Fluctuation Modes in Multi-gap Superconductors

Yanagisawa, Takashi

doi:10.1007/978-3-319-59355-5_8

Cited by 2 publications

(6 citation statements)

References 119 publications

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“…This is proportional to the inverse of the Fourier transform of the Higgs Green function. This agrees with the effective action for the Higgs mode obtained by means of the functional integral method given as [62,63] S (2)…”

Section: A Higgs Green's Functionsupporting

confidence: 88%

“…In the finite-temperature formulation using the Matsubara Green's functions, the integral with respect to k 0 is replaced by the Matsubara frequency summation. There is a relation between the vertex function Λ nℓ and the self-energy Σ n based on the Ward-Takahashi identity [61,62]. We put the vertex function in the form:…”

Section: The Equation For Ng Bosonmentioning

confidence: 99%

“…The Ward-Takahashi identity is used to obtain a relation between the self-energy and the vertex function. The Ward-Takahashi identity is given as [61,62]…”

Section: Ward-takahashi Identity and Impurity Scatteringmentioning

confidence: 99%

“…The plasma mode is represented by the spatial derivative of the phase variables θ n where the order parameters are parametrized as ∆ n = e i2θn (∆ n + h n ). The action density for θ j is written as [60,62]…”

Section: Ward-takahashi Identity and Impurity Scatteringmentioning

confidence: 99%

“…There appear many interesting properties in multi-band superconductors such as time-reversal symmetry breaking [27][28][29][30][31][32][33][34][35][36][37][38][39][40], the existence of massless modes [41][42][43][44][45][46], unusual isotope effect [47][48][49] and the existence of fractionally quantizedflux vortices [50][51][52][53][54][55]. We have multiple order parameters, and thus there appear multiple Nambu-Goldstone bosons and Higgs bosons [41,[56][57][58][59][60][61][62][63][64]. This will result in significant excitation modes that are unique in multi-band superconductors.…”

Section: Introductionmentioning

confidence: 99%

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Theory of Green’s Functions of Nambu-Goldstone and Higgs Modes in Superconductors

Yanagisawa

2019

J Supercond Nov Magn

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We examine fundamental properties of Green's functions of Nambu-Goldstone and Higgs modes in superconductors with multiple order parameters. Nambu-Goldstone and Higgs modes are determined once the symmetry of the system and that of the order parameters are specified. Multiple Nambu-Goldstone modes and Higgs modes exist when we have multiple order parameters. The Nambu-Goldstone Green function D(ω, q) has the form 1/(gN (0)) 2 · (2∆) 2 /(ω 2 − c 2 s q 2 ) with the coupling constant g and cs = vF / √ 3 for small ω and q, with a pole at ω = 0 and q = 0 indicating the existence of a massless mode. It is shown, based on the Ward-Takahashi identity, that the massless mode remains massless in the presence of intraband scattering due to nonmagnetic and magnetic impurities. The pole of D(ω, q), however, disappears as ω increases as large as 2∆: ω ∼ 2∆. The Green function H(ω, q) of the Higgs mode is given by H(ω, q) ∝ (2∆) 2 /((2∆) 2 − 1 3 ω 2 + 1 3 c 2 s q 2 ) for small ω and q. H(ω, q) is proportional to 1/(gN (0)) 2 · ∆/ (2∆) 2 + c 2 s q 2 − ω 2 for ω ∼ 2∆ and ω < ω(q) where ω(q) = (2∆) 2 + c 2 s q 2 . This behavior is similar to that of the σ-particle Green function in the Gross-Neveu model. That is, the Higgs Green function H(ω, q) has the same singularity as the Green function of the σ boson of the Gross-Neveu model. The constant part of the action for the Higgs modes is important since it determines the coherence length of a superconductor. There is the case that it has a large eigenvalue, indicating that the large upper critical field Hc2 may be realized in a superconductor with multiple order parameters.

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Section: A Higgs Green's Functionsupporting

confidence: 88%

Section: The Equation For Ng Bosonmentioning

confidence: 99%

“…The Ward-Takahashi identity is used to obtain a relation between the self-energy and the vertex function. The Ward-Takahashi identity is given as [61,62]…”

Section: Ward-takahashi Identity and Impurity Scatteringmentioning

confidence: 99%

Section: Ward-takahashi Identity and Impurity Scatteringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Theory of Green’s Functions of Nambu-Goldstone and Higgs Modes in Superconductors

Yanagisawa

2019

J Supercond Nov Magn

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Mechanism of High-Temperature Superconductivity in Correlated-Electron Systems

Yanagisawa¹

2019

Condensed Matter

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It is very important to elucidate the mechanism of superconductivity for achieving room temperature superconductivity. This paper is a short review article on the mechanism of high-temperature superconductivity. In the first half of this paper, we give a brief review on mechanisms of superconductivity in many-electron systems. We believe that hightemperature superconductivity may occur in a system with interaction of large-energy scale. Empirically, this is true for superconductors that have been found so far. In the second half of this paper, we discuss cuprate high-temperature superconductors. We argue that superconductivity of high temperature cuprates is induced by the strong on-site Coulomb interaction, that is, the origin of high-temperature superconductivity is the strong electron correlation. We show the results on the ground state of electronic models for high temperature cuprates on the basis of the optimization variational Monte Carlo method. A high-temperature superconducting phase will exist in the strongly correlated region.

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Fluctuation Modes in Multi-gap Superconductors

Cited by 2 publications

References 119 publications

Theory of Green’s Functions of Nambu-Goldstone and Higgs Modes in Superconductors

Theory of Green’s Functions of Nambu-Goldstone and Higgs Modes in Superconductors

Mechanism of High-Temperature Superconductivity in Correlated-Electron Systems

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