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.     

Imaging nanoscale electronic inhomogeneity in the lightly doped Mott insulator Ca(2-x)NaxCuO2Cl2

The spatial variation of electronic states was imaged in the lightly doped Mott insulator Ca(2-x)NaxCuO2Cl2 using scanning tunneling microscopy or spectroscopy. We observed nanoscale domains with a high local density of states within an insulating background. The observed domains have a characteristic length scale of 2 nm (approximately 4-5a, a: lattice constant) with preferred orientations along the tetragonal [100] direction. We argue that such spatially inhomogeneous electronic states are inherent to slightly doped Mott insulators and play an important role for the insulator to metal transition.     

Mott-Hubbard transition versus Anderson localization in correlated electron systems with disorder

The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory using the geometrically averaged ("typical") local density of states. Correlated metal, Mott insulator, and Anderson insulator phases, as well as coexistence and crossover regimes, are identified. The Mott and Anderson insulators are found to be continuously connected.     

Momentum-resolved charge excitations in a prototype one-dimensional mott insulator

We report momentum-resolved charge excitations in a one-dimensional (1D) Mott insulator studied using high resolution inelastic x-ray scattering over the entire Brillouin zone for the first time. Excitations at the insulating gap edge are found to be highly dispersive (momentum dependent) compared to excitations observed in two-dimensional Mott insulators. The observed dispersion in 1D cuprates ( SrCuO2 and Sr2CuO3) is consistent with charge excitations involving holons which is unique to spin-1/2 quantum chain systems. These results point to the potential utility of momentum-resolved inelastic x-ray scattering in providing valuable information about electronic structure of strongly correlated insulators.     

Traces of the evolution from Mott insulator to a band insulator in the pair excitation spectra

We inspect the fundamental difference between the correlated band insulators (BI) and the Mott insulators (MI) from the perspective of the dynamical pair excitations. To this end, we investigated the physics of the two-plane Hubbard model by employing the well-tested dynamical mean field theory (DMFT) together with the quantum Monte Carlo (QMC) method. At half-filling our results clearly indicate that while the spectral weight of the pair excitation becomes minimal at MI which corresponds to a diminishing of the double occupancy, the opposite occurs at BI. We then discuss the effect of doping and find that the correlated band insulator and the Mott insulator robust at low doping concentration and the metallic state emerges at larger doping. The pair spectral function demonstrates that the metallic state of doped MI is strongly different from that of doped BI and it is readily reflected in the lineshape of the spectra. We discuss the implication of our results in the context of the two-particle spectroscopy.     

The insulating state of matter: a geometrical theory

In 1964 Kohn published the milestone paper “Theory of the insulating state”, according to which insulators and metals differ in their ground state. Even before the system is excited by any probe, a different organization of the electrons is present in the ground state and this is the key feature discriminating between insulators and metals. However, the theory of the insulating state remained somewhat incomplete until the late 1990s; this review addresses the recent developments. The many-body ground wavefunction of any insulator is characterized by means of geometrical concepts (Berry phase, connection, curvature, Chern number, quantum metric). Among them, it is the quantum metric which sharply characterizes the insulating state of matter. The theory deals on a common ground with several kinds of insulators: band insulators, Mott insulators, Anderson insulators, quantum Hall insulators, Chern and topological insulators.     

Mott transition in a valence-bond solid insulator with a triangular lattice

We have investigated the Mott transition in a quasi-two-dimensional Mott insulator EtMe{3}P[Pd(dmit){2}]{2} with a spin-frustrated triangular-lattice in hydrostatic pressure and magnetic-field [Et and Me denote C2H5 and CH3, respectively, and Pd(dmit){2} (dmit=1,3-dithiole-2-thione-4,5-dithiolate,dithiolate) is an electron-acceptor molecule]. In the pressure-temperature (P-T) phase diagram, a valence-bond solid phase is found to neighbor the superconductor and metal phases at low temperatures. The profile of the phase diagram is common to those of Mott insulators with antiferromagnetic order. In contrast to the antiferromagnetic Mott insulators, the resistivity in the metallic phase exhibits anomalous temperature dependence, rho=rho{0}+AT(2.5).     

Spin and charge order in Mott insulators and d-wave superconductors

We argue that aspects of the anomalous, low temperature, spin and charge dynamics of the high temperature superconductors can be understood by studying the corresponding physics of undoped Mott insulators. Such insulators display a quantum transition from a magnetically ordered Néel state to a confining paramagnet with a spin gap; the latter state has bond-centered charge order, a low energy S=1 spin exciton, confinement of S=1/2 spinons, and a free S=1/2 moment near non-magnetic impurities. We discuss how these characteristics, and the quantum phase transitions, evolve upon doping the insulator into a d-wave superconductor. This theoretical framework was used to make a number of predictions for STM measurements and for the phase diagram of the doped Mott insulator in an applied magnetic field.     

Evidence for Multiple Underlying Fermi Surface and Isotropic Energy Gap in the Cuprate Parent Compound Ca_2CuO_2Cl_2

The parent compounds of the high-temperature cuprate superconductors are Mott insulators.It has been generally agreed that understanding the physics of the doped Mott insulators is essential to understanding the mechanism of high temperature superconductivity.A natural starting point is to elucidate the basic electronic structure of the parent compound.Here we report comprehensive high resolution angle-resolved photoemission measurements on Ca_2CuO_2Cl_2,a Mott insulator and a prototypical parent compound of the cuprates.Multiple underl.ying Fermi surface sheets are revealed for the first time.The high energy waterfall-like band dispersions exhibit different behaviors near the nodal and antinodal regions.Two distinct energy scales are identified:a d-wave-like low energy peak dispersion and a nearly isotropic lower Hubbard band gap.These observations provide new information of the electronic structure of the cuprate parent compound,which is important for understanding the anomalous physical properties and superconductivity mechanism of the high temperature cuprate superconductors.     

Born effective charge reversal and metallic threshold state at a band insulator-Mott insulator transition

We study the quantum phase transition between a band (“ionic”) insulator and a Mott-Hubbard insulator, realized at a critical value in a bipartite Hubbard model with two inequivalent sites, whose on-site energies differ by an offset . The study is carried out both in D=1 and D=2 (square and honeycomb lattices), using exact Lanczos diagonalization, finite-size scaling, and Berry's phase calculations of the polarization. The Born effective charge jump from positive infinity to negative infinity previously discovered in D=1 by Resta and Sorella is confirmed to be directly connected with the transition from the band insulator to the Mott insulating state, in agreement with recent work of Ortiz et al. In addition, symmetry is analysed, and the transition is found to be associated with a reversal of inversion symmetry in the ground state, of magnetic origin. We also study the D=1 excitation spectrum by Lanczos diagonalization and finite-size scaling. Not only the spin gap closes at the transition, consistent with the magnetic nature of the Mott state, but also the charge gap closes, so that the intermediate state between the two insulators appears to be metallic. This finding, rationalized within Hartree-Fock as due to a sign change of the effective on-site energy offset for the minority spin electrons, underlines the profound difference between the two insulators. The band-to-Mott insulator transition is also studied and found in the same model in D=2. There too we find an associated, although weaker, polarization anomaly, with some differences between square and honeycomb lattices. The honeycomb lattice, which does not possess an inversion symmetry, is used to demonstrate the possibility of an inverted piezoelectric effect in this kind of ionic Mott insulator. Received 21 May 1999     

Electronic structure of Mott insulators

Mott insulators are identified here with ordinary magnetic insulators. The insulating gap, local moment, and effective spin hamiltonian aspects are qualitatively explained by means of a novel set of solutions of the Hartree-Fock equations. The apparent conflict between Bloch's theorem and localized-electron phenomenology is thereby resolved in an elementary manner. This Hartree-Fock approach also sheds considerable light on the physical mechanisms responsible for the associated metal-insulator (Mott) and other related phase transitions, as observed in V₂O₃ and several other materials. With some generalizations and refinements, this theoretical picture is shown to also account semiquantitatively for a number of detailed properties of NiO and CoO, two of the most extensively studied Mott insulator materials. A wide variety of experimental data for NiO is surveyed in order to determine reasonable values for its effective Hubbard hamiltonian parameters, suitably generalized for the 3d electrons. The problems of formally deriving effective spin hamiltonians for macroscopic magnetic insulator systems are also carefully examined. The old non-orthogonality catastrophe is fully resolved by means of a degenerate (open-shell) analogue of the linked cluster perturbation expansion of Brueckner and Goldstone. Although many quantitative issues remain, these results indicate that there is now a reasonably adequate conceptual understanding of the Mott insulating state.     

How are spin gap and pairing correlations of doped Mott insulators controlled by the geometry of the lattice structure?

Proposals to enhance the spin excitation gap and the pairing correlations in doped Mott insulators are reviewed. Design and tuning of flat dispersions near the Fermi level extend the critical region of the metal-to-Mott insulator transition thereby inducing stronger pairing instabilities. Several one- and two-dimensional decorated lattices are studied. We also discuss the tuning for stronger d-wave pairing instabilities in a microscopic model of high-T_c cuprates.     

Experimental observation of pseudogap in a modulation-doped Mott insulator: Sn/Si(111)-(√30×√30)R30°

Unusual quantum phenomena usually emerge upon doping Mott insulators. Using a molecular beam epitaxy system integrated with cryogenic scanning tunneling microscope, we investigate the electronic structure of a modulation-doped Mott insulator Sn/Si(111)-($\sqrt{3}\times \sqrt{3})R$30$^\circ$. In underdoped regions, we observe a universal pseudogap opening around the Fermi level, which changes little with the applied magnetic field and the occurrence of Sn vacancies. The pseudogap gets smeared out at elevated temperatures and alters in size with the spatial confinement of the Mott insulating phase. Our findings, along with the previously observed superconductivity at a higher doping level, are highly reminiscent of the electronic phase diagram in the doped copper oxide compounds.     

Competing orders and superconductivity in the doped mott insulator on the Shastry-Sutherland lattice

Quantum antiferromagnets on geometrically frustrated lattices often allow a number of unusual paramagnetic ground states. The fate of these Mott insulators upon doping is an important issue that may shed some light on the high T(c) cuprate problem. We consider the doped Mott insulator on the Shastry-Sutherland lattice via the t-J model. The U(1) slave-boson mean-field theory reveals the strong competition between different broken symmetry states. It is found that, in some ranges of doping, there exist superconducting phases with or without coexisting translational-symmetry-breaking orders such as the staggered flux or dimerization. Our results will be directly relevant to SrCu2(BO3)(2) when this material is doped in future.     

Dual vortex theory of doped Mott insulators

We present a general framework for describing the quantum phases obtained by doping paramagnetic Mott insulators on the square lattice. The undoped insulators are efficiently characterized by the projective transformations of various fields under the square lattice space group (the PSG). We show that the PSG also imposes powerful constraints on the doped system, and on the effective action for the vortex and Bogoliubov quasiparticle excitations of superconducting states. This action can also be extended across transitions to supersolid or insulating states at non-zero doping. For the case of a valence bond solid (VBS) insulator, we show that the doped system has the same PSG as that of elementary bosons with density equal to the density of electron Cooper pairs. We also discuss aspects of the action for a d-wave superconductor obtained by doping a “staggered-flux” spin liquid state.     

Electronic model for CoO2 layer based systems: chiral resonating valence bond metal and superconductivity

Takada et al. have reported superconductivity in layered Na(x)CoO(2)yH(2)O (T(c) approximately equal to 5 K). We model a reference neutral CoO2 layer as an orbitally nondegenerate spin-1/2 antiferromagnetic Mott insulator on a triangular lattice and Na(x)CoO(2)yH(2)O as electron doped Mott insulators described by a t-J model. It is suggested that at optimal doping chiral spin fluctuations enhanced by the dopant dynamics lead to a gapful d-wave superconducting state. A chiral resonating valence bond (RVB) metal, a parity and time (PT) reversal violating state with condensed RVB gauge fields, with a possible weak ferromagnetism, and low temperature p-wave superconductivity are also suggested at higher dopings.     

Mottness

We review several of the normal state properties of the cuprates in an attempt to establish an organizing principle from which pseudogap phenomena, broad spectral features, T-linear resistivity, and spectral weight transfer emerge. We first show that standard field theories with a single critical length scale cannot capture the T-linear resistivity as long as the charge carriers are critical. What seems to be missing is an additional length scale, which may or may not be critical. Second, we prove a generalised version of Luttinger’s theorem for a Mott insulator. In particular, we show that for Mott insulators, regardless of the spatial dimension, the Fermi surface of the non-interacting system is converted into a surface of zeros of the single-particle Green function when the underlying band structure has particle-hole symmetry. Only in the presence of particle-hole symmetry does the volume of the surface of zeros equal the particle density. The surface of zeros persists at finite doping and is shown to provide a framework from which pseudogaps, broad spectral features, spectral weight transfer on the Mott gap scale, and the additional length scale required to capture T-linear resistivity can be understood.     

Five-fold way to new high <Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript> superconductors

Discovery of high T _c superconductivity in La_2?x Ba _x CuO₄ by Bednorz and Muller in 1986 was a breakthrough in the 75-year long search for new superconductors. Since then new high T _c superconductors, not involving copper, have also been discovered. Superconductivity in cuprates also inspired resonating valence bond (RVB) mechanism of superconductivity. In turn, RVB theory provided a new hope for finding new superconductors through a novel electronic mechanism. This article first reviews an electron correlation-based RVB mechanism and our own application of these ideas to some new noncuprate superconducting families. In the process we abstract, using available phenomenology and RVB theory, that there are five directions to search for new high T _c superconductors. We call them five-fold way. As the paths are reasonably exclusive and well-defined, they provide more guided opportunities, than before, for discovering new superconductors. The five-fold ways are (i) copper route, (ii) pressure route, (iii) diamond route, (iv) graphene route and (v) double RVB route. Copper route is the doped spin-½ Mott insulator route. In this route one synthesizes new spin-½ Mott insulators and dopes them chemically. In pressure route, doping is not external, but internal, a (chemical or external) pressure-induced self-doping suggested by organic ET-salts. In the diamond route we are inspired by superconductivity in boron-doped diamond and our theory. Here one creates impurity band Mott insulators in a band insulator template that enables superconductivity. Graphene route follows from our recent suggestion of superconductivity in doped graphene, a two-dimensional broadband metal with moderate electron correlations, compared to cuprates. Double RVB route follows from our recent theory of doped spin-1 Mott insulator for superconductivity in iron pnictide family.     

Artificial gauge fields for the Bose-Hubbard model on a checkerboard superlattice and extended Bose-Hubbard model

We study the effects of an artificial gauge field on the ground-state phases of the Bose-Hubbard model on a checkerboard superlattice in two dimensions, including the superfluid phase and the Mott and alternating Mott insulators. First, we discuss the single-particle Hofstadter problem, and show that the presence of a checkerboard superlattice gives rise to a magnetic flux-independent energy gap in the excitation spectrum. Then, we consider the many-particle problem, and derive an analytical mean-field expression for the superfluid-Mott and superfluid-alternating-Mott insulator phase transition boundaries. Finally, since the phase diagram of the Bose-Hubbard model on a checkerboard superlattice is in many ways similar to that of the extended Bose-Hubbard model, we comment on the effects of magnetic field on the latter model, and derive an analytical mean-field expression for the superfluid-insulator phase transition boundaries as well.