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arXiv:2309.05984 · Physical review. B./Physical review. B

Temperature-driven change in band structure reflecting spin-charge separation of Mott and Kondo insulators

Masanori Kohno

Published Nov 8, 2023• 4 citations
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Abstract

The electronic band structure can change with temperature in Mott and Kondo insulators, even without a phase transition. Here, to clarify the underlying mechanism, the spectral function at nonzero temperature is studied. By considering the selection rules, the spin excited states of Mott and Kondo insulators, whose excitation energies are lower than the charge gap, are shown to emerge in the electronic spectral function at nonzero temperature, exhibiting momentum-shifted magnetic dispersion relations from the band edges, as in the case of the doping-driven Mott transition at zero temperature. Based on this characteristic, we interpret the numerical results for the temperature-driven change in the band structure in the one- and two-dimensional Hubbard models, Hubbard ladder, and one-dimensional periodic Anderson model at half-filling obtained using the cluster perturbation theory with the low-temperature Lanczos method. This characteristic also explains why the band structures of Mott and Kondo insulators can change with temperature even in the energy regime far higher than the temperature and why spectral weights emerge in the energy regime within the band gap, where the excitation energies are lower than the lowest electronic excitation energy from the ground state. Furthermore, if the bandwidth of the spin excitation is comparable to the electronic band gap, the emergent electronic modes can cross the Fermi level and gain spectral weight as the temperature increases, which leads to an insulator-metal crossover. These features are primarily caused by the spin excited states that are transparent in electronic measurements at zero temperature, in contrast to the conventional view where thermal effects on electron-added states, electron-removed states, and static spin correlations are considered to mainly affect the band structure. This innovative perspective provides a different understanding from the conventional view on the electronic states at nonzero temperatures.

DOI
10.1103/physrevb.108.195116

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The electronic band structure can change with temperature in Mott and Kondo insulators, even without a phase transition. Here, to clarify the underlying mechanism, the spectral function at nonzero temperature is studied. By considering the selection rules, the spin excited states of Mott and Kondo insulators, whose excitation energies are lower than the charge gap, are shown to emerge in the electronic spectral function at nonzero temperature, exhibiting momentum-shifted magnetic dispersion relations from the band edges, as in the case of the doping-driven Mott transition at zero temperature. Based on this characteristic, we interpret the numerical results for the temperature-driven change in the band structure in the one- and two-dimensional Hubbard models, Hubbard ladder, and one-dimensional periodic Anderson model at half-filling obtained using the cluster perturbation theory with the low-temperature Lanczos method. This characteristic also explains why the band structures of Mott and Kondo insulators can change with temperature even in the energy regime far higher than the temperature and why spectral weights emerge in the energy regime within the band gap, where the excitation energies are lower than the lowest electronic excitation energy from the ground state. Furthermore, if the bandwidth of the spin excitation is comparable to the electronic band gap, the emergent electronic modes can cross the Fermi level and gain spectral weight as the temperature increases, which leads to an insulator-metal crossover. These features are primarily caused by the spin excited states that are transparent in electronic measurements at zero temperature, in contrast to the conventional view where thermal effects on electron-added states, electron-removed states, and static spin correlations are considered to mainly affect the band structure. This innovative perspective provides a different understanding from the conventional view on the electronic states at nonzero temperatures.
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
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.
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.
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.
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.
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.