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Physics Procedia

Doping-induced States in the Single-particle Spectrum Originating from Magnetic Excitation of a Mott Insulator

Masanori Kohno

Published Jan 1, 2015• 11 citations
Publisher

Abstract

By infinitesimal doping of a Mott insulator, states are induced in the Mott gap in the single- particle spectrum. To clarify the nature of these states, their relationships with the magnetically excited states of the Mott insulator are investigated. By using the commutator between the Hamiltonian and an electron creation operator of the t-J model, it is shown that the doping- induced states generally have considerable overlaps with the magnetically excited states of the Mott insulator. In addition, the electron-addition spectral weight of spin-1 states from the spin- 1/2 ground state is shown to be three times as large as that of spin-0 states in the t-J model. These results imply that the doping-induced states in the small-doping limit of a continuous Mott transition can generally be interpreted as essentially the magnetically excited states of the Mott insulator which exhibit the momentum-shifted magnetic dispersion relation primarily outside the free-electron Fermi surface in the electron-addition spectrum following the doping. This picture is supported by numerical results for the one- and two-dimensional t-J models.

DOI
10.1016/j.phpro.2015.12.026

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By infinitesimal doping of a Mott insulator, states are induced in the Mott gap in the single- particle spectrum. To clarify the nature of these states, their relationships with the magnetically excited states of the Mott insulator are investigated. By using the commutator between the Hamiltonian and an electron creation operator of the t-J model, it is shown that the doping- induced states generally have considerable overlaps with the magnetically excited states of the Mott insulator. In addition, the electron-addition spectral weight of spin-1 states from the spin- 1/2 ground state is shown to be three times as large as that of spin-0 states in the t-J model. These results imply that the doping-induced states in the small-doping limit of a continuous Mott transition can generally be interpreted as essentially the magnetically excited states of the Mott insulator which exhibit the momentum-shifted magnetic dispersion relation primarily outside the free-electron Fermi surface in the electron-addition spectrum following the doping. This picture is supported by numerical results for the one- and two-dimensional t-J models.
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.
An intuitive interpretation of the relationship between the dispersion relation of the single-particle excitation in a metal and that of the spin excitation in a Mott insulator is presented, based on the results for the one- and two-dimensional Hubbard models obtained by using the Bethe ansatz, dynamical density-matrix renormalization group method, and cluster perturbation theory. The dispersion relation of the spin excitation in the Mott insulator is naturally constructed from that of the single-particle excitation in the zero-doping limit in both one- and two-dimensional Hubbard models, which allows us to interpret the doping-induced states as the states that lose charge character toward the Mott transition. The characteristic feature of the Mott transition is contrasted with the feature of a Fermi liquid and that of the transition between a band insulator and a metal.
An intuitive interpretation of the relationship between the dispersion relation of the single-particle excitation in a metal and that of the spin excitation in a Mott insulator is presented, based on the results for the one- and two-dimensional Hubbard models obtained by using the Bethe ansatz, dynamical density-matrix renormalization group method, and cluster perturbation theory. The dispersion relation of the spin excitation in the Mott insulator is naturally constructed from that of the single-particle excitation in the zero-doping limit in both one- and two-dimensional Hubbard models, which allows us to interpret the doping-induced states as the states that lose charge character toward the Mott transition. The characteristic feature of the Mott transition is contrasted with the feature of a Fermi liquid and that of the transition between a band insulator and a metal.
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.
The Mott transition is usually considered as resulting from the divergence of the effective mass of the quasiparticle in the Fermi-liquid theory; the dispersion relation around the Fermi level is considered to become flat toward the Mott transition. Here, to clarify the characterization of the Mott transition under the assumption of a Fermi-liquid-like ground state, the electron-addition excitation from the Gutzwiller wavefunction in the $t\text{\ensuremath{-}}J$ model is investigated on a chain, ladder, square lattice, and bilayer square lattice in the single-mode approximation using a Monte Carlo method. The numerical results demonstrate that an electronic mode that is continuously deformed from a noninteracting band at zero electron density loses its spectral weight and gradually disappears toward the Mott transition. It exhibits essentially the magnetic dispersion relation shifted by the Fermi momentum in the small-doping limit as indicated by recent studies for the Hubbard and $t\text{\ensuremath{-}}J$ models, even if the ground state is assumed to be a Fermi-liquid-like state exhibiting gradual disappearance of the quasiparticle weight. This implies that, rather than as the divergence of the effective mass or disappearance of the carrier density that is expected in conventional single-particle pictures, the Mott transition can be better understood as freezing of the charge degrees of freedom while the spin degrees of freedom remain active, even if the ground state is like a Fermi liquid.
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.