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Physical Review B

Phases of Mott-Hubbard bilayers: Theoretical model

Jung Hoon Han, Chenglong Jia

Published Aug 18, 2006• 6 citations
Publisher

Abstract

A phase diagram of two Mott-Hubbard planes interacting with a short-range Coulomb repulsion is presented. Considering the case of equal amount of doping by holes in one layer as electrons in the other, a holon-doublon interlayer exciton formation is shown to be a natural consequence of Coulomb attraction. Quasiparticle spectrum is gapped and incoherent below a critical doping ${\ensuremath{\delta}}_{c}$ due to the formation of excitons. A spin-liquid-insulator (SLI) phase is thus realized without the lattice frustration. The critical value ${\ensuremath{\delta}}_{c}$ sensitively depends on the interlayer interaction strength. In the $t\text{\ensuremath{-}}J$ model description of each layer with the $d$-wave pairing, ${\ensuremath{\delta}}_{c}$ marks the crossover between SLI and $d$-wave superconductor. The SLI phase, despite being nonsuperconducting and charge gapped, still shows an electromagnetic response similar to that of a superfluid due to the exciton transport. Including antiferromagnetic order in the $t\text{\ensuremath{-}}J$ model introduces magnetically ordered phases at low doping and pushes the spin-liquid phase to a larger interlayer interaction strength and higher doping concentrations.

DOI
10.1103/physrevb.74.075105

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A phase diagram of two Mott-Hubbard planes interacting with a short-range Coulomb repulsion is presented. Considering the case of equal amount of doping by holes in one layer as electrons in the other, a holon-doublon interlayer exciton formation is shown to be a natural consequence of Coulomb attraction. Quasiparticle spectrum is gapped and incoherent below a critical doping \ensuremathδc{\ensuremath{\delta}}_{c}\ensuremathδc​ due to the formation of excitons. A spin-liquid-insulator (SLI) phase is thus realized without the lattice frustration. The critical value \ensuremathδc{\ensuremath{\delta}}_{c}\ensuremathδc​ sensitively depends on the interlayer interaction strength. In the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model description of each layer with the ddd-wave pairing, \ensuremathδc{\ensuremath{\delta}}_{c}\ensuremathδc​ marks the crossover between SLI and ddd-wave superconductor. The SLI phase, despite being nonsuperconducting and charge gapped, still shows an electromagnetic response similar to that of a superfluid due to the exciton transport. Including antiferromagnetic order in the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model introduces magnetically ordered phases at low doping and pushes the spin-liquid phase to a larger interlayer interaction strength and higher doping concentrations.
A phase diagram of two Mott-Hubbard planes interacting with a short-range Coulomb repulsion is presented. Considering the case of equal amount of doping by holes in one layer as electrons in the other, a holon-doublon inter-layer exciton formation is shown to be a natural consequence of Coulomb attraction. Quasiparticle spectrum is gapped and incoherent below a critical doping δcδ_cδc​ due to the formation of excitons. A spin liquid insulator (SLI) phase is thus realized without the lattice frustration. The critical value δcδ_{c}δc​ sensitively depends on the inter-layer interaction strength. In the tJtJtJ model description of each layer with the d-wave pairing, δcδ_{c}δc​ marks the crossover between SLI and d-wave superconductor. The SLI phase, despite being non-superconducting and charge-gapped, still shows electromagnetic response similar to that of a superfluid due to the exciton transport. Including antiferromagnetic order in the tJtJtJ model introduces magnetically ordered phases at low doping and pushes the spin liquid phase to a larger inter-layer interaction strength and higher doping concentrations.
We study the effect of Coulomb interaction between two oppositely doped low-dimensional tJ model systems. We exactly show that, in the one-dimensional case, an arbitrarily weak interaction leads to the formation of charge neutral electron-hole pairs. We then use two different mean-field theories to address the two-dimensional case, where inter-layer excitons also form and condense. We propose that this results in new features which have no analog in single layers, such as the emergence of an insulating spin liquid phase. Our simple bilayer model might have relevance to the physics of doped Mott insulator interfaces and of the new four layer Ba 2 Ca 3 Cu 4 O 8 compound.
The bilayer Hubbard model with electron-hole doping is an ideal platform to study excitonic orders due to suppressed recombination via spatial separation of electrons and holes. However, suffering from the sign problem, previous quantum Monte Carlo studies could not arrive at an unequivocal conclusion regarding the presence of phases with clear signatures of excitonic condensation in bilayer Hubbard models. Here, we develop a determinant quantum Monte Carlo algorithm for the bilayer Hubbard model that is sign-problem-free for equal and opposite doping in the two layers and study excitonic order and charge and spin density modulations as a function of chemical potential difference between the two layers, on-site Coulomb repulsion, and interlayer interaction. In the intermediate coupling regime and in proximity to the SU(4)-symmetric point, we find a biexcitonic condensate phase at finite electron-hole doping, as well as a competing (π,π) charge density wave state. We extract the Berezinskii-Kosterlitz-Thouless transition temperature from superfluid density and a finite-size scaling analysis of the correlation functions and explain our results in terms of an effective biexcitonic hard-core boson model.
We study the doping of a Mott insulator in the presence of quenched frustrating disorder in the magnitude and sign of the magnetic exchange. Two quite different doping regimes $\ensuremath{\delta}<{\ensuremath{\delta}}^{*}$ and $\ensuremath{\delta}>{\ensuremath{\delta}}^{*}$ are found, with ${\ensuremath{\delta}}^{*}\ensuremath{\simeq}J/t (J$ is the characteristic magnitude of the exchange, and t the hopping amplitude). In the high-doping regime, a (Brinkman-Rice) Fermi-liquid description applies with a coherence scale of order $\ensuremath{\delta}t.$ In the low-doping regime, local magnetic correlations strongly affect the formation of quasiparticles, resulting in a very low coherence scale ${\ensuremath{\epsilon}}_{F}^{*}\ensuremath{\simeq}J(\ensuremath{\delta}/{\ensuremath{\delta}}^{*}{)}^{2}.$ Fermi-liquid behavior does apply below ${\ensuremath{\epsilon}}_{F}^{*},$ but a ``quantum-critical regime'' ${\ensuremath{\epsilon}}_{F}^{*}<T<J$ holds, in which marginal Fermi-liquid behavior of several physical properties is found: NMR relaxation time ${1/T}_{1}\ensuremath{\sim}\mathrm{const},$ resistivity ${\ensuremath{\rho}}_{\mathrm{dc}}(T)\ensuremath{\propto}T,$ optical lifetime ${\ensuremath{\tau}}_{\mathrm{opt}}^{\ensuremath{-}1}\ensuremath{\propto}\ensuremath{\omega}/\mathrm{ln}(\ensuremath{\omega}/{\ensuremath{\epsilon}}_{F}^{*})$ together with $\ensuremath{\omega}/T$ scaling of response functions, e.g., $J{\ensuremath{\sum}}_{\stackrel{\ensuremath{\rightarrow}}{q}}{\ensuremath{\chi}}^{\ensuremath{''}}(\stackrel{\ensuremath{\rightarrow}}{q},\ensuremath{\omega})\ensuremath{\propto}\mathrm{tanh}(\ensuremath{\omega}/2T).$ In contrast, single-electron properties display stronger deviations from Fermi-liquid theory in this regime with a $\sqrt{\ensuremath{\omega}}$ dependence of the inverse single-particle lifetime and a $1/\sqrt{\ensuremath{\omega}}$ decay of the photoemission intensity. On the basis of this model and of various experimental results, it is argued that the proximity of a quantum-critical point separating a glassy Mott-Anderson insulator from a metallic ground state is an important ingredient in the physics of the normal state of cuprate superconductors. In this picture the corresponding quantum critical regime is a spin liquid with incoherent holes and a slow state of spins and holes with slow spin and charge dynamics responsible for the anomalous properties of the normal state. This picture may be particularly relevant to Zn-doped materials.
The ground-state phase diagram of the half-filled repulsive Hubbard model in a bilayer is investigated using cluster dynamical mean-field theory. For weak to intermediate values of Coulomb repulsion UUU, the system undergoes a transition from a Mott-insulating phase to a metallic phase and then onto a band-insulating phase as the interlayer hopping is increased. In the strong-coupling case, the model exhibits a direct crossover from a Mott-insulating phase to a band-insulating phase. These results are robust with respect to the presence or absence of magnetic order.
We introduce a slave-fermion formulation in which to study the charge dynamics of the half-filled Hubbard model on the square lattice. In this description, the charge degrees of freedom are represented by fermionic holons and doublons and the Mott-insulating characteristics of the ground state are the consequence of holon–doublon bound-state formation. The bosonic spin degrees of freedom are described by the antiferromagnetic Heisenberg model, yielding long-ranged (Néel) magnetic order at zero temperature. Within this framework and in the self-consistent Born approximation, we perform systematic calculations of the average double occupancy, the electronic density of states, the spectral function and the optical conductivity. Qualitatively, our method reproduces the lower and upper Hubbard bands, the spectral-weight transfer into a coherent quasiparticle band at their lower edges and the renormalisation of the Mott gap, which is associated with holon–doublon binding, due to the interactions of both quasiparticle species with the magnons. The zeros of the Green function at the chemical potential give the Luttinger volume, the poles of the self-energy reflect the underlying quasiparticle dispersion with a spin-renormalised hopping parameter and the optical gap is directly related to the Mott gap. Quantitatively, the square-lattice Hubbard model is one of the best-characterised problems in correlated condensed matter and many numerical calculations, all with different strengths and weaknesses, exist with which to benchmark our approach. From the semi-quantitative accuracy of our results for all but the weakest interaction strengths, we conclude that a self-consistent treatment of the spin-fluctuation effects on the charge degrees of freedom captures all the essential physics of the antiferromagnetic Mott–Hubbard insulator. We remark in addition that an analytical approximation with these properties serves a vital function in developing a full understanding of the fundamental physics of the Mott state, both in the antiferromagnetic insulator and at finite temperatures and dopings.