Doped Mott insulators are insulators: hole localization in the cuprates

We demonstrate that a Mott insulator lightly doped with holes is still an insulator at low temperature even without disorder. Hole localization obtains because the chemical potential lies in a pseudogap which has a vanishing density of states at zero temperature. The energy scale for the pseudogap is set by the nearest-neighbor singlet-triplet splitting. As this energy scale vanishes if transitions, virtual or otherwise, to the upper Hubbard band are not permitted, the fundamental length scale in the pseudogap regime is the average distance between doubly occupied sites. Consequently, the pseudogap is tied to the noncommutativity of the two limits U-->infinity (U the on-site Coulomb repulsion) and L -->infinity (the system size).     

The short-range correlations of a doped Mott insulator

This paper presents numerical studies of the single hole model that address the interplay between the kinetic energy of itinerant electrons and the exchange energy of local moments as of interest to doped Mott insulators. Due to this interplay, two different spin correlations coexist around a mobile vacancy. These local correlations provide an effective two-band picture that explains the two-band structure observed in various theoretical and experimental studies, the doping dependence of the momentum space anisotropic pseudogap phenomena and the asymmetry between hole and electron doped cuprates.     

Strongly correlated superconductivity and pseudogap phase near a multiband Mott insulator

Near a Mott transition, strong electron correlations may enhance Cooper pairing. This is demonstrated in the dynamical mean field theory solution of a twofold-orbital degenerate Hubbard model with an inverted on-site Hund rule exchange, favoring local spin-singlet configurations. Close to the Mott insulator (which here is a local version of a valence bond insulator) a pseudogap non-Fermi-liquid metal, a superconductor, and a normal metal appear, in striking similarity with the physics of cuprates. The strongly correlated s-wave superconducting state has a larger Drude weight than the corresponding normal state. The role of the impurity Kondo problem is underscored.     

Superconductivity close to the Mott state: From condensed-matter systems to superfluidity in optical lattices

Since the discovery of high-temperature superconductivity in 1986 by Bednorz and Müller, great efforts have been devoted to finding out how and why it works. From the d-wave symmetry of the order parameter, the importance of antiferromagnetic fluctuations, and the presence of a mysterious pseudogap phase close to the Mott state, one can conclude that high-T_c superconductors are clearly distinguishable from the well-understood BCS superconductors. The d-wave superconducting state can be understood through a Gutzwiller-type projected BCS wavefunction. In this review article, we revisit the Hubbard model at half-filling and focus on the emergence of exotic superconductivity with d-wave symmetry in the vicinity of the Mott state, starting from ladder systems and then studying the dimensional crossovers to higher dimensions. This allows to confirm that short-range antiferromagnetic fluctuations can mediate superconductivity with d-wave symmetry. Ladders are also nice prototype systems allowing to demonstrate the truncation of the Fermi surface and the emergence of a Resonating Valence Bond (RVB) state with preformed pairs in the vicinity of the Mott state. In two dimensions, a similar scenario emerges from renormalization group arguments. We also discuss theoretical predictions for the d-wave superconducting phase as well as the pseudogap phase, and address the crossover to the overdoped regime. Finally, cold atomic systems with tunable parameters also provide a complementary insight into this outstanding problem.     

Nodal-antinodal dichotomy and the two gaps of a superconducting doped Mott insulator

We study the superconducting state of the hole-doped two-dimensional Hubbard model using cellular dynamical mean-field theory, with the Lanczos method as impurity solver. In the underdoped regime, we find a natural decomposition of the one-particle (photoemission) energy gap into two components. The gap in the nodal regions, stemming from the anomalous self-energy, decreases with decreasing doping. The antinodal gap has an additional contribution from the normal component of the self-energy, inherited from the normal-state pseudogap, and it increases as the Mott insulating phase is approached.     

Hidden charge 2e Boson in doped Mott insulators

We construct the low-energy theory of a doped Mott insulator, such as the high-temperature superconductors, by explicitly integrating over the degrees of freedom far away from the chemical potential. For either hole or electron doping, a charge 2e bosonic field emerges at low energy. The charge 2e boson mediates dynamical spectral weight transfer across the Mott gap and creates a new charge e excitation by binding a hole. The result is a bifurcation of the electron dispersion below the chemical potential as observed recently in angle-resolved photoemission on Pb-doped Bi2Sr2CaCu2O8+delta (Pb2212).     

Microscopic study of a spin-orbit-induced Mott insulator in Ir oxides

Motivated by recent experiments of a novel 5d Mott insulator in Sr2IrO4, we have studied the two-dimensional three-orbital Hubbard model with a spin-orbit coupling λ. The variational Monte Carlo method is used to obtain the ground state phase diagram with varying an on-site Coulomb interaction U as well as λ. It is found that the transition from a paramagnetic metal to an antiferromagnetic insulator occurs at a finite U=U(MI), which is greatly reduced by a large λ, characteristic of 5d electrons, and leads to the "spin-orbit-induced" Mott insulator. It is also found that the Hund's coupling induces the anisotropic spin exchange and stabilizes the in-plane antiferromagnetic order. We have further studied the one-particle excitations by using the variational cluster approximation and revealed the internal electronic structure of this novel Mott insulator. These findings are in agreement with experimental observations on Sr2IrO4.     

Quantum critical transport near the Mott transition

We perform a systematic study of incoherent transport in the high temperature crossover region of the half filled one-band Hubbard model. We demonstrate that the family of resistivity curves displays characteristic quantum critical scaling of the form ρ(T, δU) = ρ(c)(T)f(T/T?(δU)), with T?(δU) ~ |δU|(zν), and ρ(c)(T) ~ T. The corresponding β function displays a "strong coupling" form β ~ ln(ρ(c)/ρ), reflecting the peculiar mirror symmetry of the scaling curves. This behavior, which is surprisingly similar to some experimental findings, indicates that Mott quantum criticality may be acting as the fundamental mechanism behind the unusual transport phenomena in many systems near the metal-insulator transition.     

Theory of the excitonic Mott transition in quasi-two-dimensional systems

The excitonic Mott transition in single and double quantum wells is studied using the Green’s function technique. An abrupt jump in the value of the ionization degree, which happens with an increase of the carrier density or temperature, is found in a certain density–temperature region. The opposite effect–the collapse of the electron–hole plasma into an insulating exciton system–is predicted to occur at lower densities. The critical density of the Mott transition for spatially indirect excitons may be much smaller than that for direct excitons.     

Single-particle spectral function of the Hubbard chain: frustration induced

The one-electron spectral function of a frustrated Hubbard chain is computed by making use of the cluster perturbation theory. The spectral weight we found turns out to be strongly dependent on the frustrating next-nearest-neighbor hopping t'. A frustration induced pseudogap arises when the system evolves from a gapful Mott insulator to a gapless conductor for an intermediate value of the frustration parameter |t'|. Furthermore, the opening of a pseudogap in the density of states already in the metallic side leads to a continuous opening of the true gap in the insulator. For the hole-doped case, the pseudogap is pinned at the Fermi energy, while the Mott gap is shifted in energy with increasing Hubbard interaction U. The separation of the pseudogap and Mott gap in the hole-doped system demonstrates the validity of the existence of a pseudogap.     

Vanishing of the Mott transition in semiconductor nanocrystals

The dynamics of the system of photoexcited electron–hole pairs in semiconductor nanocrystals of different size with increasing excitation intensity was experimentally studied by utilizing the luminescence spectra of semiconductor-doped glasses in order to elucidate the peculiarities of many-body effects in structures approaching the zero-dimensional limit. Vanishing of effects causing the Mott transition in bulk crystals was observed with decreasing nanocrystal radius, and a new type of transformation of excitons to unbound electron–hole pairs was shown to take place in nanocrystals where the energy shift for electrons and holes due to quantum confinement becomes comparable with the exciton binding energy.     

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 tt) 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.     

Gossamer superconductivity near antiferromagnetic Mott insulator in layered organic conductors

Layered organic superconductors are on the verge of the Mott insulator. We use the Gutzwiller variational method to study a two-dimensional Hubbard model including a spin exchange coupling term as a minimal model for the compounds. The ground state is found to be a Gossamer superconductor at small on-site Coulomb repulsion U and an antiferromagnetic Mott insulator at large U, separated by a first order phase transition. Our theory is qualitatively consistent with major experiments reported in organic superconductors.     

Probing states in the Mott insulator regime in the case of coherent bosons trapped in an optical lattice

We propose a method to probe states in the Mott insulator regime produced from a condensate in an optical lattice. We consider a system in which we create time-dependent number fluctuations in a given site by turning off the atomic interactions and lowering the potential barriers on a nearly pure Mott state to allow the atoms to tunnel between sites. We calculate the expected interference pattern and number fluctuations from such a system and show that one can potentially observe a deviation from a pure Mott state. We also discuss a method in which to detect these number fluctuations using time-of-flight imaging.     

Cluster dynamical mean field theory of the Mott transition

We address the nature of the Mott transition in the Hubbard model at half-filling using cluster dynamical mean field theory (DMFT). We compare cluster-DMFT results with those of single-site DMFT. We show that inclusion of the short-range correlations on top of the on-site correlations does not change the order of the transition between the paramagnetic metal and the paramagnetic Mott insulator, which remains first order. However, the short range correlations reduce substantially the critical U and modify the shape of the transition lines. Moreover, they lead to very different physical properties of the metallic and insulating phases near the transition point. Approaching the transition from the metallic side, we find an anomalous metallic state with very low coherence scale. The insulating state is characterized by the narrow Mott gap with pronounced peaks at the gap edge.     

Hall Effect in a Doped Mott Insulator: DMFT Approximation

JETP Letters - In the framework of dynamical mean-field theory, we analyze the Hall effect in a doped Mott insulator as a parent cuprate superconductor. We consider the partial filling (hole...     

Disorder and pseudogap in strongly correlated systems: Phase diagram in the DMFT + Σ approach

The influence of disorder and pseudogap fluctuations on the Mott insulator-metal transition in strongly correlated systems has been studied in the framework of the generalized dynamic mean field theory (DMFT + Σ approach). Using the results of investigations of the density of states (DOS) and optical conductivity, a phase diagram (disorder-Hubbard interaction-temperature) is constructed for the paramagnetic Anderson-Hubbard model, which allows both the effects of strong electron correlations and the influence of strong disorder to be considered. Strong correlations are described using the DMFT, while a strong disorder is described using a generalized self-consistent theory of localization. The DOS and optical conductivity of the paramagnetic Hubbard model have been studied in a pseudogap state caused by antiferromagnetic spin (or charge) short-range order fluctuations with a finite correlation length, which have been modeled by a static Gaussian random field. The effect of a pseudogap on the Mott insulator-metal transition has been studied. It is established that, in both cases, the static Gaussian random field (related to the disorder or pseudogap fluctuations) leads to suppression of the Mott transition, broadening of the coexistence region of the insulator and metal phases, and an increase in the critical temperature at which the coexistence region disappears.     

Breakdown of Luttinger's theorem in two-orbital Mott insulators

An analysis of Luttinger's theorem shows that – contrary to recent claims – it is not valid for a generic Mott insulator. For a two-orbital Hubbard model with two electrons per site the crossover from a non-magnetic correlated insulating phase (Mott or Kondo insulator) to a band insulator is investigated. Mott insulating phases are characterized by poles of the self-energy and corresponding zeros in the Greens functions defining a “Luttinger surface” which is absent for band insulators. Nevertheless, the ground states of such insulators with two electrons per unit cell are adiabatically connected.     

Quantum phases in a doped Mott insulator on the Shastry-Sutherland lattice

We propose the projected BCS wave function as the ground state for the doped Mott insulator SrCu2(BO3)2 on the Shastry-Sutherland lattice. At half filling this wave function yields the exact ground state. Adding mobile charge carriers, we find a strong asymmetry between electron and hole doping. Upon electron doping an unusual metal with strong valence bond correlations forms. Hole doped systems are d-wave resonating valence bond superconductors in which superconductivity is strongly enhanced by the emergence of spatially varying plaquette bond order.