Mott State Research Articles

The Simplest Model for Doped Poly(3,4‐ethylenedioxythiophene) (PEDOT): Single‐crystalline EDOT Dimer Radical Cation Salts

Invited for the cover of this issue is the group of Tomoko Fujino and Hatsumi Mori at the University of Tokyo. The image depicts the structural information of doped PEDOT uncovered by the single-crystalline EDOT dimer model. Read the full text of the article at 10.1002/chem.202005333.

Jeff=32 metallic phase and unconventional superconductivity in GaTa4Se8

By means of density functional theory plus dynamical mean-field theory (DFT+DMFT) calculations and resonant inelastic x-ray scattering (RIXS) experiments, we investigate the high-pressure phases of the spin-orbit-coupled $J_{\rm{eff}}=3/2$ insulator GaTa$_4$Se$_8$. Its metallic phase, derived from the Mott state by applying pressure, is found to carry $J_{\rm{eff}}=3/2$ moments. The characteristic excitation peak in the RIXS spectrum maintains its destructive quantum interference of $J_{\rm{eff}}$ at the Ta $L_2$-edge up to 10.4 GPa. Our exact diagonalization based DFT+DMFT calculations including spin-orbit coupling also reveal that the $J_{\rm{eff}}=3/2$ character can be clearly identified under high pressure. These results establish the intriguing nature of the correlated metallic magnetic phase, which represents the first confirmed example of $J_{\rm{eff}}$=3/2 moments residing in a metal. They also indicate that the pressure-induced superconductivity is likely unconventional and influenced by these $J_{\rm{eff}}=3/2$ moments. Based on a self-energy analysis, we furthermore propose the possibility of doping-induced superconductivity related to a spin-freezing crossover.

The Simplest Model for Doped Poly(3,4-ethylenedioxythiophene) (PEDOT): Single-crystalline EDOT Dimer Radical Cation Salts.

Although doped poly(3,4-ethylenedioxythiophene) (PEDOT) is extensively used in electronic devices, their molecular-weight distributions and inadequately defined structures have hindered the elucidation of their underlying conduction mechanism. In this study, we introduce the simplest discrete oligomer models: EDOT dimer radical cation salts. Single-crystal structural analyses revealed their one-dimensional (1D) columnar structures, in which the donors were uniformly stacked. Band calculations identified 1D metallic band structures with a strong intracolumnar orbital interaction (band width W≈1 eV), implying the origin of the high conductivity of doped PEDOT. Interestingly, the salts exhibited semiconducting behavior reminiscent of genuine Mott states as a result of electron-electron repulsion (U) dominant over W. This study realized basic models with tunable W and U to understand the conduction mechanism of doped PEDOT through structural modification in oligomers, including the conjugation length.

Oxygen vacancy induced site-selective Mott transition in LaNiO3

While defects such as oxygen vacancies in correlated materials can modify their electronic properties dramatically, understanding the microscopic origin of electronic correlations in materials with defects has been elusive. Lanthanum nickelate with oxygen vacancies, LaNiO$_{3-x}$, exhibits the metal-to-insulator transition as the oxygen vacancy level $x$ increases from the stoichiometric LaNiO$_3$. In particular, LaNiO$_{2.5}$ exhibits a paramagnetic insulating phase, also stabilizing an antiferromagnetic state below $T_N\simeq152$K. Here, we study the electronic structure and energetics of LaNiO$_{3-x}$ using first-principles. We find that LaNiO$_{2.5}$ stabilizes a vacancy-ordered structure with an insulating ground state and the nature of the insulating phase is a "site-selective" paramagnetic Mott state as obtained using density functional theory plus dynamical mean field theory (DFT+DMFT). The Ni octahedron site develops a Mott insulating state with strong correlations as the Ni $e_g$ orbital is half-filled while the Ni square-planar site with apical oxygen vacancies becomes a band insulator. Our oxygen vacancy results can not be explained by the pure change of the Ni oxidation state alone within the rigid band shift approximation. Our DFT+DMFT density of states explains that the peak splitting of unoccupied states in LaNiO$_{3-x}$ measured by the experimental X-ray absorption spectra originates from two nonequivalent Ni ions in the vacancy-ordered structure.

Spin-selective insulators in Bose-Fermi mixtures

We investigate an imbalanced mixture composed of two-color fermions and scalar bosons in the hard-core limit, considering repulsive and attractive interspecies and intraspecies interactions. The interplay between commensurability, repulsive interactions and imbalance generates three insulating phases: a mixed Mott state and two spin-selective insulators characterized by the commensurability relations $\rho_B+\rho^{\uparrow,(\downarrow)}_F=1$. For an attractive coupling between fermions and bosons, we found the relations $\rho_B-\rho^{\uparrow,(\downarrow)}_F=0$ for the spin-selective insulators. State-of-the-art cold-atoms setups constitute ideal platforms to implement these unveiled insulating states and verify their commensurability relations.

Doping and temperature evolutions of optical response of Sr3(Ir1-xRux)2O7

We report on optical spectroscopic study of the Sr3(Ir1-xRux)2O7 system over a wide doping regime. We find that the changes in the electronic structure occur in the limited range of the concentration of Ru ions where the insulator–metal transition occurs. In the insulating regime, the electronic structure associated with the effective total angular momentum Jeff = 1/2 Mott state remains robust against Ru doping, indicating the localization of the doped holes. Upon entering the metallic regime, the Mott gap collapses and the Drude-like peak with strange metallic character appears. The evolution of the electronic structure registered in the optical data can be explained in terms of a percolative insulator–metal transition. The phonon spectra display anomalous doping evolution of the lineshapes. While the phonon modes of the compounds deep in the insulating and metallic regimes are almost symmetric, those of the semiconducting compound with x = 0.34 in close proximity to the doping-driven insulator–metal transition show a pronounced asymmetry. The temperature evolution of the phonon modes of the x = 0.34 compound reveals the asymmetry is enhanced in the antiferromagnetic state. We discuss roles of the S = 1 spins of the Ru ions and charge excitations for the conspicuous lineshape asymmetry of the x = 0.34 compound.

Nonlinear dynamical response of interacting bosons to synthetic electric field

We theoretically study the non-linear response of interacting neutral bosonic gas in a synthetically driven one-dimensional optical lattice. In particular, we examine the bosonic analogue of electronic higher harmonic generation in a strong time-dependent synthetic vector potential manifesting itself as the synthetic electric field. We show that the vector potential can generate reasonably high harmonics in the insulating regime, while the superfluid regime exhibits only a few harmonics. In the insulating regime, the number of harmonics increases with the increase in the strength of the vector potential. This originates primarily due to the field-driven resonant and non-resonant excitations in the neutral Mott state and their recombination with the ground state. If the repulsive interaction between two atoms ($U$) is close to the strength of the gauge potential ($A_0$), the resonant quasiparticle-quasihole pairs on nearest-neighbor sites, namely dipole states are found to a play a dominant role in the generating higher harmonics. However, in the strong-field limit $A_0\gg U$, the nonresonant states where quasiparticle-quasihole pairs are not on nearest-neighbor sites give rise to higher harmonics.

Comprehensive Electrical Control of Metamagnetic Transition of a Quasi-2D Antiferromagnet by In Situ Anisotropic Strain.

Effective nonmagnetic control of the spin structure is at the forefront of the study for functional quantum materials. This study demonstrates that, by applying an anisotropic strain up to only 0.05%, the metamagnetic transition field of spin-orbit-coupled Mott insulator Sr2 IrO4 can be in situ modulated by almost 300%. Simultaneous measurements of resonant X-ray scattering and transport reveal that this drastic response originates from the complete strain-tuning of the transition between the spin-flop and spin-flip limits, and is always accompanied by large elastoconductance and magnetoconductance. This enables electrically controllable and electronically detectable metamagnetic switching, despite the antiferromagnetic insulating state. The obtained strain-magnetic field phase diagram reveals that C4 -symmetry-breaking anisotropy is introduced by strain via pseudospin-lattice coupling, directly demonstrating the pseudo-Jahn-Teller effect of spin-orbit-coupled complex oxides. The extracted coupling strength is much weaker than the superexchange interactions, yet crucial for the spontaneous symmetry-breaking, affording the remarkably efficient strain-control.

Scaling theory for Mott–Hubbard transitions: I. T = 0 phase diagram of the 1/2-filled Hubbard model

We present a T = 0 K renormalization group (RG) phase diagram for the electronic Hubbard model in two dimensions on the square lattice at half filling. The RG procedure treats quantum fluctuations in the single particle occupation number nonperturbatively via the unitarily decoupling of one electronic state at every RG step. The resulting phase diagram thus possesses the quantum fluctuation energy scale (ω) as one of its axes. A relation is derived between ω and the effective temperature scale upto which gapless, as well as emergent gapped phases can be obtained. We find that the normal and insulating phases of the half-filled Hubbard model correspond, for any on-site repulsion, to a marginal Fermi liquid normal phase and a topologically-ordered gapped Mott insulating liquid respectively. The marginal Fermi liquid is found to arise from singular forward scattering in directions normal to the nested Fermi surface, while singular backscattering events lead to Mott liquid state. The transition between these two phases involves passage through a pseudogapped phase bookended by Fermi surface topology-changing Lifshitz transitions. The pseudogap phase is observed to arise from the electronic differentiation encoded within the nested Fermi surface, and involves the gradual gapping of the Fermi surface from antinodes to nodes via charge and spin excitations that are mutually entangled. We obtain effective Hamiltonians for various phases, as well as wavefunctions for the low-energy many-body eigenstates of the Mott liquid. Benchmarking of the ground-state energy per particle and the double-occupancy fraction for the Mott liquid against existing numerical results yields excellent agreement. Presence of a Néel ordering symmetry-breaking perturbation in the RG leads to an antiferromagnetic spin-ordered charge insulating Mott state. Our results thus offer novel insights on a variety of aspects of the Mott–Hubbard problem, and can be extended to the doped system.

Doublon bottleneck in the ultrafast relaxation dynamics of hot electrons in 1T−TaS2

Employing time-resolved photoelectron spectroscopy we analyze the relaxation dynamics of hot electrons in the charge density wave / Mott material 1T-TaS_2. At 1.2 eV above the Fermi level we observe a hot electron lifetime of 12 +- 5 fs in the metallic state and of 60 +- 10 fs in the broken symmetry ground state - a direct consequence of the reduced phase space for electron-electron scattering determined by the Mott gap. Boltzmann equation calculations which account for the interaction of hot electrons in a Bloch band with a doublon-holon excitation in the Mott state provide insight into the unoccupied electronic structure in the correlated state.

Strong antiferromagnetic interaction owing to a large trigonal distortion in the spin-orbit-coupled honeycomb lattice iridate CdIrO3

We investigated the magnetic properties of the ilmenite-type iridate CdIrO$_3$ with a honeycomb lattice formed by Ir$^{4+}$ ions prepared via a solid-state metathesis. The magnetization measurements with using the powder sample reveal a large effective magnetic moment and a fairly strong antiferromagnetic interaction, indicating a deviation from the Kitaev model. Considering the relationship between magnetism and crystal structure in CdIrO$_3$ with comparing with the other ilmenite-type iridates ZnIrO$_3$ and MgIrO$_3$, we conclude that insulating CdIrO$_3$ cannot be describe as a $J_{\rm eff} = 1/2$ Mott state owing to a metathetically-stabilized large trigonal distortion of IrO$_6$ octahedra.

Charge and spin degrees of freedom in strongly correlated systems: Mott states opposite Hund’s metals

A correlated metallic state can arise as a result of the presence either strong charge or strong spin fluctuations. In the first case, as was shown first in (2004 Phys. Today 57 53) for the Hubbard model on the Bethe lattice, the system is a correlated metallic state close to the Mott-insulator state if the ratio of the value of the Coulomb interaction parameter U and the band width W is . The later case exist if and Hund’s exchange parameter . In both cases narrowing of the bands near the Fermi level and renormalization of the effective electron mass is observed, although the mechanism for realizing this state will be fundamentally different. We performed the electronic structure calculations of the paramagnetic phase -iron which is a typical Hund’s metal. We showed that the statistical distribution of charge between possible electronic d-configurations has a very weak dependence on the exchange interaction and is specific for metals. At the same time, the distribution of statistical weights between different spin configurations fundamentally changes with the inclusion of J. If we neglect Hund’s interaction by setting J = 0, the contributions from the low-spin configurations for all possible charge states dominate. The exchange interaction causes a redistribution of probability in favor of high-spin multiplets, leading to the formation of a larger local moment. We also performed calculations for the two-bands half-filled model. By varying the values of the Coulomb and Hund’s exchange interaction parameters, we reproduced the region of the phase diagram of the model in which the system undergoes a transition from the Mott-insulator state to the Hund’s metal. This transition is accompanied by a change in the statistical probability distribution of possible multiple configurations. In the region corresponding to the Hund’s metal state, a change of J leads to the effect of weights redistribution similar that we observe in -iron.

Hybridization fluctuations in the half-filled periodic Anderson model

Motivated by recent photoemission and pump-probe experiments, we report determinant Quantum Monte Carlo simulations of hybridization fluctuations in the half-filled periodic Anderson model. A tentative phase diagram is constructed based solely on hybridization fluctuation spectra and reveals a crossover regime between an unhybridized selective Mott state and a fully hybridized Kondo insulating state. This intermediate phase exhibits nonlocal hybridization fluctuations and consequentially the so-called "band bending" and a direct hybridization gap as observed in angle-resolved photoemission spectroscopy and optical conductivity. This connects the band bending with the nonlocal hybridization fluctuations as proposed in latest ultrafast optical pump-probe experiment. The Kondo insulating state is only established at lower temperatures with the development of sufficiently strong inter-site hybridization correlations. Our work suggests a unified picture for interpreting recent photoemission, pump-probe, and optical observations and provides numerical evidences for the importance of hybridization fluctuations in heavy fermion physics.

Momentum-Space Atom Correlations in a Mott Insulator

We report on the investigation of the three-dimensional single-atom-resolved distributions of bosonic Mott insulators in momentum-space. Firstly, we measure the two-body and three-body correlations deep in the Mott regime, finding a perfectly contrasted bunching whose periodicity reproduces the reciprocal lattice. In addition, we show that the two-body correlation length is inversely proportional to the in-trap size of the Mott state with a pre-factor in agreement with the prediction for an incoherent state occupying a uniformly filled lattice. Our findings indicate that the momentum-space correlations of a Mott insulator at small tunnelling is that of a many-body ground-state with Gaussian statistics. Secondly, in the Mott insulating regime with increasing tunnelling, we extract the spectral weight of the quasi-particles from the momentum density profiles. On approaching the transition towards a superfluid, the momentum spread of the spectral weight is found to decrease as a result of the increased mobility of the quasi-particles in the lattice. While the shapes of the observed spectral weight agree with the ones predicted by perturbative many-body calculations, the fitted mobilities are larger than the theoretical ones. This discrepancy is similar to that previously reported on the time-of-flight visibility.

High-temperature superconductivity in monolayer Bi2Sr2CaCu2O8+δ.

Although copper oxide high-temperature superconductors constitute a complex and diverse material family, they all share a layered lattice structure. This curious fact prompts the question of whether high-temperature superconductivity can exist in an isolated monolayer of copper oxide, and if so, whether the two-dimensional superconductivity and various related phenomena differ from those of their three-dimensional counterparts. The answers may provide insights into the role of dimensionality in high-temperature superconductivity. Here we develop a fabrication process that obtains intrinsic monolayer crystals of the high-temperature superconductor Bi2Sr2CaCu2O8+δ (Bi-2212; here, a monolayer refers to a half unit cell that contains two CuO2 planes). The highest superconducting transition temperature of the monolayer is as high as that of optimally doped bulk. The lack of dimensionality effect on the transition temperature defies expectations from the Mermin-Wagner theorem, in contrast to the much-reduced transition temperature in conventional two-dimensional superconductorssuch as NbSe2. The properties of monolayer Bi-2212 become extremely tunable; our survey of superconductivity, the pseudogap, charge order and the Mott state at various doping concentrations reveals that the phases are indistinguishable from those in the bulk. Monolayer Bi-2212 therefore displays all the fundamental physics of high-temperature superconductivity. Our results establish monolayer copper oxides as a platform for studying high-temperature superconductivity and other strongly correlated phenomena in two dimensions.

Atomic-scale fragmentation and collapse of antiferromagnetic order in a doped Mott insulator

Disentangling the relationship between the insulating state with a charge gap and the magnetic order in an antiferromagnetic (AF) Mott insulator remains difficult due to inherent phase separation as the Mott state is perturbed. Measuring magnetic and electronic properties at the atomic length scales would provide crucial insight, but this is yet to be experimentally achieved. Here we use spectroscopic-imaging spin-polarized scanning tunneling microscopy (SP-STM) to visualize periodic spin-resolved modulations originating from the AF order in a relativistic Mott insulator Sr2IrO4, and study these as a function of doping. We find that near insulator-to-metal transition (IMT), the long-range AF order melts into a fragmented state with short-range AF correlations. Crucially, we discover that the short-range AF order is locally uncorrelated with the observed spectral gap magnitude. This strongly suggests that short range AF correlations are unlikely to be the culprit behind inhomogeneous gap closing and the emergence of pseudogap regions near IMT. Our work establishes SP-STM as a powerful tool for revealing atomic-scale magnetic information in complex oxides.

Interfacial charge-transfer Mott state in iridate–nickelate superlattices

We investigate [Formula: see text]/[Formula: see text] superlattices in which we observe a full electron transfer at the interface from Ir to Ni, triggering a massive structural and electronic reconstruction. Through experimental characterization and first-principles calculations, we determine that a large crystal field splitting from the distorted interfacial [Formula: see text] octahedra surprisingly dominates over the spin-orbit coupling and together with the Hund's coupling results in the high-spin (S = 1) configurations on both the Ir and Ni sites. This demonstrates the power of interfacial charge transfer in coupling lattice, charge, orbital, and spin degrees of freedom, opening fresh avenues of investigation of quantum states in oxide superlattices.

Topological Mott insulator with bosonic edge modes in one-dimensional fermionic superlattices

We investigate topological phase transitions driven by interaction and identify a novel topological Mott insulator state in one-dimensional fermionic optical superlattices through numerical density matrix renormalization group (DMRG) method. Remarkably, the low-energy edge excitations change from spin-1/2 fermionic single-particle modes to spin-1 bosonic collective modes across the phase transition. Due to spin-charge separation, the low-energy theory is governed by an effective spin superexchange model, whereas the charge degree of freedom is fully gapped out. Such topological Mott state can be characterized by a spin Chern number and gapless magnon modes protected by a finite spin gap. The proposed experimental setup is simple and may pave the way for the experimental observation of exotic topological Mott states.

Doping induced Mott collapse and possible density wave instabilities in (Sr1\u2212xLax)3Ir2O7

The path from a Mott insulating phase to high temperature superconductivity encounters a rich set of unconventional phenomena involving the insulator-to-metal transition (IMT), such as emergent electronic orders and pseudogaps, that ultimately affect the condensation of Cooper pairs. A huge hindrance to understanding the origin of these phenomena is the difficulty in accessing doping levels near the parent state. The Jeff = 1/2 Mott state of the perovskite strontium iridates has revealed intriguing parallels to the cuprates, with the advantage that it provides unique access to the Mott transition. Here, we exploit this accessibility to study the IMT and the possible nearby electronic orders in the electron-doped bilayer iridate (Sr1 − xLax)3Ir2O7. Using spectroscopic imaging scanning tunneling microscopy, we image the La dopants in the top as well as the interlayer SrO planes. Surprisingly, we find a disproportionate distribution of La between these layers with the interlayer La being primarily responsible for the IMT. This reveals the distinct site-dependent effects of dopants on the electronic properties of bilayer systems. Electron doping also results in charge reordering. We find unidirectional electronic order concomitant with the structural distortion known to exist in this system. Intriguingly, similar to the single layer iridate, we also find local resonant states forming a checkerboard-like pattern trapped by La. This suggests that multiple charge orders may exist simultaneously in Mott systems, even with only one band crossing the Fermi energy.

Signatures of tunable superconductivity in a trilayer graphene moiré superlattice

Understanding the mechanism of high-transition-temperature (high-Tc) superconductivity is a central problem in condensed matter physics. It is often speculated that high-Tc superconductivity arises in a doped Mott insulator1 as described by the Hubbard model2-4. An exact solution of the Hubbard model, however, is extremely challenging owing to the strong electron-electron correlation in Mott insulators. Therefore, it is highly desirable to study a tunable Hubbard system, in which systematic investigations of the unconventional superconductivity and its evolution with the Hubbard parameters can deepen our understanding of the Hubbard model. Here we report signatures of tunable superconductivity in an ABC-trilayer graphene (TLG) and hexagonal boron nitride (hBN) moiré superlattice. Unlike in 'magic angle' twisted bilayer graphene, theoretical calculations show that under a vertical displacement field, the ABC-TLG/hBN heterostructure features an isolated flat valence miniband associated with a Hubbard model on a triangular superlattice5,6 where the bandwidth can be tuned continuously with the vertical displacement field. Upon applying such a displacement field we find experimentally that the ABC-TLG/hBN superlattice displays Mott insulating states below 20 kelvin at one-quarter and one-half fillings of the states, corresponding to one and two holes per unit cell, respectively. Upon further cooling, signatures of superconductivity ('domes') emerge below 1 kelvin for the electron- and hole-doped sides of the one-quarter-filling Mott state. The electronic behaviour in the ABC-TLG/hBN superlattice is expected to depend sensitively on the interplay between the electron-electron interaction and the miniband bandwidth. By varying the vertical displacement field, we demonstrate transitions from the candidate superconductor to Mott insulator and metallic phases. Our study shows that ABC-TLG/hBN heterostructures offer attractive model systems in which to explore rich correlated behaviour emerging in the tunable triangular Hubbard model.