On-site Electron-electron Repulsion Research Articles

Charge singlets and orbital-selective charge density wave transitions

The possibility of ``orbitally selective Mott transitions'' within a multiband Hubbard model, in which one orbital with large on-site electron-electron repulsion ${U}_{1}$ is insulating and another orbital, to which it is hybridized, with small ${U}_{\ensuremath{-}1}$, is metallic, is a problem of long-standing debate and investigation. In this paper we study an analogous phenomenon, the coexistence of metallic and insulating bands in a system of orbitals with different electron-phonon coupling. To this end, we examine two variants of the bilayer Holstein model: a uniform bilayer and a ``Holstein-metal interface'' where the electron-phonon coupling, $\ensuremath{\lambda}$, is zero in the ``metallic'' layer. In the uniform bilayer Holstein model, charge density wave (CDW) order dominates at small interlayer hybridization ${t}_{3}$, but decreases and eventually vanishes as ${t}_{3}$ grows, providing a charge analog of singlet (spin liquid) physics. In the interface case, we show that CDW order penetrates into the metal layer and forms long-range CDW order at an intermediate ratio of inter- to intralayer hopping strengths, $1.4\ensuremath{\lesssim}{t}_{3}/t\ensuremath{\lesssim}3.4$. This is consistent with the occurrence of an ``orbitally selective CDW'' regime at weak ${t}_{3}$ in which the layer with ${\ensuremath{\lambda}}_{1}\ensuremath{\ne}0$ exhibits long-range charge order, but the ``metallic layer'' with ${\ensuremath{\lambda}}_{\ensuremath{-}1}=0$, to which it is hybridized, does not.

Unified formulations for RKKY interaction, side Kondo behavior, and Fano antiresonance in a hybrid tripartite quantum dot device with filtered density of states

Hybrid quantum dot structures are potential building blocks for spintronic devices and quantum logic gates, within which the understanding of many-body correlations is a prerequisite for implementing quantum information processing and generating controlled entanglement. Herein, we consider a hybrid tripartite quantum dot device, one of which is embedded directly between the source and drain electrodes, while the other two dots are side coupled to the first one. Modeling the system using the three-impurity Anderson model, we concentrate on the Ruderman-Kittel-Kasuya-Yosida interaction, the suppression of the Kondo behavior in the side dots, the destructive quantum interference, the gate-controlled quantum phase transitions, the Dicke effect, the ferromagnetic Kondo effect, and the thermodynamical properties in various parameter regimes using the numerical renormalization group method. Unified formulations are established, which are associated with the effective width of the zero-energy peak of the central dot without side dots, the central-side exchange coupling, as well the on-site electron-electron repulsion. We demonstrate that these formulas are well suitable for the non-, weak-, and strong-interacting cases.

Frustration-controlled quantum phase transition between multiple singular two-stage Kondo behaviors in a tetrahedral quadruple quantum dot structure

Semiconductor quantum dots are considered to be promising candidates for the hardware of quantum information technology and optoelectronic devices. Herein, motivated by a tetrahedrally shaped colloidal quadruple quantum dot structure made from In-based III--V semiconductors, which has been synthesized very recently by Leemans et al. [J. Am. Chem. Soc., 143, 4290 (2021)], we provide timely insight into the electronic transport and the quantum phase transition (QPT) for such an architecture. When the interdot hopping between different side dots (${t}_{2}$) is absent, a singular two-stage Kondo effect is revealed for small central-side coupling ${t}_{1}$. The two screening processes are separated by an energy scale of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, and the fitting parameters deviate from the regular ones of the side-coupled double dot system. The RKKY interaction and temperature are well illustrated by functions of ${t}_{1}^{4}/(U{T}_{K1}^{2})$, where $U$ and ${T}_{K1}$ are the on-site electron-electron repulsion and the first Kondo temperature, respectively. When ${t}_{2}$ turns on, the ground state of the side dots transits from a spin quadruplet to a magnetic frustration phase, and then to a singlet, through two first-order QPTs. In the frustration phase, another new two-stage Kondo effect is demonstrated, which includes the process of screening the local spin on the central dot firstly, and then that on the neighborless side dot is screened at a lower temperature. Both the Kondo temperatures are found to be rather sensitive to ${t}_{2}$. When ${t}_{2}$ is large enough, the reappearance of the regular Kondo effect is found. With fixed ${t}_{2}=0$, charging the central dot triggers a transition from an antiferromagnetic correlation among the side dots to a ferromagnetic one, accompanied by a Kondo behavior in the central dot. We adopt the state-of-the-art numerical renormalization group method to implement the above behaviors, combined with analytical arguments.

Dynamic Hubbard model for solids with hydrogen-like atoms

We discuss how to construct a tight binding model Hamiltonan for the simplest possible solid, composed of hydrogen-like atoms. A single orbital per atom is not sufficient because the on-site electron-electron repulsion mixes in higher energy orbitals. The essential physics is captured by a dynamic Hubbard model with one electronic orbital and an auxiliary spin degree of freedom per site. We point out that this physics can lead to a substantial shift in the position and width of electronic energy bands relative to what is predicted by conventional band structure calculations.

Magnetic transition in a correlated band insulator

The effect of on-site electron-electron repulsion $U$ in a band insulator is explored for a bilayer Hubbard Hamiltonian with opposite sign hopping in the two sheets. The ground state phase diagram is determined at half-filling in the plane of $U$ and the interplanar hybridization $V$ through a computation of the antiferromagnetic (AF) structure factor, local moments, single particle and spin wave spectra, and spin correlations. Unlike the case of the ionic Hubbard model, no evidence is found for a metallic phase intervening between the Mott and band insulators. Instead, upon increase of $U$ at large $V$, the behavior of the local moments and of single-particle spectra give quantitative evidence of a crossover to a Mott insulator state preceding the onset of magnetic order. Our conclusions generalize those of single-site dynamical mean field theory, and show that including interlayer correlations results in an increase of the single particle gap with $U$.

Enhancing the stability of a fractional Chern insulator against competing phases

We construct a two-band lattice model whose bands can carry the Chern numbers $C=0,\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}2$. By means of numerical exact diagonalization, we show that the most favorable situation that selects fractional Chern insulators (FCIs) is not necessarily the one that mimics Landau levels, namely a flat band with Chern number 1. First, we find that the gap, measured in units of the on-site electron-electron repulsion, can increase by almost two orders of magnitude when the bands are flat and carry a Chern number $C=2$ instead of $C=1$. Second, we show that giving a width to the bands can help to stabilize a FCI. Finally, we put forward a tool to characterize the real-space density profile of the ground state that is useful to distinguish FCI from other competing phases of matter supporting charge density waves or phase separation.

Local properties of an inhomogeneous two-component correlated superconductor

The effect of random point-like impurities on correlated superconductor has been studied. We use the two component (also called boson-fermion (BF)) model formulated in a real space supplemented with strong on-site electron-electron repulsion U and solve it by means of the real space Bogoliubov-de Gennes approach. It has been shown that due to electron correlations the gap is larger near the impurity sites, contrary to the results for the same model but without U. This naturally leads to positive correlations between the gap magnitude and the position of impurities, as was observed in various scanning tunneling measurements performed on d-wave symmetry BSCCO-2122 superconductors. Strong correlations are responsible for the protection of the low energy quasiparticles against disorder.

Retardation effects in the Holstein-Hubbard chain at half filling

The ground-state phase diagram of the half filled one-dimensional Holstein-Hubbard model contains a charge-density-wave (CDW) phase, driven by the electron-phonon (e-ph) coupling, and a spin-density-wave (SDW) phase, driven by the on-site electron-electron (e-e) repulsion. Recently, the existence of a third phase, which is metallic and lies in a finite region of parameter space between these two gapped phases, has been claimed. We study this claim using a renormalization-group method for interacting electrons that has been extended to include also e-ph couplings. Our method [Tsai et al., Phys. Rev. B 72, 054531 (2005); Philos. Mag. B 86, 2631 (2006)] treats e-e and e-ph interactions on an equal footing and takes retardation effects fully into account. We find a direct transition between the SDW and CDW states. We study the effects of retardation, which are particularly important near the transition, and find that umklapp processes at finite frequencies drive the CDW instability close to the transition.

Superconductivity from long-range interaction: A crossover between the electron gas and the lattice model

We explore how the superconductivity arising from the on-site electron-electron repulsion will change when the repulsion is changed to a long-ranged, 1/r-like one by introducing an extended Hubbard model with the repulsion extending to distant (12th) neighbors. With a simplified fluctuation-exchange approximation, we have found for the square lattice that (i) as the band filling becomes dilute enough, the charge susceptibility becomes comparable with the spin susceptibility, where p and then s pairings become dominant, in agreement with the result for the electron gas by Takada, while (ii) the d-wave, which reflects the lattice structure, dominates well away from the half filling. All these can be understood in terms of the spin and charge structures along with the shape and size of the Fermi surface.

Spin correlation on the main chain of a quasi-one-dimensional polymerferromagnet: a density matrix renormalization group study

The spin correlation (SC) function on the main chain of a theoretical model fororganic ferromagnets is studied by using a density matrix renormalizationgroup method with both periodic boundary conditions and open boundaryconditions (OBCs). It is found that the chain–radical interaction, the on-siteelectron–electron repulsion, and the electron–phonon coupling affect the SCgreatly and play important roles in the stability of the ferromagnetic state. Thereexist some types of ‘weak’ OBC, diminishing the alternation of the SC.

Crystal structure, spectral and electrochemical properties of [TBA] 2[Ni(i-MNT) 2], [TBA][Ni(i-MNT) 2], [TBA] 2[Ni(i-MNS) 2] and related bis(1,2-dithiolene) metal complexes

The synthesis, crystal structure and physical properties of bis(1,1-dithiolene) or bis (1,1-diselenolene) metal complexes of [TBA] 2[Ni(i-MNT) 2], [TBA][Ni(i-MNT) 2] and [TBA] 2[Ni(i-MNS) 2] (i-MNT = 2,2-dicyanoethylene-1,1-dithiolate,i-MNS = 2, 2-dicyanoethylene-1, 1-diselenolate) were studied and compared to one another or to the related bis (1,2-dithiolene) metal complexes of 5,6-dihydro-1,4-dithiin-2,3-dithiolate, 1,3-dithiole-2-thione-4,5-dithiolate and 1,3-dithiole-2-one-4,5-dithiolate ligands. The structures of the complexes contain equidistant anionic stacks well separated by the counter cation sheets. The planarity and short C-S or C-Se distances in the structures indicate extensive delocalization of the π-system in the compounds. The relative low conductivities for the complexes are due to the low polarizability, large intra-and inter-stack S ··· S distances, and the relative high on-site electron-electron repulsion energy in the compounds.

Two-electron self-consistent-field study of 2kF broken-symmetry states in correlated monatomic and diatomic Peierls-Hubbard chains.

The two-electron-self-consistent-field (SCF2) approach in which the wave function is constructed from spin-unrestricted geminals (UG's) optimized variationally is developed. It combines restricted-geminal (RG)-SCF2 and unrestricted Hartree-Fock methods, thus accounting for both short-range (intrapair) and long-range electron correlations. On this basis ground-state properties of the extended half-filled Peierls-Hubbard chains are calculated in a wide range of site-energy modulation \ensuremath{\alpha} and on-site electron-electron repulsion U. Treating a generalized-Peierls transition in slight-to-strong correlation regimes within the same framework, the electronic-Peierls and spin-Peierls transition areas can be conventionally differentiated by bifurcation points in which UG-SCF2 solutions separate from RG solutions. The corresponding phase diagram in the U-\ensuremath{\alpha} plane is obtained. For the monatomic (\ensuremath{\alpha}=0) chain, the predicted dimerization amplitude is in a good agreement with the earlier Peierls and spin-Peierls calculations. For the diatomic strongly correlated chain, dimerization sharply rises with \ensuremath{\alpha} at the bifurcation point ${\mathrm{\ensuremath{\alpha}}}_{0}$ and then rapidly drops near \ensuremath{\alpha}=U/2; a property that can be related to phase transitions in some donor-acceptor molecular crystals.

Influence of long-range and strong correlation effects on the electron-phonon coupling in high-T c oxides

Calculations of the Eliashberg functionα 2F and the corresponding transport functionα 2 F for high-T c oxides are presented using a screened ionic model (rigidly shifted ionic potentials screened by charge carriers in the CuO2 planes within the RPA) for the electron-phonon coupling. It is shown that this model yields a large difference between the transport and the superconducting electron-phonon interaction due to imperfect screening and contributions beyond nearest-neighbor interactions. Using these results, the electron and the lattice heat conductivities are calculated both in the normal and the superconducting state and compared with experiment. Finally, effects due to a strong on-site electron-electron repulsion are included in leading order in an 1/N expansion, whereN is the number of spin degrees of freedom. In particular, it is shown for the infiniteU, one-band Hubbard model that correlations tend to suppressα 2 F strongly andα 2 F somewhat.

The concept of anti-integrability applied to dynamical systems and to structural and electronic models in condensed matter physics

Many models for structures in condensed matter can be associated with Hamiltonian dynamical systems with discrete time. This connection is due to the fact that both models are defined by the minimisation or the extremalisation of the same variational form called “free energy” in the first case and “action” in the second case. Thus, the results obtained for the first class of problems turn out to have applications for the second class and vice-versa, but however, with a physical interpretation which is totally different. For example, the breaking of the KAM tori and the occurrence of chaos in the standard map turns out to correspond to a pinning transition and the occurrence of chaotic metastable states in the associated Frenkel-Kontorowa models. The anti-integrable limit for structural problems is a very natural limit where the “atoms” of the structure become disconnected. It corresponds to a highly singular limit for the associated dynamical system which up to now did not focus much attention. The associated dynamical system becomes undeterministic and just reduces to a Bernoulli shift. Nevertheless, a perturbation theorem can be established at this limit which proves the persistence of chaotic trajectories when the dynamical system returns to be deterministic. This result is extended to a large class of dynamical systems with discrete time including non-Hamiltonian systems. An anti-integrable limit can also be found in the adiabatic Holstein model describing electrons coupled to phonons at several dimensions and some extensions which are not apparently connected to any dynamical system. Then the anti-integrable limit is obtained when the electronic kinetic energy vanishes. Treating this kinetic energy in an exact perturbation theory, allows one to prove new results concerning the existence of bipolaronic, polaronic and mixed polaronic-bipolaronic insulators. The possible extension of the KAM theory to the small electron-phonon coupling regime and especially in the one-dimensional adiabatic Holstein model is still an open problem. A similar anti-integrable limit is also found in the Holstein-Hubbard model involving in addition an on-site electron-electron repulsion. Some partial but exact results were recently obtained in that model proving the persistance of bipolaronic, polaronic magnetic and mixed structures with a non-vanishing electronic kinetic energy while this Hubbard term is rigorously taken into account. Another family of open problems concerns dynamical systems with a continuous time such as arrays of coupled nonlinear oscillators. Such models can be useful for understanding the transport of the vibrational energy in nonlinear solids such as quasi-crystals, in polymers or in DNA chains (etc.). The anti-integrable limit corresponds to the uncoupled limit when the oscillators oscillate independently with random amplitudes, periods and phase. Can these solutions or some of these solutions be continued at non-zero coupling? R. MacKay recently proved that the anti-integrable solution corresponding to a single oscillator moving can be continued as a localised breather solution when the coupling constant is not too large.

Excitations of the one-dimensional, two-band Peierls-Hubbard model at three-quarters filling in the large-U limit.

We investigate the ground state and the excitation spectrum associated with the localized defect states of the three-quarter-filled, one-dimensional Peierls-Hubbard model. In the continuum limit with an infinite, on-site electron-electron repulsion energy U, the Hamiltonian is mapped onto the N=1 Gross-Neveu model, in which irrationally charged soliton-antisoliton pairs are formed upon doping, while polarons are unstable. Corrections due to finite-U effects are discussed. However, discreteness effects are found to support excitations absent from the continuum field theory. In particular, for large band separation a novel type of polaron can be formed with a highly localized electronic wave function surrounded by an extended pattern of local lattice distortion.

Magnetism and covalency in the two-dimensional three-band Peierls-Hubbard model.

Stoichiometric phases and doping states are studied in a two-dimensional, three-band extended Peierls-Hubbard model, using an inhomogeneous Hartree-Fock approximation. Magnetism and covalency are investigated in a parameter space of strong intersite electron-lattice coupling and varying on-site electron-electron repulsion strength. In a crossover region between a charge-density-wave phase driven by intersite electron-lattice coupling and an antiferromagnetic phase driven by on-site electron-electron repulsion, a bond-order-wave state, a spin-Peierls state, and a mixed state of spin-Peierls bonds and antiferromagnetic spins are found to be stable and caused by competing magnetism and covalency of different relative strengths. Doping states depend qualitatively upon the nature of these global phases. In particular, separation of spin and charge is observed in the background of the bond-order-wave state as a consequence of local competition between magnetism and covalency.

Self-consistent calculation of solitons in polyacetylene

We present a self-consistent calculation of the electronic structure of a single-site soliton present in a infinite chain of trans -polyacetylene. It is shown that the inclusion of on-site (Hubbard) electron-electron repulsion terms induces a spin redistribution of the system giving origin to sites of negative spin density. The importance of including off-diagonal repulsion terms is discussed.

Attractive interaction and pairing in fermion systems with strong on-site repulsion.

It is shown that an effective attractive interaction between nearest-neighbor antiparallel spins a-rises in the Hubbard and Anderson lattice models in the limit of large on-site electron-electron repulsion. Results of Monte Carlo simulations of the Hubbard model show enhancement of anisotropic single-pairing correlations and suppression of triplet-pairing correlations. It is proposed that this interaction leads to an anisotropic singlet superconducting state in the heavy-fermion superconductors.

Magnetic susceptibility, electrical resistivity, and thermoelectric power measurements ofbis(tetrathiotetracene)-triiodide

The magnetic susceptibility ($\ensuremath{\chi}$), electrical resistivity ($\ensuremath{\rho}$), and thermoelectric power ($S$) of bis(tetrathiotetracene)-triiodide were measured for $9<T<300$ K. Bis(tetrathiotetracene)-triiodide crystals were synthesized by vapor-phase cosublimation. X-ray crystal-structure determination on crystals prepared by this technique indicates a potential range of stoichiometries, i.e., TTT-${({\mathrm{I}}_{3})}_{x}$ where $0.5\ensuremath{\le}x\ensuremath{\le}0.52$. TTT-${({\mathrm{I}}_{3})}_{0.5}$ is highly conducting at room temperature ($\ensuremath{\rho}\ensuremath{\sim}{10}^{\ensuremath{-}3}$ \ensuremath{\Omega}cm). The properties of TTT-${({\mathrm{I}}_{3})}_{0.5}$ are consistent with a metallic state: (i) resistivity $\ensuremath{\rho}={\ensuremath{\rho}}_{0}+{\ensuremath{\rho}}_{1}{T}^{2}$; ${\ensuremath{\rho}}_{0}\ensuremath{\sim}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ \ensuremath{\Omega}cm, ${\ensuremath{\rho}}_{1}\ensuremath{\sim}8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ \ensuremath{\Omega}cm/${\mathrm{K}}^{2}$ for $T>100$ K, and (ii) thermopower $S=\frac{{S}_{0}}{T}+{S}_{1}T$ where ${S}_{0}=1124$ \ensuremath{\mu}V and ${S}_{1}=1.07\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}1}$ \ensuremath{\mu}V/${\mathrm{K}}^{2}$. The magnetic susceptibility, corrected for 0.25% spin-\textonehalf{} impurities, is + 2.2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}4}$ emu/mol at room temperature. The term in the thermopower data linear in temperature is interpreted using a one-dimensional tight-binding model to yield a value for the transfer integral ($t$) of 0.16 eV. The high-temperature value of $\ensuremath{\chi}$ is enhanced by Coulomb correlations. Using the antiferromagnetic Heisenberg-chain model appropriate to this limit we find that the on-site electron-electron repulsion ($U$) is \ensuremath{\sim} 2.0 eV. Phase transitions have been found at 50 K in $\ensuremath{\chi}$ and at 21 K in $\frac{d\mathrm{ln}\ensuremath{\rho}}{\mathrm{dT}}$. The conductivity of TTT-${({\mathrm{I}}_{3})}_{0.5}$ remains large at low temperatures [$\ensuremath{\rho}(10 \mathrm{K})\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ \ensuremath{\Omega}cm], and the magnetic susceptibility, corrected for spin-\textonehalf{} impurities has a large paramagnetic value (1.2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}4}$ emu/mol) at low temperature ($T<20$ K).