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Journal of the Physical Society of Japan

Many-Polaron Theory for CDW, SDW and Superconducting Phases in One-Dimensional N-Sites N-Elctrons System –Quantum-Classic Crossover–

Keiichirō Nasu

Published Jul 15, 1985• 0 citations
Publisher
DOI
10.1143/jpsj.54.2781

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Many-Polaron Theory for CDW, SDW and Superconducting Phases in One-Dimensional N-Sites N-Elctrons System –Quantum-Classic Crossover–

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A one-dimensional many-electron system with on-site electron-electron(e-e) and electron-phonon(e-p) interactions is studied in the context of polaron theory, so as to clarify the quantum effect of phonon on the phase diagram. Lattice distortions moving with electrons as well as a frozen one are taken into account by a variational method combined with mean field theory. The phase diagram is given in a tetrahedral coordinate, spanned by four parameters : inter-site transfer of electron T , e-e repulsion U , e-p coupling S and phonon energy ω. This “T-U-S-ω tetrahedron” is shown to be divided into CVW and SDW regions by the boundary S = U . In the CDW region, the polaron radius increases as the retardation effect increases, and in its long limit the superconducting state(SCS) becomes far unstable than CDW, while in its short limit, SCS is degenerate with CDW, indicating the importance of this radius in quantum-classic crossover.

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The Holstein-Hubbard model serves as a useful framework to investigate this interplay between the phonon-induced electron-electron attractive interaction and the direct Coulomb repulsion and can afford interesting phase diagrams due to competition among charge-density wave (CDW), spin-density wave (SDW), and superconductivity. However the detailed nature of the CDW-SDW transition is still not very well known. It is generally believed that the system undergoes a direct insulator to insulator transition from CDW to SDW with the increase of the on-site Coulomb repulsion for a given strength of the electron-phonon coupling and this is the main bottleneck for the polaronic/bipolaronic mechanism of high-temperature superconductivity. We have recently made an investigation to study the nature of the transition from SDW phase to CDW phase within the framework of a one-dimensional Holstein-Hubbard model at half-filling using a variational method. We find that an intervening metallic phase may exist at the crossover region of the CDW-SDW transition. We have also observed that if the anharmonicity of the phonons is taken into account, this metallic phase widens and the polarons become more mobile, which is a more favorable situation from the point of view of superconductivity. We shall finally show that an improved variational calculation widens the metallic phase and makes the polarons more mobile, which reconfirms the existence of the intermediate metallic phase at the SDW-CDW crossover region.

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Charge Transfer Instability with Structural Change. II. Mean Field Theory for One-Dimensional N-Sites N-Electrons System

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Stable and metastable phases of a one-dimensional many-electron system with short range electron-electron (e-e) repulsion and site-diagonal electron-phonon (e-p) interaction are studied within the mean field theory and in the adiabatic limit. The total energy of the system is calculated as a function of the three parameters: the transfer energy of the electron between neighbouring two sites T , the on-site e-e repulsive energy U and the e-p coupling energy S . The resultant phase diagram is such that the “ T - U - S triangle ” is bisected into the SDW and the CDW regions by the border-line with U = S . The metastable SDW (CDW) phase exists in addition to the stable CDW (SDW) phase in a narrow region around the bisector. The border-lines for the metastable phases and the bisector between the two stable phases flow together into the T - vertex of the triangle, indicating the intriguing instability of one-dimensional metal against U and S .

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Phase diagram of the Holstein polaron in one dimension

O. S. Barišić, S. Barišić

arXiv:0802.1154•The European Physical Journal B•Jul 1, 2008•25 citations
A one-dimensional many-electron system with on-site electron-electron(e-e) and electron-phonon(e-p) interactions is studied in the context of polaron theory, so as to clarify the quantum effect of phonon on the phase diagram. Lattice distortions moving with electrons as well as a frozen one are taken into account by a variational method combined with mean field theory. The phase diagram is given in a tetrahedral coordinate, spanned by four parameters : inter-site transfer of electron T , e-e repulsion U , e-p coupling S and phonon energy ω. This “T-U-S-ω tetrahedron” is shown to be divided into CVW and SDW regions by the boundary S = U . In the CDW region, the polaron radius increases as the retardation effect increases, and in its long limit the superconducting state(SCS) becomes far unstable than CDW, while in its short limit, SCS is degenerate with CDW, indicating the importance of this radius in quantum-classic crossover.
The Holstein-Hubbard model serves as a useful framework to investigate this interplay between the phonon-induced electron-electron attractive interaction and the direct Coulomb repulsion and can afford interesting phase diagrams due to competition among charge-density wave (CDW), spin-density wave (SDW), and superconductivity. However the detailed nature of the CDW-SDW transition is still not very well known. It is generally believed that the system undergoes a direct insulator to insulator transition from CDW to SDW with the increase of the on-site Coulomb repulsion for a given strength of the electron-phonon coupling and this is the main bottleneck for the polaronic/bipolaronic mechanism of high-temperature superconductivity. We have recently made an investigation to study the nature of the transition from SDW phase to CDW phase within the framework of a one-dimensional Holstein-Hubbard model at half-filling using a variational method. We find that an intervening metallic phase may exist at the crossover region of the CDW-SDW transition. We have also observed that if the anharmonicity of the phonons is taken into account, this metallic phase widens and the polarons become more mobile, which is a more favorable situation from the point of view of superconductivity. We shall finally show that an improved variational calculation widens the metallic phase and makes the polarons more mobile, which reconfirms the existence of the intermediate metallic phase at the SDW-CDW crossover region.
Stable and metastable phases of a one-dimensional many-electron system with short range electron-electron (e-e) repulsion and site-diagonal electron-phonon (e-p) interaction are studied within the mean field theory and in the adiabatic limit. The total energy of the system is calculated as a function of the three parameters: the transfer energy of the electron between neighbouring two sites T , the on-site e-e repulsive energy U and the e-p coupling energy S . The resultant phase diagram is such that the “ T - U - S triangle ” is bisected into the SDW and the CDW regions by the border-line with U = S . The metastable SDW (CDW) phase exists in addition to the stable CDW (SDW) phase in a narrow region around the bisector. The border-lines for the metastable phases and the bisector between the two stable phases flow together into the T - vertex of the triangle, indicating the intriguing instability of one-dimensional metal against U and S .