Doped Mott Insulator Research Articles

Strongly Enhanced Thermal Transport in a Lightly Doped Mott Insulator at Low Temperature

We show how a lightly doped Mott insulator has hugely enhanced electronic thermal transport at low temperature. It displays universal behavior independent of the interaction strength when the carriers can be treated as nondegenerate fermions and a nonuniversal "crossover" region where the Lorenz number grows to large values, while still maintaining a large thermoelectric figure of merit. The electron dynamics are described by the Falicov-Kimball model which is solved for arbitrary large on-site correlation with a dynamical mean-field theory algorithm on a Bethe lattice. We show how these results are generic for lightly doped Mott insulators as long as the renormalized Fermi liquid scale is pushed to very low temperature and the system is not magnetically ordered.

Possible charge instabilities in two-dimensional doped Mott insulators

Motivated by the growing evidence of the importance of charge fluctuations in the pseudogap phase in high-temperature cuprate superconductors, we apply a large-N expansion formulated in a path integral representation of the two-dimensional t-J model on a square lattice. We study all possible charge instabilities of the paramagnetic state in leading order of the 1/N expansion. While the d-wave charge density wave (flux phase) becomes the leading instability for various choices of model parameters, we find that a d-wave Pomeranchuk (electronic nematic phase) instability occurs as a next leading one. In particular, the nematic state has a strong tendency to become inhomogeneous. In the presence of a large second nearest-neighbor hopping integral, the flux phase is suppressed and the electronic nematic instability becomes leading in a high doping region. Besides these two major instabilities, bond-order phases occur as weaker instabilities close to half-filling. Phase separation is also detected in a finite temperature region near half-filling.

Superconductivity and magnetic fluctuations in electron-doped cobaltate superconductors

We study the interplay between superconductivity and antiferromagnetic spin fluctuations in electron-doped cobaltate NaxCoO2·yH2O based on the kinetic energy driven superconductivity mechanism. We show that the superconducting state is governed by both charge carrier pairing and quasiparticle coherent, and displays a common dome-shaped phase diagram in agreement with experimental results. By calculating the dynamical spin structure factor, we theoretically find that the magnetic excitation shows a commensurate resonance peak, which locates at antiferromagnetic wave vector Q(2π/3,2π/3) for a broad range of low energies, then evolves outward into six incommensurate magnetic scattering peaks with increasing energy. Such commensurate–incommensurate spin resonance excitation should be measured by the inelastic neutron scattering (INS) technique. Our present results strongly suggest that magnetic resonance can indeed be one of the fundamental features in doped Mott insulators.

First-Matsubara-frequency rule in a Fermi liquid. II. Optical conductivity and comparison to experiment

Motivated by recent optical measurements on a number of strongly correlated electron systems, we revisit the dependence of the conductivity of a Fermi liquid $\ensuremath{\sigma}(\ensuremath{\Omega},T)$ on the frequency $\ensuremath{\Omega}$ and temperature $T$. Using the Kubo formalism and taking full account of vertex corrections, we show that the Fermi-liquid form $\mathrm{Re}{\ensuremath{\sigma}}^{\ensuremath{-}1}(\ensuremath{\Omega},T)\ensuremath{\propto}{\ensuremath{\Omega}}^{2}+4{\ensuremath{\pi}}^{2}{T}^{2}$ holds under very general conditions, namely, in any dimensionality above one, for a Fermi surface of an arbitrary shape (but away from nesting and van Hove singularities), and to any order in the electron-electron interaction. We also show that the scaling form of $\mathrm{Re}{\ensuremath{\sigma}}^{\ensuremath{-}1}(\ensuremath{\Omega},T)$ is determined by the analytic properties of the conductivity along the Matsubara axis. If a system contains not only itinerant electrons but also localized degrees of freedom which scatter electrons elastically, e.g., magnetic moments or resonant levels, the scaling form changes to $\mathrm{Re}{\ensuremath{\sigma}}^{\ensuremath{-}1}(\ensuremath{\Omega},T)\ensuremath{\propto}{\ensuremath{\Omega}}^{2}+b{\ensuremath{\pi}}^{2}{T}^{2}$, with $1\ensuremath{\le}b<\ensuremath{\infty}$. For purely elastic scattering, $b=1$. Our analysis implies that the value of $b\ensuremath{\approx}1$, reported for ${\mathrm{URu}}_{2}{\mathrm{Si}}_{2}$ and some rare-earth-based doped Mott insulators, indicates that the optical conductivity in these materials is controlled by an elastic scattering mechanism, whereas the values of $b\ensuremath{\approx}2.3$ and $5.6$, reported for underdoped cuprates and organics, correspondingly, imply that both elastic and inelastic mechanisms contribute to the optical conductivity.

Pseudogap temperature as a Widom line in doped Mott insulators

The pseudogap refers to an enigmatic state of matter with unusual physical properties found below a characteristic temperature T* in hole-doped high-temperature superconductors. Determining T* is critical for understanding this state. Here we study the simplest model of correlated electron systems, the Hubbard model, with cluster dynamical mean-field theory to find out whether the pseudogap can occur solely because of strong coupling physics and short nonlocal correlations. We find that the pseudogap characteristic temperature T* is a sharp crossover between different dynamical regimes along a line of thermodynamic anomalies that appears above a first-order phase transition, the Widom line. The Widom line emanating from the critical endpoint of a first-order transition is thus the organizing principle for the pseudogap phase diagram of the cuprates. No additional broken symmetry is necessary to explain the phenomenon. Broken symmetry states appear in the pseudogap and not the other way around.

Superconductivity in mutual Chern-Simons gauge theory

In this work, we present a topological characterization of superconductivity in a prototype electron fractionalization model for doped Mott insulators. In this model, spinons and holons are coupled via the mutual Chern-Simons gauge fields. We obtain a low-lying effective description of the collective current fluctuations by integrating out the matter fields, which replaces the conventional Ginzburg-Landau action to describe the generalized rigidity of superconductivity. The superconducting phase coherence is essentially characterized by a topological order parameter related to a Gaussian linking number, and an experiment is proposed to probe this topological property. We further show that a gauge-neutral fermionic mode can naturally emerge in this model, which behaves like a Bogoliubov quasiparticle.

Strong Coupling Superconductivity, Pseudogap, and Mott Transition

An intricate interplay between superconductivity, pseudogap, and Mott transition, either bandwidth driven or doping driven, occurs in materials. Layered organic conductors and cuprates offer two prime examples. We provide a unified perspective of this interplay in the two-dimensional Hubbard model within cellular dynamical mean-field theory on a 2×2 plaquette and using the continuous-time quantum Monte Carlo method as impurity solver. Both at half filling and at finite doping, the metallic normal state close to the Mott insulator is unstable to d-wave superconductivity. Superconductivity can destroy the first-order transition that separates the pseudogap phase from the overdoped metal, yet that normal state transition leaves its marks on the dynamic properties of the superconducting phase. For example, as a function of doping one finds a rapid change in the particle-hole asymmetry of the superconducting density of states. In the doped Mott insulator, the dynamical mean-field superconducting transition temperature T(c)(d) does not scale with the order parameter when there is a normal-state pseudogap. T(c)(d) corresponds to the local pair formation temperature observed in tunneling experiments and is distinct from the pseudogap temperature.

High-temperature superconductivity and antiferromagnetism in multilayer cuprates:63Cu and19F NMR on five-layer Ba2Ca4Cu5O10(F,O)2

We report systematic Cu- and F-NMR measurements of five-layered high-Tc cuprates Ba2Ca4Cu5O10(F,O)2. It is revealed that antiferromagnetism (AFM) uniformly coexists with superconductivity (SC) in underdoped regions, and that the critical hole density pc for AFM is ~ 0.11 in the five-layered compound. We present the layer-number dependence of AFM and SC phase diagrams in hole-doped cuprates, where pc for n-layered compounds, pc(n), increases from pc(1) ~ 0.02 in LSCO or pc(2) ~ 0.05 in YBCO to pc(5) ~ 0.11. The variation of pc(n) is attributed to interlayer magnetic coupling, which becomes stronger with increasing n. In addition, we focus on the ground-state phase diagram of CuO2 planes, where AFM metallic states in slightly doped Mott insulators change into the uniformly mixed phase of AFM and SC and into simple d-wave SC states. The maximum Tc exists just outside the quantum critical hole density, at which AFM moments on a CuO2 plane collapse at the ground state, indicating an intimate relationship between AFM and SC. These characteristics of the ground state are accounted for by the Mott physics based on the t-J model; the attractive interaction of high-Tc SC, which raises Tc as high as 160 K, is an in-plane superexchange interaction Jin (~ 0.12 eV), and the large Jin binds electrons of opposite spins between neighboring sites. It is the Coulomb repulsive interaction U ~ (> 6 eV) between Cu-3d electrons that plays a central role in the physics behind high-Tc phenomena.

High-TcSuperconductivity and Antiferromagnetism in Multilayered Copper Oxides –A New Paradigm of Superconducting Mechanism–

High-temperature superconductivity (HTSC) in copper oxides emerges on a layered CuO 2 plane when an antiferromagnetic Mott insulator is doped with mobile hole carriers. We review extensive studies of multilayered copper oxides by site-selective nuclear magnetic resonance (NMR), which have uncovered the intrinsic phase diagram of antiferromagnetism (AFM) and HTSC for a disorder-free CuO 2 plane with hole carriers. We present our experimental findings such as the existence of the AFM metallic state in doped Mott insulators, the uniformly mixed phase of AFM and HTSC, and the emergence of d -wave SC with a maximum T c just outside a critical carrier density, at which the AFM moment on a CuO 2 plane disappears. These results can be accounted for by the Mott physics based on the t – J model. The superexchange interaction J in among spins plays a vital role as a glue for Cooper pairs or mobile spin-singlet pairs, in contrast to the phonon-mediated attractive interaction among electrons established in the Bardeen–Cooper–Schrieffer (BCS) theory. We remark that the attractive interaction for raising the T c of HTSC up to temperatures as high as 160 K is the large J in (∼0.12 eV), which binds electrons of opposite spins to be on neighboring sites, and that there are no bosonic glues. It is the Coulomb repulsive interaction U (> 6 eV) among Cu-3 d electrons that plays a central role in the physics behind high- T c phenomena. A new paradigm of the SC mechanism opens to strongly correlated electron matter.

Cluster-size dependence in cellular dynamical mean-field theory

We examine the cluster-size dependence of the cellular dynamical mean-field theory (CDMFT) applied to the two-dimensional Hubbard model. Employing the continuous-time quantum Monte Carlo method as the solver for the effective cluster model, we obtain CDMFT solutions for 4-, 8-, 12-, and 16-site clusters at a low temperature. Comparing various periodization schemes, which are used to construct the infinite-lattice quantities from the cluster results, we find that the cumulant periodization yields the fastest convergence for the hole-doped Mott insulator where the most severe size dependence is expected. We also find that the convergence is much faster around (0,0) and (pi/2,pi/2) than around (pi,0) and (pi,pi). The cumulant-periodized self-energy seems to be close to its thermodynamic limit already for a 16-site cluster in the range of parameters studied. The 4-site results remarkably agree well with the 16-site results, indicating that the previous studies based on the 4-site cluster capture the essence of the physics of doped Mott insulators.

Response of a Doped Mott Insulator to a Local Charge: Implications for Muon Spin Resonance

A charged impurity (such as a muon) in a metal induces a charge inhomogeneity which screens the electric field of the impurity and may also cause the spin fluctuation spectrum near the impurity to differ from that of thebulk. Doped Mott insulators (such as the high Tc copper-oxide superconductors are believed to be) present a particularly delicate case: the Mott correlations suppress the charge response, but also increasethe sensitivityof magnetic propertiesto changesinthe charge density. Here we summarize the implications of recent dynamical mean field calculations for this physics.

Strongly correlated nature of d-wave superconductivity in cuprates

Abstract With the high- T c cuprates in mind, properties of correlated d -wave superconducting (SC) states are studied for a Hubbard model on square lattices with a diagonal transfer ( t - t’ - U model), using a variational Monte Carlo method. We employ a simple wave function, which includes crucial parameters, in particular, a doublon-holon (D-H) binding factor important for correlated SC and normal states as doped Mott insulators. We first check that the range of dominant superconductivity is limited to a strongly correlated regime ( U > W , U : onsite correlation strength, W : band width), and coincides with the effective range of the D-H binding factors. In this range of U/t and δ (doping rate), holons (in hole-doped cases) are classified into two types: doped holons and ones created as D-H pairs. Only the former holons participate in current, whereas the latter contribute to singlet-pair formation. Next, we show that the SC properties undergo a crossover at U = U co∼ W . For U U co, the behavior is appropriately interpreted with the conventional BCS mechanism, whereas for U > U co (the regime of cuprates), a new idea is needed to understand the peculiar SC behavior.

Unconventional Mott transition in KxFe2−ySe2

The newly discovered 122-iron-chalcogenide superconductors show clear signatures of Mott-insulating and strange, incoherent metal normal states. Motivated thereby, we use local-density approximation plus dynamical mean-field theory (LDA + DMFT) to study the electronic structure and transport properties of K${}_{x}$Fe${}_{2\ensuremath{-}y}$Se${}_{2}$. We find that the undoped KFe${}_{1.6}$Se${}_{2}$ system is a new kind of Mott-Kondo insulator (MKI). Electron doping this MKI drives a Mott transition to an orbital-selective non-Fermi-liquid metal. Good agreement with spectral and transport responses supports our view, implying that superconductivity arises from a doped Mott insulator, as in the high-${T}_{c}$ cuprates.

Recent Progress in Physics of High-Temperature Superconductors

One hundred years after the discovery of superconductivity, we are now facing a new era that demands an increase in the superconducting transition temperature Tc. In addition to copper-based superconductors, iron-based superconductors that have been discovered recently have been considered high-temperature superconductors. The similarity and difference between the two high-Tc systems are discussed on the basis of our recent theoretical and experimental understandings. While the pairing mechanism and non-Fermi liquid behaviors in transport properties may have a common origin between the two systems, the strengths of electron correlation are different: Cuprate is a doped Mott insulator, while iron pnictide is an itinerant system with a weak correlation. Pseudogap phenomena in hole-doped cuprates and their absence in electron-doped cuprate are regarded as a consequence of a strong correlation. Recent topics in cuprates about electron–hole asymmetry and pseudogap phenomenon are reviewed from a theoretical viewpoint. For iron pnictides, anisotropic behaviors in antiferromagnetic phases and new iron-selenide superconductors are discussed.

The emergence of gauge invariance: The stay-at-home gauge versus local–global duality

In condensed matter physics, gauge symmetries other than the U(1) of electromagnetism are of an emergent nature. Two emergence mechanisms for gauge symmetry are well established: the way in which it arises in Kramers–Wannier type local–global dualities, and the way in which local constraints encountered in (doped) Mott insulators are encoded. We demonstrate that these gauge structures are closely related, and appear as counterparts in the canonical and field-theoretical languages. The restoration of symmetry in a disorder phase transition is due to having the original local variables subjected to a coherent superposition of all possible topological defect configurations, with the effect that correlation functions are no longer well-defined. This is completely equivalent to assigning gauge freedom to those variables. Two cases are considered explicitly: the well-known vortex duality in bosonic Mott insulators serves to illustrate the principle; and the acquired wisdom is then applied to the less familiar context of dualities in quantum elasticity, where we elucidate the relation between the quantum nematic and linearized gravity. We reflect on some deeper implications for the emergence of gauge symmetry in general.

Mott physics, sign structure, ground state wavefunction, and high-T c superconductivity

In this article I give a pedagogical illustration of why the essential problem of high-Tc superconductivity in the cuprates is about how an antiferromagnetically ordered state can be turned into a short-range state by doping. I will start with half-filling where the antiferromagnetic ground state is accurately described by the Liang-Doucot-Anderson (LDA) wavefunction. Here the effect of the Fermi statistics becomes completely irrelevant due to the no double occupancy constraint. Upon doping, the statistical signs reemerge, albeit much reduced as compared to the original Fermi statistical signs. By precisely incorporating this altered statistical sign structure at finite doping, the LDA ground state can be recast into a short-range antiferromagnetic state. Superconducting phase coherence arises after the spin correlations become short-ranged, and the superconducting phase transition is controlled by spin excitations. I will stress that the pseudogap phenomenon naturally emerges as a crossover between the antiferromagnetic and superconducting phases. As a characteristic of non Fermi liquid, the mutual statistical interaction between the spin and charge degrees of freedom will reach a maximum in a high-temperature "strange metal phase" of the doped Mott insulator.

Dynamical spin response of electron doped Mott insulators on a triangular lattice

The spin dynamics of electron doped Mott insulators on a triangular lattice is studied based on the t – J model. It is found that the particularly universal behaviors of integrated dynamical spin structure factor seen in the doped Mott insulators on a square lattice, are absent in the doped Mott insulators on a triangular lattice, indicating the presence of the normal state gap. As a result, the spin–lattice relaxation rate 1 / T 1 divided by T reduces with decreasing temperatures in the temperature region above 0.2 J ≈ 50 K , then follows a Curie–Weiss-like behavior at the temperature less than 50 K, in qualitative agreement with experimental observations.

Superconducting ground state of a doped Mott insulator

A d-wave superconducting ground state for a doped Mott insulator is obtained. It is distinguished from a Gutzwiller-projected Bardeen–Cooper–Schrieffer (BCS) superconductor by an explicit separation of Cooper pairing and resonating valence bond (RVB) pairing. Such a state satisfies the precise sign structure of the t–J model, just as a BCS state satisfies the Fermi–Dirac statistics. This new class of wavefunctions can be intrinsically characterized and effectively manipulated by electron fractionalization with neutral spinons and ‘backflow’ spinons forming a two-component RVB structure. While the former spinon is bosonic, originating from the superexchange correlation, the latter spinon is found to be fermionic, accompanying the hopping of bosonic holons. The low-lying emergent gauge fields associated with such a specific fractionalization are of mutual Chern–Simons type. Corresponding to this superconducting ground state, three types of elementary excitations are identified. Among them a Bogoliubov nodal quasiparticle is conventional, while the other two are neutral excitations of non-BCS type that play crucial roles in higher-energy/temperature regimes. Their unique experimental implications for the cuprates are briefly discussed.

Magnetic properties of lightly doped antiferromagnetic YBa2Cu3Oy

The present work addresses YBa${}_{2}$Cu${}_{3}$O${}_{y}$ at doping below $x=6%$ where the compound is a collinear antiferromagnet. In this region YBa${}_{2}$Cu${}_{3}$O${}_{y}$ is a normal conductor with finite resistivity at zero temperature. The value of the staggered magnetization at zero temperature is $\ensuremath{\approx}$$0.6\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{B}$, the maximum value allowed by spin quantum fluctuations. The staggered magnetization is almost independent of doping. On the other hand, the N\'eel temperature decays very quickly, from ${T}_{N}=420\phantom{\rule{0.28em}{0ex}}\text{K}$ at $x=0$ to practically zero at $x\ensuremath{\approx}6%$. The present paper explains these remarkable properties and demonstrates that the properties result from the physics of a lightly doped Mott insulator with small hole pockets. Nuclear quadrupole resonance data are also discussed. The data shed light on mechanisms of stability of the antiferromagnetic order at $x<6%$.

Theory of pseudogap and superconductivity in doped Mott insulators

AbstractUnderdoped Mott insulators provide us with a challenge of many‐body physics. Recent renewed understanding is discussed in terms of the evolution of pole and zero structure of the single‐particle Green's function. Pseudogap as well as Fermi arc/pocket structure in the underdoped cuprates is well reproduced from the recent cluster extension of the dynamical mean‐field theory. Emergent coexisting zeros and poles set the underdoped Mott insulator apart from the Fermi liquid, separated by topological transitions. The cofermion proposed as a generalization of exciton in the slave‐boson framework accounts for the origin of the zero surface formation. The cofermion‐quasiparticle hybridization gap offers a natural understanding of the pseudogap and various unusual Mottness. Furthermore the cofermion offers a novel pairing mechanism, where the cofermion has two roles: It reinforces the Cooper pair as a pair partner of the quasiparticle and acts as a glue as well. It provides a strong insight for solving the puzzle found in the dichotomy of the gap structure.