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arXiv:1310.2821 · Physical Review B

Competition between band and Mott insulators in the bilayer Hubbard model: A dynamical cluster approximation study

Hunpyo Lee, Yu‐Zhong Zhang, Harald O. Jeschke, Roser Valentí

Published Jan 23, 2014• 20 citations
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Abstract

We investigate the nature of the insulating phases in a bilayer Hubbard model with intralayer coupling $t$ and interlayer coupling ${t}_{\ensuremath{\perp}}$ at large interaction strength $U/t$ and half-filling. We consider a dynamical cluster approximation with a cluster size of ${N}_{c}=2\ifmmode\times\else\texttimes\fi{}4$, where short-range spatial fluctuations as well as on-site dynamical fluctuations are emphasized. By varying the band splitting (${t}_{\ensuremath{\perp}}/t$), we find that at ${t}_{\ensuremath{\perp}}/t\ensuremath{\simeq}1.5$ the Mott behavior is rapidly suppressed in the momentum sectors ($\ensuremath{\pi},0$) and ($0,\ensuremath{\pi}$). At ${t}_{\ensuremath{\perp}}/t\ensuremath{\simeq}2.5$, Mott features dominate in the momentum sectors ($\ensuremath{\pi},\ensuremath{\pi}$) of the bonding band and ($0,0$) of the antibonding band, and at ${t}_{\ensuremath{\perp}}/t\ensuremath{\simeq}3.0$, a tiny scattering rate is observed in all momentum sectors at the Fermi level, indicating a transition from a Mott to a band insulator. We attribute such a momentum-dependent evolution of the insulating behavior to the competition and cooperation between short-range spatial fluctuations and interlayer coupling ${t}_{\ensuremath{\perp}}$ with the help of the Coulomb interaction $U$. Finally, we also discuss the possible appearance of non-Fermi liquid behavior away from half-filling.

DOI
10.1103/physrevb.89.035139

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We investigate the nature of the insulating phases in a bilayer Hubbard model with intralayer coupling ttt and interlayer coupling t\ensuremath⊥{t}_{\ensuremath{\perp}}t\ensuremath⊥​ at large interaction strength U/tU/tU/t and half-filling. We consider a dynamical cluster approximation with a cluster size of Nc=2\ifmmode×\else\texttimes\fi4{N}_{c}=2\ifmmode\times\else\texttimes\fi{}4Nc​=2\ifmmode×\else\texttimes\fi4, where short-range spatial fluctuations as well as on-site dynamical fluctuations are emphasized. By varying the band splitting (t\ensuremath⊥/t{t}_{\ensuremath{\perp}}/tt\ensuremath⊥​/t), we find that at t\ensuremath⊥/t\ensuremath≃1.5{t}_{\ensuremath{\perp}}/t\ensuremath{\simeq}1.5t\ensuremath⊥​/t\ensuremath≃1.5 the Mott behavior is rapidly suppressed in the momentum sectors (\ensuremathπ,0\ensuremath{\pi},0\ensuremathπ,0) and (0,\ensuremathπ0,\ensuremath{\pi}0,\ensuremathπ). At t\ensuremath⊥/t\ensuremath≃2.5{t}_{\ensuremath{\perp}}/t\ensuremath{\simeq}2.5t\ensuremath⊥​/t\ensuremath≃2.5, Mott features dominate in the momentum sectors (\ensuremathπ,\ensuremathπ\ensuremath{\pi},\ensuremath{\pi}\ensuremathπ,\ensuremathπ) of the bonding band and (0,00,00,0) of the antibonding band, and at t\ensuremath⊥/t\ensuremath≃3.0{t}_{\ensuremath{\perp}}/t\ensuremath{\simeq}3.0t\ensuremath⊥​/t\ensuremath≃3.0, a tiny scattering rate is observed in all momentum sectors at the Fermi level, indicating a transition from a Mott to a band insulator. We attribute such a momentum-dependent evolution of the insulating behavior to the competition and cooperation between short-range spatial fluctuations and interlayer coupling t\ensuremath⊥{t}_{\ensuremath{\perp}}t\ensuremath⊥​ with the help of the Coulomb interaction UUU. Finally, we also discuss the possible appearance of non-Fermi liquid behavior away from half-filling.
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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 study the real-frequency structure of the self-energy in the bilayer Hubbard model, using the dynamical cluster approximation. At half filling, the Mott insulator-band insulator (MI-BI) crossover involves a rearrangement of self-energy poles between the bonding and antibonding bands; these poles cross as the interlayer hopping t⊥t_{\perp}t⊥​ is varied. Upon doping, this pole structure produces a band-selective pseudogap and enhances s±s^{\pm}s±-wave superconductivity. The order parameter is maximized near the MI-BI boundary, where low-energy anomalous self-energy poles develop simultaneously in both bands and cooperatively enhance the pairing. We further show that these self-energy poles can be interpreted as emergent fermionic excitations, offering an enhanced-pairing mechanism in common with the single-layer Hubbard model. The controllability of these poles through t⊥t_{\perp}t⊥​ makes the bilayer system an unconventional platform for optimizing strongly correlated superconductivity.
We investigate the phase diagram of the square lattice bilayer Hubbard model at half-filling with the variational Monte Carlo method for both the magnetic and the paramagnetic case as a function of the interlayer hopping and on-site Coulomb repulsion U . With this study we resolve some discrepancies in previous calculations based on the dynamical mean-field theory, and we are able to determine the nature of the phase transitions between metal, Mott insulator and band insulator. In the magnetic case we find only two phases: an antiferromagnetic Mott insulator at small for any value of U and a band insulator at large . At large U values we approach the Heisenberg limit. The paramagnetic phase diagram shows at small a metal to Mott insulator transition at moderate U values and a Mott to band insulator transition at larger U values. We also observe a re-entrant Mott insulator to metal transition and metal to band insulator transition for increasing in the range of . Finally, we discuss the phase diagrams obtained in relation to findings from previous studies based on different many-body approaches.
Abstract. We investigate the phase diagram of the square lattice bilayer Hubbard model at half filling with the variational Monte Carlo method for both the magnetic and the paramagnetic case as a function of the interlayer hopping t ⊥ and on-site Coulomb repulsion U. With this study we resolve some discrepancies in previous calculations based on the dynamical mean field theory, and we are able to determine the nature of the phase transitions between metal, Mott insulator and band insulator. In the magnetic case we find only two phases: An antiferromagnetic Mott insulator at small t ⊥ for any value of U and a band insulator at large t⊥. At large U values we approach the Heisenberg limit. The paramagnetic phase diagram shows at small t ⊥ a metal to Mott insulator transition at moderate U values and a Mott to band insulator transition at larger U values. We also observe a re-entrant Mott insulator to metal transition and metal to band insulator transition for increasing t ⊥ in the range of 5.5t < U < 7.5t. Finally, we discuss the obtained phase diagrams in relation to previous studies based on different many-body approaches. PACS numbers: 71.10.Fd, 71.27.+a, 71.30.+h 1.
Cooperation and competition between the antiferromagnetic, ddd-wave superconducting, and Mott-insulating states are explored for the two-dimensional Hubbard model including nearest and next-nearest-neighbor hoppings at zero temperature. Using the variational cluster approach with clusters of different shapes and sizes up to 10 sites, it is found that the doping-driven transition from a phase with microscopic coexistence of antiferromagnetism and superconductivity to a purely superconducting phase is discontinuous for strong interaction and accompanied by phase separation. At half-filling the system is in an antiferromagnetic Mott-insulating state with vanishing charge compressibility. Upon decreasing the interaction strength UUU below a certain critical value of roughly ${U}_{c}\ensuremath{\sim}4$ (in units of the nearest-neighbor hopping), however, the filling-dependent magnetic transition changes its character and becomes continuous. Phase separation or, more carefully, the tendency towards the formation of inhomogeneous states disappears. This critical value is in contrast to previous studies, where a much larger value was obtained. Moreover, we find that the system at half-filling undergoes the Mott transition from an insulator to a state with a finite charge compressibility at essentially the same value. The weakly correlated state at half-filling exhibits superconductivity microscopically admixed to the antiferromagnetic order. This scenario suggests a close relation between phase separation and the Mott-insulator physics.