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arXiv:1801.03709 · Physical review. B./Physical review. B

Influence of magnetism and correlation on the spectral properties of doped Mott insulators

Yao Wang, Brian Moritz, Cheng-Chien Chen, Thomas Devereaux, Krzysztof Wohlfeld

Published Mar 12, 2018• 13 citations
arXivHTMLPDF

Abstract

Unraveling the nature of the doping-induced transition between a Mott insulator and a weakly correlated metal is crucial to understanding novel emergent phases in strongly correlated materials. For this purpose, we study the evolution of spectral properties upon doping Mott insulating states by utilizing the cluster perturbation theory on the Hubbard and $t--J$-like models. Specifically, a quasifree dispersion crossing the Fermi level develops with small doping, and it eventually evolves into the most dominant feature at high doping levels. Although this dispersion is related to the free-electron hopping, our study shows that this spectral feature is, in fact, influenced inherently by both electron-electron correlation and spin-exchange interaction: the correlation destroys coherence, while the coupling between spin and mobile charge restores it in the photoemission spectrum. Due to the persistent impact of correlations and spin physics, the onset of gaps or the high-energy anomaly in the spectral functions can be expected in doped Mott insulators.

DOI
10.1103/physrevb.97.115120

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Unraveling the nature of the doping-induced transition between a Mott insulator and a weakly correlated metal is crucial to understanding novel emergent phases in strongly correlated materials. For this purpose, we study the evolution of spectral properties upon doping Mott insulating states by utilizing the cluster perturbation theory on the Hubbard and t−−Jt--Jt−−J-like models. Specifically, a quasifree dispersion crossing the Fermi level develops with small doping, and it eventually evolves into the most dominant feature at high doping levels. Although this dispersion is related to the free-electron hopping, our study shows that this spectral feature is, in fact, influenced inherently by both electron-electron correlation and spin-exchange interaction: the correlation destroys coherence, while the coupling between spin and mobile charge restores it in the photoemission spectrum. Due to the persistent impact of correlations and spin physics, the onset of gaps or the high-energy anomaly in the spectral functions can be expected in doped Mott insulators.
In strongly correlated electron systems, the emergence of states in the Mott gap in the single-particle spectrum following the doping of the Mott insulator is a remarkable feature that cannot be explained in a conventional rigid-band picture. Here, based on an analysis of the quantum numbers and the overlaps of relevant states, as well as through a demonstration using the ladder and bilayer $t\text{\ensuremath{-}}J$ models, it is shown that in a continuous Mott transition due to hole doping, the magnetically excited states of the Mott insulator generally emerge in the electron-addition spectrum with the dispersion relation shifted by the Fermi momentum in the momentum region where the lower Hubbard band is not completely filled. This implies that the dispersion relation of a free-electron-like mode in the electron-addition spectrum eventually transforms into essentially the momentum-shifted magnetic dispersion relation of the Mott insulator, while its spectral weight gradually disappears toward the Mott transition. This feature reflects the spin-charge separation of the Mott insulator.
Abstract How a Mott insulator develops into a weakly coupled metal upon doping is a central question to understanding various emergent correlated phenomena. To analyze this evolution and its connection to the high-Tc cuprates, we study the single-particle spectrum for the doped Hubbard model using cluster perturbation theory on superclusters. Starting from extremely low doping, we identify a heavily renormalized quasiparticle dispersion that immediately develops across the Fermi level, and a weakening polaronic side band at higher binding energy. The quasiparticle spectral weight roughly grows at twice the rate of doping in the low doping regime, but this rate is halved at optimal doping. In the heavily doped regime, we find both strong electron-hole asymmetry and a persistent presence of Mott spectral features. Finally, we discuss the applicability of the single-band Hubbard model to describe the evolution of nodal spectra measured by angle-resolved photoemission spectroscopy (ARPES) on the single-layer cuprate La2−xSrxCuO4 (0 ≤ x ≤ 0.15). This work benchmarks the predictive power of the Hubbard model for electronic properties of high-Tc cuprates.
Heavy-fermion or Kondo lattice materials are considered to be typical strongly correlated systems, for which mean-field approximations have shown that the Coulomb interaction increases the effective mass and narrows the band gap. In this paper, to clarify interaction effects on the electronic excitation, the spectral function of the Kondo lattice and periodic Anderson models is studied around Kondo insulators in the strong-coupling regime, by using the non-Abelian dynamical density-matrix renormalization group method and perturbation theory. Upon doping a Kondo insulator, an electronic mode emerges in the Kondo insulating gap, exhibiting the momentum-shifted magnetic dispersion relation. Although the ground-state properties are similar to those of a doped band insulator, the emergence of the electronic mode reflecting spin-charge separation of the Kondo insulator is a crucial interaction effect that allows us to regard the Kondo-insulator--metal transition as a type of Mott transition. In addition, electronic modes emerge even in the high-energy regime by doping in the periodic Anderson model. These strong-correlation effects have not been expected in conventional mean-field approximations and would bring a different perspective on heavy-fermion or Kondo lattice systems.
Electronic band structures usually remain unaffected by doping via a chemical-potential shift or by increasing the temperature in conventional band insulators. In contrast, it has been shown that those of Mott and Kondo insulators can be altered by doping or by increasing the temperature: electronic modes are induced within the band gap, exhibiting momentum-shifted magnetic dispersion relations from the band edges. Here, this study demonstrates that the underlying mechanism of the remarkable strong-correlation effects can be generalized to the emergence of electronic modes caused by various spin and charge perturbations, including magnetization of spin-gapped Mott and Kondo insulators. These emergent modes can alter the band structure if a macroscopic number of spins or charges are excited by the perturbations at a given moment. The origins and dispersion relations of these emergent modes, particularly why and how the dispersion relations depend on the momentum and energy of the perturbations, are elucidated by investigating the selection rules and using the Bethe ansatz and the effective theory for weak inter-unit-cell hopping. The validity and generality of the theoretical results across different models and spatial dimensions are verified by numerical calculations for the one- and two-dimensional Hubbard models, periodic Anderson models, Kondo lattice models, and ladder and bilayer Hubbard models. This study provides crucial insights into why and how spin and charge perturbations can alter the band structure in strongly correlated insulators, thereby paving the way for band-structure engineering in strong-correlation electronics, which enables previously unexplored functionalities by exploiting the unconventional characteristics revealed in this paper.
The electronic band structures of conventional band insulators generally remain unchanged under doping via chemical-potential shifts or increasing temperature. However, in Mott and Kondo insulators described by models such as the Hubbard and Kondo lattice models, distinct electronic modes with momentum-shifted magnetic dispersion relations have been shown to emerge from band edges into the gap. Here, by investigating the two-orbital Kanamori-Hubbard model, this study elucidates how and why the band structures of spin-1 antiferromagnetic insulators change with doping and temperature, revealing emergent spectral features characteristic of orbitally degenerate systems. The nature of the emergent electronic modes is clarified using weak-hopping effective theory, selection-rule analysis, and numerical calculations. In a typical parameter regime, the doping-induced modes in each orbital reflect distinct types of spin modes, while the temperature-induced modes primarily reflect the low-energy spin mode in both orbitals; in both cases, the emergent modes exhibit momentum-shifted spin-mode dispersion relations. The momentum regimes of these emergent modes can differ between orbitals if signs of the hopping parameters differ. For small inter-orbital repulsion, onsite spin-triplet pairs can form after doping, leading to a pair-breaking gap, while the temperature-induced electronic modes continue to reflect the low-energy spin mode without a pair-breaking gap. Moreover, the emergence and characteristics of electronic modes in nonequilibrium states by spin or charge perturbations are elucidated. These findings provide a comprehensive understanding of how the interplay among the spin, charge, and orbital degrees of freedom in large-spin antiferromagnetic insulators leads to emergent electronic modes, opening avenues for exploring unconventional quantum phenomena in strongly correlated systems.
Electronic modes emerge within the band gap at nonzero temperature in strongly correlated insulators such as Mott and Kondo insulators, exhibiting momentum-shifted magnetic dispersion relations from the band edges. As the temperature increases, the emergent modes gain considerable spectral weights and form robust bands that differ from the zero-temperature bands. Here, the origin of the emergent modes, their relation to doping-induced modes, and how their spectral weights increase with temperature are clarified in the ladder and bilayer Hubbard models and one- and two-dimensional Kondo lattice models using effective theory for weak inter-unit-cell hopping and numerical calculations. The results indicate that the temperature-driven change in the band structure reflecting spin excitation, including the change in the number of bands, can be observed in various strongly correlated insulators even with a spin gap, provided that the temperature increases up to about spin-excitation energies. The controlled analyses developed in this study significantly contribute to the fundamental understanding of the band structure of strongly correlated insulators at nonzero temperature. Published by the American Physical Society 2024