Doped Mott-Hubbard Insulators Research Articles

Thermoelectric Power and Hall Effect in Correlated Metals and Doped Mott–Hubbard Insulators: DMFT Approximation

We present comparative theoretical investigation of thermoelectric power and Hall effect in the Hubbard model for correlated metal and Mott insulator (considered as prototype cuprate superconductor) for different concentrations of current carriers. Analysis is performed within standard DMFT approximation. For Mott insulator we consider the typical case of partial filling of the lower Hubbard band (hole doping). We calculate the dependence of thermopower on doping level and determine the critical concentration of carriers corresponding to sign change of thermopower. An anomalous dependence of thermopower on temperature is obtained significantly different from linear temperature dependence typical for the usual metals. The role of disorder scattering is analyzed on qualitative level. The comparison with similar studies of the Hall effect shows, that breaking of electron-hole symmetry leads to the appearance of the relatively large interval of band-fillings (close to the half-filling) where thermopower and Hall effects have different signs. We propose a certain scheme allowing to determine the number of carriers from ARPES data and perform semi-quantitative estimate of both thermopower and Hall coefficient using the usual DFT calculations of electronic spectrum.

Thermoelectric Power and Hall Effect in Correlated Metals and Doped Mott–Hubbard Insulators: DMFT Approximation

Thermoelectric Power and Hall Effect in Correlated Metals and Doped Mott–Hubbard Insulators: DMFT Approximation

Hall Effect in Doped Mott–Hubbard Insulator

We present theoretical analysis of Hall effect in doped Mott–Hubbard insulator, considered as a prototype of cuprate superconductor. We consider the standard Hubbard model within DMFT approximation. As a typical case we consider the partially filled (hole doping) lower Hubbard band. We calculate the doping dependence of both the Hall coefficient and Hall number and determine the value of carrier concentration, where Hall effect changes its sign. We obtain a significant dependence of Hall effect parameters on temperature. Disorder effects are taken into account in a qualitative way. We also perform a comparison of our theoretical results with some known experiments on doping dependence of Hall number in the normal state of YBCO and Nd-LSCO, demonstrating rather satisfactory agreement of theory and experiment. Thus the doping dependence of Hall effect parameters obtained within Hubbard model can be considered as an alternative to a popular model of the quantum critical point.

Hall Effect in Doped Mott–Hubbard Insulator

We present theoretical analysis of Hall effect in doped Mott-Hubbard insulator, considered as a prototype of cuprate superconductor. We consider the standard Hubbard model within DMFT approximation. As a typical case we consider the partially filled (hole doping) lower Hubbard band. We calculate the doping dependence of both the Hall coefficient and Hall number and determine the value of carrier concentration, where Hall effect changes its sign. We obtain a significant dependence of Hall effect parameters on temperature. Disorder effects are taken into account in a qualitative way.We also perform a comparison of our theoretical results with some known experiments on doping dependence of Hall number in the normal state of YBCO and Nd-LSCO, demonstrating rather satisfactory agreement of theory and experiment. Thus the doping dependence of Hall effect parameters obtained within Hubbard model can be considered as an alternative to a popular model of the quantum critical point.

Coulomb localization in orbital degenerate, doped Mott insulators

We study electron localization in a three-band extended Hubbard model describing the t2g electrons of doped vanadium perovskites such as La1−xCaxVO3, where Ca defects are represented by Coulomb potentials. The main goal of this paper is to explore what happens when long-range electron-electron (e-e) interactions are switched on. The electronic structure of these doped Mott-Hubbard insulators is calculated using the unrestricted Hartree-Fock approximation that allows to perform the required statistical averages over many distinct defect realizations. The Mott gap is found to persist up to large doping and the defect states, appearing inside of it, are seen to develop a defect states gap centered at the Fermi energy. The internal kinetic energy of the doped holes, forming spin-orbital polarons bound to the defects, induces the defect states gap even in the absence of e-e interactions. Such kinetic gap survives disorder fluctuations and is amplified by long-range e-e interactions. A study of the inverse participation ratio reveals the small size of such spin-orbital polarons and provides an explanation for the persistence of spin and orbital order up to high doping.

Fingerprints of spin-orbital polarons and of their disorder in the photoemission spectra of doped Mott insulators with orbital degeneracy

We explore the effects of disordered charged defects on the electronic excitations observed in the photoemission spectra of doped transition metal oxides in the Mott insulating regime by the example of the $R_{1-x}$Ca$_x$VO$_3$ perovskites, where $R=$La,$\dots$,Lu. A fundamental characteristic of these vanadium $d^2$ compounds with partly filled $t_{2g}$ valence orbitals is the persistence of spin and orbital order up to high doping, in contrast to the loss of magnetic order in high-$T_c$ cuprates at low defect concentration. We demonstrate that the disordered electronic structure of doped Mott-Hubbard insulators can be obtained with high precision within the unrestricted Hartree-Fock approximation. In particular: (i) the atomic multiplet excitations in the inverse photoemission spectra and the various defect-related states and satellites are well reproduced, (ii) a robust Mott gap survives up to large doping, and (iii) we show that the defect states inside the Mott gap develop a soft gap at the Fermi energy. The soft defect states gap can be characterized by a shape and a scale parameter extracted from a Weibull statistical sampling of the density of states near the chemical potential. We demonstrate that charge defects trigger small spin-orbital polarons, with their internal kinetic energy responsible for the opening of the soft defect states gap. The small size of spin-orbital polarons is inferred by an analysis of the inverse participation ratio which explains the origin of the robustness of spin and orbital order. Using realistic parameters for La$_{1-x}$Ca$_x$VO$_3$, we show that its soft gap is well reproduced as well as the marginal doping dependence of the position of the chemical potential relative to the center of the lower Hubbard band.

Coherence and spectral weight transfer in the dynamic structure factor of cold lattice bosons

Ultracold atoms have been used to create novel correlated quantum phases allowing to address many solid-state physics problems using the quasi-particle concept, which is the foundation of our understanding of many-body quantum systems. For bosons, the simplest kinds of excited states involve two particles and they are connected to the dynamic structure factor S(k,ω), measured using Bragg spectroscopy, similarly to the angle-resolved photoemission spectroscopy (ARPES) in solid state physics – a major tool in the study of high-Tc cuprates. Calculation of S(k,ω) requires a significant numerical effort to determine multidimensional convolutions of momentum and frequency dependent constituents functions, which we achieve using parallelized fast Fourier transform. As a result, we are able to show that spectral weight transfer between low and high energies is an intrinsic property of the strongly correlated Bose system in close analogy to the doped Mott-Hubbard electronic insulator. Furthermore, the appearance of sharp coherence peaks in the superfluid phase of the cold bosons closely resembles the formation of sharply defined quasiparticle excitations below Tc in cuprates suggesting an intimate connection between the intrinsic nature of these seemingly different systems.

Possible Bose-condensate behavior in a quantum phase originating in a collective excitation in the chemically and optically doped Mott-Hubbard system UO2+x

X-ray pair distribution function (pdf) and U L${}_{3}$ extended x-ray absorption fine structure (EXAFS) and neutron pdf measurements that give identical results for UO${}_{2}$ show U(VI)-oxo moieties with x rays for mixed valence U${}_{4}$O${}_{9}$ and U${}_{3}$O${}_{7}$, in contrast to the neutron data that indicate only U(V) sites with no short U-O bonds as well as other differences. In addition, although the EXAFS spectra of UO${}_{2}$ are essentially identical at 30, 100, and 200 K, those of the UO${}_{2+x}$ compounds exhibit different nearest-neighbor U-O distributions at each temperature. Further tunneling polaron-type behavior is found in the broadening of the features of the O K-edge x-ray absorption spectra (XAS) of the UO${}_{2+x}$ compounds. Raman spectra of powders also show a large increase in scattering cross section with increasing O content that would originate in a change in the electronic structure that increases the overall polarizability. The XAS and Raman also show that U${}_{4}$O${}_{9}$ does not behave as a linear combination of the UO${}_{2}$ and U${}_{3}$O${}_{7}$ fluorite endpoints. The properties induced by mobile rather than static charged quasiparticles were explored by optical pumping of the metal-to-metal charge-transfer transition. The temperature dependence of 4.71 eV pump--1.57 eV probe reflectivity on UO${}_{2}$ that initially populates the U 6$d$-dominated portion of the upper Hubbard band (UHB) shows a sharp 28-\ensuremath{\mu}sec lifetime peak at 25 K that may be associated with the fluctuations of its antiferromagnetic transition. Pumping at 3.14 eV into the 5$f$-dominated portion of the UHB shows an analogous 2.8-\ensuremath{\mu}sec peak but also a plateau bracketing this peak that ends in a cusp at 50--60 K and an abrupt change in the hardening rate of a novel 12--15 GHz phonon that is the signature for the quasiparticle quantum phase. The different results for the different excitation channels indicate a highly specific nonthermal relaxation mechanism. These results constitute the first observation of a distinct phase of photoinduced quasiparticles that is sufficiently coupled to the lattice to undergo a gap-opening transition. When the intragap state is probed with a terahertz time domain spectroscopy (TTDS) measurement 33 psec after a 3.14 excitation pulse, it shows increased absorption in the 0.5--1.1 THz range with a decrease in temperature from \ensuremath{\sim}30 to 10 K instead of the expected decrease, a result consistent with the presence of a condensate. These results are too extreme to originate in the dynamical, nonadiabatic, coupled charge-transfer--phonon/tunneling polaron scenario previously used for doped Mott-Hubbard insulators with intermediate electron-phonon coupling and therefore indicate novel physics. One possibility that could cause all of these behaviors is that a collective, dynamical, charge transfer-coupled Peierls distortion involving the 2 U(V) \ensuremath{\leftrightarrow} U(IV)+U(VI)-oxo excitation occurs coherently over an entire domain to cause the atoms in this domain to condense into a system with Bose-Einstein or Bose-Einstein-Hubbard properties.

Anomalous thermodynamics of the doped Mott-Hubbard insulators

The concentration dependence of the entropy of doped Mott-Hubbard insulators has been considered within the t-J model. It has been shown that a change in the type and statistics of charge carriers as compared to the Fermi gas leads to a radical change in the entropy s, in particular, to the giant growth of the entropy upon doping. The quantity ∂s/∂x ≈ kB is approximately consistent with the experimental data for HTSC cuprates in the pseudogap phase.

Splitting of the lower subband of Hubbard fermions in the Shubin–Vonsowsky model under the influence of strong intersite correlations

The diagram technique for Hubbard operators is used to investigate the influence of intersite Coulomb interactions on the energy structure and Cooper instability of strongly correlated fermions. Allowance for intersite correlations in doped Mott-Hubbard insulators is shown to lead to a splitting of the lower subband of Hubbard fermions and to the formation of a band of fluctuation states as soon as the intersite interaction energy becomes comparable to or exceeds the mean kinetic energy. The spectral intensity of the splitoff band is proportional to the root-mean-square fluctuation of the occupation numbers and increases with doping level. The predicted effect changes significantly the structure of the density of electronic states. This leads to a renormalization of the pole of the scattering amplitude in the Cooper channel and manifests itself as a nonuniform (in electron concentration) modification of the dependence of the critical superconducting transition temperature.

Superconductivity in a Hubbard-Fröhlich model and in cuprates

Using the variational Monte Carlo method, we find that a relatively weak long-range electron-phonon interaction induces a $d$-wave superconducting state in doped Mott-Hubbard insulators and/or strongly correlated metals with a condensation energy significantly larger than can be obtained with Coulomb repulsion only. Moreover, the superconductivity is shown to exist for infinite on-site Coulomb repulsion without the need for additional mechanisms such as spin fluctuations to mediate $d$-wave superconductivity. We argue that our superconducting state is robust with respect to a more intricate choice of the trial-wave function and that a possible origin of high-temperature superconductivity lies in a proper combination of strong electron-electron correlations with poorly screened Fr\"ohlich electron-phonon interaction.

Unconventional Pairs Glued by Conventional Phonons in Cuprate Superconductors

It has gone almost unquestioned that superexchange in the t−J (or Hubbard) model, and not phonons, is responsible for the unconventional (“d-wave”) pairing symmetry of cuprate superconductors. However, a number of advanced numerical studies have not found superconductivity in the Hubbard (or t−J) model. On the other hand, compelling experimental evidence for a strong electron–phonon interaction (EPI) has currently arrived. Here I briefly review some phonon-mediated unconventional pairing mechanisms. In particular the anisotropy of sound velocity makes the phonon-mediated attraction of electrons non-local in space providing unconventional Cooper pairs with a non-zero orbital momentum already in the framework of the conventional BCS theory with weak EPI. In the opposite limit of strong EPI rotational symmetry breaking appears as a result of a reduced Coulomb repulsion between unconventional bipolarons. Using the variational Monte Carlo method we have found that a relatively weak finite-range EPI induces a d-wave BCS state also in doped Mott–Hubbard insulators or strongly-correlated metals. These results tell us that poorly screened EPI with conventional phonons is responsible for the unconventional pairing in cuprate superconductors.

Spectral microscopic mechanisms and quantum phase transitions in a 1D correlatedproblem

In this paper we study the dominant microscopic processes that generatenearly the whole one-electron removal and addition spectral weight of theone-dimensional Hubbard model for all values of the on-site repulsionU. We find that for the doped Mott–Hubbard insulator there is a competition between themicroscopic processes that generate the one-electron upper-Hubbard-band spectral-weightdistributions of the Mott–Hubbard insulating phase and finite-doping-concentrationmetallic phase, respectively. The spectral-weight distributions generated by thenon-perturbative processes studied here are shown elsewhere to agree quantitatively for thewhole momentum and energy bandwidth with the peak dispersions observed byangle-resolved photoelectron spectroscopy in quasi-one-dimensional compounds.

Electronic state of a doped Mott-Hubbard insulator at finite temperatures studied using the dynamical mean-field theory

We study the electronic state of the doped Mott-Hubbard insulator within Dynamical Mean Field Theory. The evolution of the finite temperature spectral functions as a function of doping show large redistributions of spectral weight in both antiferromagnetic and paramagnetic phases. In particular, a metallic antiferromagnetic state is obtained with a low frequency Slater-splitted quasiparticle peak coexisting with Hubbard bands. In the high temperature paramagnetic metallic phase, upon reducing doping, the system has a crossover through a ``bad metal'' state characterized by an anomalous shift of the quasiparticle peak away from the Fermi energy. We find that the {\it charge} compressibility of the antiferromagnetic metal is dramatically enhanced upon approaching the second order N\'eel line.

Electrodynamics of high-Tcsuperconductors

Recent studies of the electromagnetic response of high-Tc superconductors using terahertz, infrared, and optical spectroscopies are reviewed. In combination these experimental techniques provide a comprehensive picture of the low-energy excitations and charge dynamics in this class of materials. These results are discussed with an emphasis on conceptual issues, including evolution of the electronic spectral weight in doped Mott-Hubbard insulators, the d-wave superconducting energy gap and the normal-state pseudogap, anisotropic superfluid response, electronic phase segregation, emergence of coherent electronic state as a function of both temperature and doping, the vortex state, and the energetics of the superconducting transition. Because the theoretical understanding of these issues is still evolving the review is focused on the analysis of the universal trends that are emerging out of a large body of work carried on by many research teams. Where possible data generated by infrared/optical techniques are compared with the data from other spectroscopic and transport methods.

Doping dependence of density response and bond-stretching phonons in cuprates

We explain the anomalous doping dependence of zone boundary ( π , 0 ) and ( π , π ) bond-stretching phonons in La 2 - δ Sr δ CuO 4 in the range 0 < δ < 0.35 . Our calculations are based on a theory for the density response of doped Mott–Hubbard insulators.

Inhomogeneity of the pseudogap state of a doped layered cuprate antiferromagnet

The features of the pseudogap state in doped layered cuprate antiferromagnets and underdoped high-Tc superconductors (HTSCs) are investigated. It is shown that the transition to the pseudogap state is a dimensional crossover from three-dimensional motion to two-dimensional motion of charges in the copper–oxygen planes, which leads to the coexistence of light charge carriers and Jahn–Teller polarons and to the development of strong local correlations, as are characteristic for two-dimensional doped Mott–Hubbard insulators. In a doped antiferromagnet the d-wave pairing of light charge carriers and Jahn–Teller polarons leads to the formation of magnetic and bosonic clusters, i.e., substantial inhomogeneity of the copper–oxygen planes arises. It is found that the change in the properties of a doped layered cuprate antiferromagnetic insulator and in the metallic and superconducting states of an underdoped HTSC with decreasing temperature is due to a repeated dynamic reduction of their dimensionality. A model phase diagram in terms of the temperature and dopant concentration is proposed.

A new study on the doped Mott-Hubbard insulator

By introducing a rotationally invariant Stratonovich–Hubbard (S-H) field we studied the doped Mott insulator phase of the two-dimension Hubbard model for U/t∼4–8. The static spin is decoupled by the S–H field and the static charge interaction is then treated by Hartree–Fock approximation. We sample random spin configurations by Monte Carlo simulation with the Metropolis updating algorithm. The Mott–Hubbard gap and static susceptibilities are studied near the half-filling at low temperature.

Reduction of ordered moment in strongly correlatedLaTiO3+δupon band filling

Neutron diffraction and magnetic susceptibility experiments were performed on single crystals of the doped Mott-Hubbard insulator ${\mathrm{LaTiO}}_{3+\ensuremath{\delta}}.$ The magnetic properties of the three-dimensional correlated electron system were investigated upon hole doping. The size of the ordered moment of ${\mathrm{Ti}}^{3+}$ in the canted antiferromagnetically ordered phase reaches a maximum of $0.46(2){\ensuremath{\mu}}_{B}$ for ${\mathrm{LaTiO}}_{3}.$ Upon increasing the band filling, i.e., upon increasing the amount of nonstoichiometric oxygen \ensuremath{\delta} from 0 to \ensuremath{\sim}0.08, the ordered moment on ${\mathrm{Ti}}^{3+}$ is shown to decrease rapidly. The weak-ferromagnetic saturation moment of ${\mathrm{LaTiO}}_{3.07(1)},$ on the verge of the insulator-to-metal transition, is reached via a series of steps in the magnetization curve.

Cuprate superconductors from the viewpoint of strong correlation

There is now a growing consensus that the physics of cuprate superconductors is dominated by strong correlation and that the fundamental challenge to the theorist is to achieve an understanding of the doped Mott-Hubbard insulator. From this viewpoint, the Hubbard and the t-J models are reasonable Hamiltonians to study. I shall review the gauge theory description of the t-J model. I shall discuss two recent advances: 1) the study of bosons in a strongly fluctuating gauge field in collaboration with Derek Lee and Don Kim, and 2) the descripton of the underdoped regime, focusing on the photoemission spectra and the relation to the spin gap phenomenon, in collaboration with Xiao-Gang Wen.