Theory of coexistence of superconductivity and ferroelectricity: A dynamical symmetry model

Birman, Joseph L.; Weger, M.

doi:10.1103/physrevb.64.174503

Cited by 12 publications

(10 citation statements)

References 89 publications

(69 reference statements)

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“…7. We showed here that contrary to the mean-field results, an exact solution of the model demonstrates that the ferroelectric order parameter is affected by the coupling, but the superconducting order parameter is not.…”

Section: ͑3͒contrasting

confidence: 79%

“…͑4͒ below, can then be treated using the double-mean-field approximation as in Ref. 7. Results obtained for the mutual dependence of each order parameter on the other are physically reasonable and, as shown, also graphically based on numerical solution of the resulting equations, giving support to the Matthias conjecture that the FE and SC orders tend to exclude each other.…”

supporting

confidence: 57%

“…͑27͔͒ in Ref. 7. This Hamiltonian is not exactly solvable; therefore, we make a mean-field approximation in the form…”

Section: ͑3͒mentioning

confidence: 99%

“…7 They start with two separate Hamiltonians for the superconducting and ferroelectric sectors. The superconducting sector is a mean-field reduced BCS pseudospin model ͑we corrected a misprint in Ref.…”

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confidence: 99%

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Theory of coexistence of superconductivity and ferroelectricity

2007

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A new investigation of the coexistence and competition of ferroelectricity and superconductivity is reported. In particular we show that the starting Hamiltonian of a previous study by Birman and Weger (2001) can be exactly diagonalized. The result differs significantly from mean-field theory. A Hamiltonian with a different realization of the coupling between ferroelectricity and superconductivity is proposed. We report the results for mean-field theory applied to this Hamiltonian. We find that the order parameters are strongly affected by this coupling.PACS numbers: 74.20.-z, 77.80.-e, 64.90.+b, 77.90.+k In the present paper we report two related results from a reexamination of previous work on nearly ferroelectric superconductors 1 . In that paper a coupling term was introduced into the original Hamiltonian (Eq. 27 of Ref. 1). An investigation of that coupling term shows that it only gives a squeezing of the phonons and no coupling to the electronic pairs, and therefore the Hamiltonian can be diagonalized exactly. However, the double mean-field approximation does result in an effective coupling between the two subsystems. (Eq. 34 of Ref. 1). Therefore the results of the analysis of that equation remain valid. Our second result follows from introducing a different biquadratic coupling term in the Hamiltonian of Eq. 27 of Ref. 1, which satisfies gauge and inversion symmetries. This term does couple the two subsystems. We will treat this new Hamiltonian in mean-field approximation.We start with the model of coexistence of superconductivity and ferroelectricity proposed by Birman and Weger 1 . For convenience we include its main features here. Birman and Weger start with two separate Hamiltonians for the superconducting and ferroelectric sectors. The superconducting sector is a mean-field reduced BCS pseudo-spin model (we corrected a misprint in Ref. 1)where ε k is the single-electron energy and ∆ k is the pairing interaction energy. The pseudo-spin operators pk obey SU (2) commutation relations and are defined aŝandâ k↑ andâ † k↑ are the electron annihilation and creation operators for wave vector k, spin (↑) , etc.The Hamiltonian of the ferroelectric sector of the model is simply a Hamiltonian of a displaced harmonic oscillator If a single k mode is isolatedHere we notice that the structure of the pseudo-spin operators in terms of the pair operators implieŝ

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confidence: 79%

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confidence: 57%

“…͑27͔͒ in Ref. 7. This Hamiltonian is not exactly solvable; therefore, we make a mean-field approximation in the form…”

Section: ͑3͒mentioning

confidence: 99%

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confidence: 99%

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Theory of coexistence of superconductivity and ferroelectricity

2007

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“…For very large values of ion , namely, about 100 or more, we do not gain much, but being close to the ferroelectric transition, we risk instabilities; in the ferroelectric state, the interaction weakens. 13 The depth of the modulation of the dielectric constant must be extremely large. We take ion min ϭ2, ion average ϭ30, and ion max ϭ58.…”

Section: Role Of the Specific Parametersmentioning

confidence: 99%

Electron-ion interaction in a nearly ferroelectric metal

Gersten

Weger

2002

Phys. Rev. B

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We calculate the electron-ion potential for a thin metallic layer ͑in the a-b plane͒ sandwiched between two semi-infinite dielectrics. The dielectric constant of the dielectrics varies strongly in the a-b plane. We show that there is an overscreening effect, and the electron-ion interaction is strongly enhanced, for certain values of the parameters. This suggests the possibility of a greatly enhanced electron-phonon coupling in a nearly ferroelectric metal, such as the high-T c perovskites.

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Quantum nonintegrability and the classical limit for usp(4) systems

Novaes

Hornos

2005

Annals of Physics

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Theory of coexistence of superconductivity and ferroelectricity: A dynamical symmetry model

Cited by 12 publications

References 89 publications

Theory of coexistence of superconductivity and ferroelectricity

Theory of coexistence of superconductivity and ferroelectricity

Electron-ion interaction in a nearly ferroelectric metal

Quantum nonintegrability and the classical limit for usp(4) systems

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