Lattice effect of strong electron correlation: implication for ferroelectricity and superconductivity

Quantum embedding for molecules using auxiliary particles - the ghost Gutzwiller Ansatz

Strong/static electronic correlation mediates the emergence of remarkable phases of matter, and underlies the exceptional reactivity properties in transition metal-based catalysts. Modeling strongly correlated molecules and solids calls for multi-reference Ansätze, which explicitly capture the competition of energy scales characteristic of such systems. With the efficient computational screening of correlated solids in mind, the ghost Gutzwiller (gGut) Ansatz has been recently developed. This is a variational Ansatz which can be formulated as a self-consistent embedding approach, describing the system within a non-interacting, quasiparticle model, yet providing accurate spectra in both low and high energy regimes. Crucially, small fragments of the system are identified as responsible for the strong correlation, and are therefore enhanced by adding a set of auxiliary orbitals, the ghosts. These capture many-body correlations through one-body fluctuations and subsequent out-projection when computing physical observables. gGut has been shown to accurately describe multi-orbital lattice models at modest computational cost. In this work, we extend the gGut framework to strongly correlated molecules, for which it holds special promise. Indeed, despite the asymmetric embedding treatment, the quasiparticle Hamiltonian effectively describes all major sources of correlation in the molecule: strong correlation through the ghosts in the fragment, and dynamical correlation through the quasiparticle description of its environment. To adapt the gGut Ansatz for molecules, we address the fact that, unlike in the lattice model previously considered, electronic interactions in molecules are not local. Hence, we explore a hierarchy of approximations of increasing accuracy capturing interactions between fragments and environment, and within the environment, and discuss how these affect the embedding description of correlations in the whole molecule. We will compare the accuracy of the gGut model with established methods to capture strong correlation within active space formulations, and assess the realistic use of this novel approximation to the theoretical description of correlated molecular clusters.

Charge order textures induced by non-linear couplings in a half-doped manganite

The self-organization of strongly interacting electrons into superlattice structures underlies the properties of many quantum materials. How these electrons arrange within the superlattice dictates what symmetries are broken and what ground states are stabilized. Here we show that cryogenic scanning transmission electron microscopy (cryo-STEM) enables direct mapping of local symmetries and order at the intra-unit-cell level in the model charge-ordered system Nd_1/2Sr_1/2MnO₃. In addition to imaging the prototypical site-centered charge order, we discover the nanoscale coexistence of an exotic intermediate state which mixes site and bond order and breaks inversion symmetry. We further show that nonlinear coupling of distinct lattice modes controls the selection between competing ground states. The results demonstrate the importance of lattice coupling for understanding and manipulating the character of electronic self-organization and that cryo-STEM can reveal local order in strongly correlated systems at the atomic scale.

In this paper, the authors demonstrate that cryogenic scanning transmission electron microscopy allows for the direct mapping of the local arrangements and symmetries of electronic order, providing a useful method for studying strongly correlated systems. They show this using the example of Nd1/2Sr1/2MnO3, a model charge ordered material.

Accurate Formula for the Macroscopic Polarization of Strongly Correlated Materials

The many-body Berry phase formula for macroscopic polarization is approximated by a sum of natural orbital geometric phases with fractional occupation numbers accounting for the dominant correlation effects. This formula accurately reproduces the exact polarization in the Rice-Mele-Hubbard model across the band insulator-Mott insulator transition. A similar formula based on a reduced Berry curvature accurately predicts the interaction-induced quenching of Thouless topological charge pumping.

Intrinsic Two-Dimensional Ferroelectricity with Dipole Locking

Out-of-plane ferroelectricity with a high transition temperature in ultrathin films is important for the exploration of new domain physics and scaling down of memory devices. However, depolarizing electrostatic fields and interfacial chemical bonds can destroy this long-range polar order at two-dimensional (2D) limit. Here we report the experimental discovery of the locking between out-of-plane dipoles and in-plane lattice asymmetry in atomically thin In_{2}Se_{3} crystals, a new stabilization mechanism leading to our observation of intrinsic 2D out-of-plane ferroelectricity. Through second harmonic generation spectroscopy and piezoresponse force microscopy, we found switching of out-of-plane electric polarization requires a flip of nonlinear optical polarization that corresponds to the inversion of in-plane lattice orientation. The polar order shows a very high transition temperature (∼700  K) without the assistance of extrinsic screening. This finding of intrinsic 2D ferroelectricity resulting from dipole locking opens up possibilities to explore 2D multiferroic physics and develop ultrahigh density memory devices.

Nonreciprocal current from electron interactions in noncentrosymmetric crystals: roles of time reversal symmetry and dissipation

In noncentrosymmetric crystals with broken inversion symmetry [Formula: see text], the I-V (I: current, V: voltage) characteristic is generally expected to depend on the direction of I, which is known as nonreciprocal response and, for example, found in p-n junction. However, it is a highly nontrivial issue in translationally invariant systems since the time-reversal symmetry T plays an essential role, where the two states at crystal momenta k and -k are connected in the band structure. Therefore, it has been considered that the external magnetic field (B) or the magnetic order which breaks the T-symmetry is necessary to realize the nonreciprocal I-V characteristics, i.e., magnetochiral anisotropy. Here we theoretically show that the electron correlation in T-broken multi-band systems can induce nonreciprocal I-V characteristics without T-breaking. An analog of Onsager's relation shows that nonreciprocal current response without T -breaking generally requires two effects: dissipation and interactions. By using nonequilibrium Green's functions, we derive general formula of the nonreciprocal response for two-band systems with onsite interaction. The formula is applied to Rice-Mele model, a representative 1D model with inversion breaking, and some candidate materials are discussed. This finding offers a coherent understanding of the origin of nonreciprocal I-V characteristics, and will pave a way to design it.

Probing the Bond Order Wave Phase Transitions of the Ionic Hubbard Model by Superlattice Modulation Spectroscopy

An exotic phase, the bond order wave, characterized by the spontaneous dimerization of the hopping, has been predicted to exist sandwiched between the band and Mott insulators in systems described by the ionic Hubbard model. Despite growing theoretical evidence, this phase still evades experimental detection. Given the recent realization of the ionic Hubbard model in ultracold atomic gases, we propose here to detect the bond order wave using superlattice modulation spectroscopy. We demonstrate, with the help of time-dependent density-matrix renormalization group and bosonization, that this spectroscopic approach reveals characteristics of both the Ising and Kosterlitz-Thouless transitions signaling the presence of the bond order wave phase. This scheme also provides insights into the excitation spectra of both the band and Mott insulators.

Concept of Quantum Geometry in Optoelectronic Processes in Solids: Application to Solar Cells

The concept of topology is becoming more and more relevant to the properties and functions of electronic materials including various transport phenomena and optical responses. A pedagogical introduction is given here to the basic ideas and their applications to optoelectronic processes in solids.

Topological nature of nonlinear optical effects in solids

There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by strong light irradiation to materials that results in nonlinear polarizations in the electric field. These are of great importance in studying the physics of excited states of the system as well as for applications to optical devices and solar cells. Nonlinear properties of materials are usually described by nonlinear susceptibilities, which have complex expressions including many matrix elements and energy denominators. On the other hand, a nonequilibrium steady state under an electric field periodic in time has a concise description in terms of the Floquet bands of electrons dressed by photons. We show theoretically, using the Floquet formalism, that various nonlinear optical effects, such as the shift current in noncentrosymmetric materials, photovoltaic Hall response, and photo-induced change of order parameters under the continuous irradiation of monochromatic light, can be described in a unified fashion by topological quantities involving the Berry connection and Berry curvature. We found that vector fields defined with the Berry connections in the space of momentum and/or parameters govern the nonlinear responses. This topological view offers a route to designing nonlinear optical materials.

Exploring competing density order in the ionic Hubbard model with ultracold fermions

We realize and study the ionic Hubbard model using an interacting two-component gas of fermionic atoms loaded into an optical lattice. The bipartite lattice has a honeycomb geometry with a staggered energy offset that explicitly breaks the inversion symmetry. Distinct density-ordered phases are identified using noise correlation measurements of the atomic momentum distribution. For weak interactions the geometry induces a charge density wave. For strong repulsive interactions we detect a strong suppression of doubly occupied sites, as expected for a Mott insulating state, and the externally broken inversion symmetry is not visible anymore in the density distribution. The local density distributions in different configurations are characterized by measuring the number of doubly occupied lattice sites as a function of interaction and energy offset. We further probe the excitations of the system using direction dependent modulation spectroscopy and discover a complex spectrum, which we compare with a theoretical model.

Resolving voltage-time dilemma using an atomic-scale lever of subpicosecond electron-phonon interaction

Nanoelectronic memory based on trapped charge need to be small and fast, but fundamentally it faces a voltage-time dilemma because the requirement of a high-energy barrier for data retention under zero/low electrical stimuli is incompatible with the demand of a low-energy barrier for fast switching under a modest programming voltage. One solution is to embed an atomic-level lever of localized electron-phonon interaction to autonomously reconfigure trap-site's barrier in accordance to the electron-occupancy of the site. Here we demonstrate an atomically levered resistance-switching memory built on locally flexible amorphous nanometallic thin films: charge detrapping can be triggered by a mechanical force, the fastest one being a plasmonic Lorentz force induced by a nearby electron or positron bunch passing in 10(-13) s. The observation provided the first real-time evidence of an electron-phonon interaction in action, which enables nanometallic memory to turn on at a subpicosecond speed yet retain long-term memory, thus suitable for universal memory and other nanoelectron applications.

Inclusion of intersite spatial correlations in the alloy analogy approach to the half-filled ionic Hubbard model

Using the nonlocal coherent-potential approximation we study the effect of intersite spatial correlations on the transition from band insulator to metal as well as from metal to Mott insulator in the 'alloy analogy' approach to the paramagnetic solution of the half-filled ionic Hubbard model. We find that intersite spatial correlations enhance the metallic phase.

Electronic ferroelectricity in a molecular crystal with large polarization directing antiparallel to ionic displacement

Ferroelectric polarization of 6.3  μC cm(-2) is induced by the neutral-to-ionic transition, upon which nonpolar molecules of electron donor tetrathiafulvalene (TTF) and acceptor p-chloranil (CA) are incompletely ionized to ±0.60e and dimerized along the molecular stacking chain. We find that the ferroelectric properties are governed by intermolecular charge transfer rather than simple displacement of static point charge on molecules. The observed polarization and poling effect on the absolute structural configuration can be interpreted in terms of electronic ferroelectricity, which not only exhibits antiparallel polarity to the ionic displacement but also enhances the polarization more than 20 times that of the point-charge model.

Dynamics in the one-dimensional extended ionic Hubbard model

We investigate single-particle spectral densities and dynamical charge and spin structure factors of the one-dimensional extended ionic Hubbard model in the band insulator regime by using the perturbative continuous unitary transformations method. The one-body staggered potential is considered as the unperturbed part and the hopping term, on-site electron-electron interaction, and the nearest-neighbor repulsive interaction are treated as the perturbations. The excitation spectrum of this model was determined in a previous work (Hafez and Jafari 2010 Eur. Phys. J. B 78 323). It was shown that when the intersite interaction is off, there are two antibound state modes and one bound state mode in the singlet channel and two bound state modes in the triplet channel, while for finite values of intersite interaction two bound state modes were found in each channel. Our results for dynamical charge and spin structure factors indicate that only one of two bound/antibound state modes can be probed by electron-energy-loss spectroscopy and inelastic neutron scattering experiments.

Metal-insulator transitions in the half-filled ionic Hubbard model

We study electronic phase transitions in the half-filled ionic Hubbard model with an on-site Coulomb repulsion U and an ionic energy Δ by using the coherent potential approximation. For a fixed and finite Δ two transitions from the band insulator via a metallic state to a Mott insulator are found with increasing U. The values of the critical correlation-driven metal-insulator transitions U(c1)(Δ) and U(c2)(Δ) are estimated. Our results are in reasonable agreement with the ones obtained by single-site dynamical mean-field theory and determinant quantum Monte Carlo simulation.

Local crystallography of crystals with disorder

The assumption of perfect periodicity in the crystal lattice is the most basic tenet of crystallography. However, many materials are not crystalline. Even when they are the atomic structure of real materials is often less than perfectly periodic, and usually deviations from perfect periodicity have significant effects on their properties. Thus in order to characterize the structure of real materials by diffraction the crystallographic approaches need to be complemented by other methods focusing on disorder. B. E. Warren was a pioneer of such alternative, non-crystallographic approaches, including the method of atomic pair-density function (PDF) analysis. With the advent of synchrotron based radiation sources, such as pulsed neutron sources and synchrotron radiation sources, it recently became possible to apply the PDF technique on crystals with and without disorder, covering the whole spectrum of structural order and disorder. Here some of the recent progresses in this approach made in my research group are reviewed.

Quantum Monte Carlo study of an interaction-driven band-insulator-to-metal transition

We study the transitions from band insulator to metal to Mott insulator in the ionic Hubbard model on a two-dimensional square lattice using determinant quantum Monte Carlo. Evaluation of the temperature dependence of the conductivity demonstrates that the metallic region extends for a finite range of interaction values. The Mott phase at strong coupling is accompanied by antiferromagnetic order. Inclusion of these intersite correlations changes the phase diagram qualitatively compared to dynamical mean field theory.

Correlated insulated phase suggests bond order between band and mott insulators in two dimensions

We investigate the ground state phase diagram of the half-filled repulsive Hubbard model in two dimensions in the presence of a staggered potential Delta, the so-called ionic Hubbard model, using cluster dynamical mean-field theory. We find that for large Coulomb repulsion, U >> Delta, the system is a Mott insulator (MI). For weak to intermediate values of Delta, on decreasing U, the Mott gap closes at a critical value Uc1(Delta) beyond which a correlated insulating phase with possible bond order is found. Further, this phase undergoes a first-order transition to a band insulator (BI) at Uc2(Delta) with a finite charge gap at the transition. For large Delta, there is a direct first-order transition from a MI to a BI with a single metallic point at the phase boundary.

Disorder-enhanced dielectric response of nanoscale and mesoscopic insulators

Enhancement of the dielectric response of insulators by disorder is theoretically proposed, where the quantum interference of electronic waves through the nanoscale or mesoscopic system and its change due to external perturbations control the polarization. In the disordered case with all the states being localized, the resonant tunneling, which is topologically protected, plays a crucial role, and enhances the dielectric response by a factor 30-40 compared with the pure case. The realization of this idea with accessible materials or structures is also discussed.

Can correlations drive a band insulator metallic?

We analyze the effects of the on-site Coulomb repulsion U on a band insulator using dynamical mean field theory (DMFT). We find the surprising result that the gap is suppressed to zero at a critical Uc1 and remains zero within a metallic phase. At a larger Uc2 there is a second transition from the metal to a Mott insulator, in which the gap increases with increasing U. These results are qualitatively different from Hartree-Fock theory which gives a monotonically decreasing but nonzero insulating gap for all finite U.

Topological nature of polarization and charge pumping in ferroelectrics

Electric polarization in insulators is represented by the transferred charge through a shift of the Bloch wave functions induced by an adiabatic change of external parameters Q-->. It is found that this covalent/quantum contribution is determined nonlocally by the topological structure in the Q--> space. The condition for the charge pumping for a cyclic change of Q--> is also obtained. Applications of this picture to various organic ferroelectrics and BaTiO3 are discussed.

Detection of topological transitions by transport through molecules and nanodevices

We analyze the phase transitions of an interacting electronic system weakly coupled to free-electron leads by considering its zero-bias conductance. This is expressed in terms of two effective impurity models for the cases with and without spin degeneracy. Using the half-filled ionic Hubbard ring, we demonstrate that the weight of the first conductance peak as a function of external flux or of the difference in gate voltages between even and odd sites allows one to identify the topological charge transition between a correlated insulator and a band insulator.

Exact bond ordered ground state for the transition between the band and the Mott insulator

We derive an effective Hamiltonian H(eff) for an ionic Hubbard chain, valid for t<<U,Delta, where t is the hopping, U is the Coulomb repulsion, and Delta is the charge-transfer energy. H(eff) is the minimal model for describing the transition between the band insulator (BI) (Delta-U>>t) and the Mott insulator (MI) (U-Delta>>t). Using spin-particle transformations [Phys. Rev. Lett. 86, 1082 (2001)]], we map H(eff)(U=Delta) into an SU(3) antiferromagnetic Heisenberg model whose exact ground state is known. In this way, we show rigorously that a spontaneously dimerized insulating ferroelectric phase appears in the transition region between the BI and the MI.

Giant infrared intensity of the Peierls mode at the neutral-ionic phase transition

We present exact diagonalization results on a modified Peierls-Hubbard model for the neutral-ionic phase transition. The ground state potential energy surface and the infrared intensity of the Peierls mode point to a strong, nonlinear electron-phonon coupling, with effects that are dominated by the proximity to the electronic instability rather than by electronic correlations. The huge infrared intensity of the Peierls mode at the ferroelectric transition is related to the temperature dependence of the dielectric constant of mixed-stack organic crystals.