Ce 4f regime in CeAs. Finally, momentum-resolved electronic spectrum function is also discussed for comparison with experimental angle-resolved photoemission spectrum (ARPES).

Spin-Orbit-Entangled Nature of Magnetic Moments and Kitaev Magnetism in Layered Halides

$\alpha$-RuCl$_3$ has been extensively studied recently because of potential bond-dependent Kitaev magnetic exchange interactions and the resulting quantum spin liquid phase that can be realized therein. It has been known that the covalency between Ru 4$d$- and Cl $p$-orbitals is crucial to induce large Kitaev interactions in this compound, therefore replacing Cl into heavier halogen elements such as Br or I can be a promising way to promote the Kitaev interaction even further. In a timely manner, there have been reports on synthesis of $\alpha$-RuBr$_3$ and $\alpha$-RuI$_3$, which are expected to host the same spin-orbit-entangled orbitals and Kitaev exchange interactions with $\alpha$-RuCl$_3$. Here in this work we investigate electronic structures of $\alpha$-RuCl$_3$, $\alpha$-RuBr$_3$, and $\alpha$-RuI$_3$ in a comparative fashion, focusing on the cooperation of the spin-orbit coupling and on-site Coulomb repulsions to realize the spin-orbit-entangled pseudospin-1/2 at Ru sites. We further estimate magnetic exchange interactions of all three compounds, showing that $\alpha$-RuBr$_3$ can be promising candidates to realize Kitaev spin liquid phases in solid-state systems.

Mixed 5f atomic configurations in two polymorphic forms of uranium pentafluoride

A first principles calculation in this work is performed on two polymorphic forms of uranium pentafluoride (UF5) by using density functional theory (DFT) merging with dynamical mean-field theory (DMFT) scheme with spin–orbit coupling (SOC) and on-site Coulomb repulsion for correlation effect due to the incompletely filled U 5f orbitals. Calculation results suggest that U j = 5/2 and j = 7/2 manifolds both are in weakly correlated states in α and β phases UF5 and, Russel-Saunders (LS) coupling scheme is appropriate for U 5f electrons. Occupation probability analysis demonstrates that U ions are mostly composed of mixed atomic configurations 5f1, 5f2 and 5f3 with average occupation numbers of nf ∼ 2.002 and 1.862 for U 5f electrons in α and β phases UF5, respectively, mainly due to the complicated quantum mechanics processes including the dual nature of localized and itinerant U 5f electrons, as well as the flexible outer electronic configuration of U ions. Finally, we estimate the momentum-resolved electronic spectrum function (the so-called quasiparticle band structure) to compare with angle-resolved photoemission spectrum (ARPES).

Structural and electronic properties of wide band gap charge transfer insulator Hg2Cl2: Insights from the first-principle calculations

The structural and electronic properties of Mercurous Chloride (Hg2Cl2) in its tetragonal (I4/mmm) phase at room temperature have been investigated from the first principle calculations. Detail calculations within the framework of density functional theory (DFT) upon incorporation of spin-orbit coupling (SOC) reveal that Hg2Cl2 is a wide band gap charge transfer (CT) insulator with band gap energy (Eg) ∼ 3.96 eV. Despite being a CT insulator, the orbital resolved PDOS of Hg2Cl2 compound exhibit energy dispositions that do not obey the Zaanen – Sawatzky – Allen (ZSA) diagram. The effect of on-site Coulomb repulsion (Hubbard +Udd) on the band gap of the compound has also been studied in detail. The Mulliken bond population, electronic charge density distribution and Bader charges analyses have been explored to unveil the covalent and ionic interactions between Hg and Cl atoms of the Hg2Cl2 compound. The Natural Bond Orbital (NBO) analyses have been performed to gain deeper insights on the CT interactions between Hg and Cl atoms of Hg2Cl2. The rationale behind the distortions of the octahedral domains within Hg2Cl2 crystal has also been elucidated in detail.

Effect of the electronic charge gap on LO bond-stretching phonons in undoped La2CuO4 calculated using LDA+U

Typical density-functional theory calculations that wrongly predict undoped cuprates to be metallic also predict Cu-O half- and full-breathing phonon energies that are significantly softer than observed, presumably because of weak on-site Coulomb repulsion on the Cu 3d orbitals. We used DFT+U calculations with antiferromagnetic supercells of La$_2$CuO$_4$ to establish correlation between the on-site repulsion strength, tuned via adjusting the value of U, and phonon dispersions. We find that breathing and half-breathing phonons reach experimental values when U is tuned to obtain the correct optical gap and magnetic moments. We demonstrate that using distorted supercells within DFT+U is a promising framework to model phonons in undoped cuprates and other perovskite oxides with complex, interrelated structural and electronic degrees of freedom.

Quantum spin compass models in two-dimensional electronic topological metasurfaces

We consider a metasurface consisting of a square lattice of cylindrical antidots in a two-dimensional topological insulator (2DTI). Each antidot supports a degenerate Kramer's pair of eigenstates formed by the helical topological edge states. We show that the on-site Coulomb repulsion leads to the onset of the Mott insulator phase in the system in a certain range of experimentally relevant parameters. Intrinsic strong spin-orbit coupling characteristic for the 2DTI supports a rich class of the emerging low-energy spin Hamiltonians which can be emulated in the considered system, which makes it an appealing solid state platform for quantum simulations of strongly correlated electron systems.

Probing Majorana zero modes by measuring transport through an interacting magnetic impurity

Motivated by recent experiments we consider transport across an interacting magnetic impurity coupled to the Majorana zero mode (MZM) observed at the boundary of a topological superconductor (SC). In the presence of a finite tunneling amplitude we observe hybridization of the MZM with the quantum dot, which is manifested by a half-integer zero-bias conductance $G_0=e^2/2h$ measured on the metallic contacts. The low-energy feature in the conductance drops abruptly by crossing the transition line from the topological to the non-topological superconducting regime. Differently from the in-gap Yu-Shiba-Rosinov-like bound states, which are strongly affected by the on-site impurity Coulomb repulsion, we show that the MZM signature in the conductance is robust and persists even at large values of the interaction. Interestingly, the topological regime is characterized by a vanishing Fano factor, $F=0$, induced by the MZM. Combined measurements of the conductance and the shot noise in the experimental set-up presented in the manuscript allow to detect the topological properties of the superconducting wire and to distinguish the low-energy contribution of a MZM from other possible sources of zero-bias anomaly. Despite being interacting the model is exactly solvable, which allows to have an exact characterization of the charge transport properties of the junction.

Topological Mott transition in a two band model of spinless fermions with on-site Coulomb repulsion

In the framework of mean field approach, we study topological Mott transition in a two band model of spinless fermions on a square lattice at half filling. We consider the combined effect of the on-site Coulomb repulsion and the spin–orbit Rashba coupling. The ground state phase diagram is calculated as a function of the strength of the spin–orbit Rashba coupling and the Coulomb repulsion. The spin–orbit Rashba coupling leads to a distinct phase of matter, the topological semimetal. We study a new type of phase transition between the non-topological insulator and topological semimetal states. Topological phase state is characterized by the zero energy Majorana states, which there are in defined region of the wave vectors and are localized at the boundaries of the sample. The region of existence of the zero energy Majorana states tends to zero at the point of the Mott phase transition. The zero energy Majorana states are dispersionless (they can be considered as flat bands), the Chern number and Hall conductance are equal to zero (note in two dimensional model).

Lattice reconstruction induced multiple ultra-flat bands in twisted bilayer WSe2

Moiré superlattices in van der Waals heterostructures provide a tunable platform to study emergent properties that are absent in the natural crystal form. Twisted bilayer transition metal dichalcogenides (TB-TMDs) can host moiré flat bands over a wide range of twist angles. For twist angle close to 60°, it was predicted that TB-TMDs undergo a lattice reconstruction which causes the formation of ultra-flat bands. Here, by using scanning tunneling microscopy and spectroscopy, we show the emergence of multiple ultra-flat bands in twisted bilayer WSe2 when the twist angle is within 3° of 60°. The ultra-flat bands are manifested as narrow tunneling conductance peaks with estimated bandwidth less than 10 meV, which is only a fraction of the estimated on-site Coulomb repulsion energy. The number of these ultra-flat bands and spatial distribution of the wavefunctions match well with the theoretical predictions, strongly evidencing that the observed ultra-flat bands are induced by lattice reconstruction. Our work provides a foundation for further study of the exotic correlated phases in TB-TMDs.

Effect of On-site Coulomb Repulsion on Ferromagnetic Fluctuations in Heavily Overdoped Cuprates

We theoretically study ferromagnetic (FM) fluctuations that are experimentally observed in the heavily overdoped region of cuprate superconductors. To explore the origin of FM fluctuations, we evaluate the spin susceptibilities of a single-band Hubbard model within the fluctuation exchange approximation. Model parameters are derived using the Wannierization technique and the constrained random phase approximation method based on the maximally localized Wannier functions. The constrained random phase approximation calculations reveal that the on-site Coulomb interaction decreases with an increase in hole doping. By taking this reduction of the on-site Coulomb interaction into account, the emergence of FM fluctuations in heavily overdoped cuprates can be explained.

Collective spin and charge excitations in the t-J-U model of high-[formula omitted] cuprates

The t-J-U model of high-Tc copper-oxide superconductors incorporates both the on-site Coulomb repulsion and kinetic exchange interaction and yields a semi-quantitative description of the static properties of those materials. We extend this analysis to dynamic quantities and address collective spin- and charge excitations in the correlated metallic state of the t-J-U model. We employ VWF+1/Nf approach that combines the variational wave function (VWF) approach with the expansion in the inverse number of fermionic flavors (1/Nf). It is shown that the resonant (paramagnon) contribution to the dynamic magnetic susceptibility remains robust as one interpolates between the Hubbard- and t-J-model limits, whereas the incoherent continuum undergoes substantial renormalization. Energy of the collective charge mode diminishes as the strong-coupling limit is approached. We also introduce the concept of effective kinetic exchange interaction that allows for a unified interpretation of magnetic dynamics in the Hubbard, t-J, and t-J-U models. The results are discussed in the context of recent resonant inelastic x-ray scattering experiments for the high-Tc cuprates.

Balancing orbital effects and on-site Coulomb repulsion through Na modulations in NaxVO2

Vanadium oxides have been highly attractive for over half a century since the discovery of the metal insulator transition near room temperatures. Here NaxVO2 is studied through a systematic comparison with other layered sodium metal oxides with early 3d transition metals, first disclosing a unified evolution pattern of Na density waves through in situ XRD analysis. Combining ab-initio simulations and theoretical modelings, a sodium-modulated Peierls-like transition mechanism is then proposed for the bonding formation of metal ion dimers. More importantly, the unique trimer structure in NaxVO2 is shown to be very sensitive to the onsite Coulomb repulsion value, suggesting a delicate balance between strong electronic correlations and orbital effects that can be precisely modulated by both Na compositions and atomic stackings. This unveils a unique opportunity to design strongly correlated materials with tailored electronic transitions through electrochemical modulations and crystallographic designs, to elegantly balance various competition effects. We think the understanding will also help further elucidate complicated electronic behaviors in other vanadium oxide systems.

Coexistence of Charge Order and Antiferromagnetic Order in an Extended Periodic Anderson ModelSupported by the National Natural Science Foundation of China (Grant Nos. 11974048 and 11974049), and the Beijing Science Foundation (Grant No. 1192011).

The competition between the RKKY interaction and the Kondo effect leads to a magnetic phase transition, which occurs ubiquitously in heavy fermion materials. However, there are more and more experimental evidences indicating that the valence fluctuation plays an essential role in the Ce- and Y-based compounds. We study an extended periodic Anderson model (EPAM) which includes the onsite Coulomb repulsion Ucf between the localized electrons and conduction electrons. By employing the density matrix embedding theory, we investigate the EPAM in the symmetric case at half filling. By fixing the onsite Coulomb repulsion U of the localized electrons to an intermediate value, the interplay between the RKKY interaction, the Kondo effect and the Coulomb repulsion Ucf brings rich physics. We find three different phases, the antiferromagnetic phase, the charge order phase and paramagnetic phase. When the hybridization strength V between the localized orbital and the conduction orbital is small, the Kondo effect is weak so that the AF phase and the CO phase are present. The phase transition between the two long-range ordered phase is of first order. We also find a coexistence region between the two phases. As V increases, the Kondo effect becomes stronger, and the paramagnetic phase appears between the other two phases.

Competing electronic orders on a heavily doped honeycomb lattice with enhanced exchange coupling

Motivated by recent discovery of correlated insulating and superconducting behavior in twisted bilayer graphene, we revisit graphene's honeycomb lattice doped close to the van Hove singularity, using the truncated unity functional renormalization group approach. We consider an extended Hubbard model on the honeycomb lattice including on-site and nearest-neighbor Coulomb repulsions, and nearest-neighbor ferromagnetic exchange and pair hopping interactions. By varying the strength of the nearest-neighbor exchange coupling and Coulomb repulsion as free parameters, we present rich ground-state phase diagrams which contain the spin-triplet $f$-wave and spin-singlet chiral $d$-wave superconducting phases, the commensurate and incommensurate spin- and charge-density-wave phases, and the ferromagnetic phase. In the absence of the exchange coupling and for small value of the nearest-neighbor repulsion, the four-sublattice spin-density-wave phase is generated right around the van Hove filling, while the chiral $d$-wave superconductivity emerges slightly away from it. Surprisingly, the chiral $d$-wave superconductivity is strongly suppressed by weak nearest-neighbor exchange coupling in our calculations. We argue that this suppression might be one of the reasons why the chiral superconductivity proposed for doped graphene has not yet been observed experimentally.

Absence of superconductivity in the repulsive Hubbard model on a square lattice in the regime of strong coupling

The possibility of the superconducting transition in the repulsive Hubbard model on a square lattice is studied using the ladder approximation of the strong coupling diagram technique. The t–U and t–t′–t″–U models are considered in the regime of strong correlations, for the on-site Coulomb repulsion U = 8t, in the range of temperatures 0.02t ≲ T ≲ 0.3t. To avoid the influence of the phase separation and size effects the calculations are performed in an infinite crystal, in the part of the phase diagram without inhomogeneities, for the electron concentration . Solutions of the Eliashberg equation for singlet and triplet pairing, which are transformed according to one-dimensional representations of the lattice point group D 4, are considered. For both models and all considered symmetries, eigenvalues of the Eliashberg equation are less than unity and demonstrate no upward trend with decreasing temperature. This result points to the absence of superconductivity in the Hubbard model in the strong-coupling regime. We discuss the reason for the small eigenvalue of the Eliashberg equation in the case of the singlet pairing.

Interplay between charge density wave and superconductivity in multiband systems with interband Coulomb interaction

In this work we study the competition or coexistence between charge density wave (CDW) and superconductivity (SC) in a two-band model system in a square lattice. One of the bands has a net attractive interaction ($J_d$) that is responsible for SC. The model includes on-site Coulomb repulsion between quasi-particles in different bands ($U_{dc}$) and the hybridization ($V$) between them. We are interested in describing inter-metallic systems with a $d$-band of moderately correlated electrons, for which a mean-field approximation is adequate, coexisting with a large $sp$-band. For simplicity, all interactions and the hybridization $V$ are considered site-independent. We obtain the eigenvalues of the Hamiltonian numerically and minimize the free energy density with respect to the relevant parameters to obtain the phase diagrams as function of $J_d$, $U_{dc}$, $V$, composition ($n_{\mathrm{tot}}$) and the relative depth of the bands ($\epsilon_{d0}$). We consider two types of superconducting ground states coexisting with the CDW. One is a homogeneous ground state and the other is a pair density wave where the SC order parameter has the same spatial modulation of the CDW. Our results show that the CDW and SC orders compete, but depending on the parameters of the model these phases may coexist. The model reproduces most of the experimental features of high dimensionality ($d>1$) metals with competing CDW and SC states, including the existence of first and second-order phase transitions in their phase diagrams.