Collective modes and implications for<i>c</i>-axis optical experiments in layered cuprates

Zha, Yuguo; Levin, K.; Liu, D. Z.

doi:10.1103/physrevb.51.6602

Cited by 17 publications

(18 citation statements)

References 26 publications

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“…Finally, it should be noted that, since both Eqs. (41) and (38) have the same poles, the condition Q ′ 22 (Q) = 0 yields the same AB mode dispersion as that determined from Eq. (43).…”

Section: A T = 0 Behavior Of the Ab Mode And Pair Susceptibilitymentioning

confidence: 61%

Pair excitations, collective modes, and gauge invariance in the BCS–Bose-Einstein crossover scenario

et al. 2000

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In this paper we study the BCS Bose Einstein condensation (BEC) crossover scenario within the superconducting state, using a T-matrix approach which yields the ground state proposed by Leggett. Here we extend this ground state analysis to finite temperatures T and interpret the resulting physics. We find two types of bosonic-like excitations of the system: long lived, incoherent pair excitations and collective modes of the superconducting order parameter, which have different dynamics. Using a gauge invariant formalism, this paper addresses their contrasting behavior as a function of T and superconducting coupling constant g. At a more physical level, our paper emphasizes how, at finite T , BCS-BEC approaches introduce an important parameter ∆ 2 pg = ∆ 2 − ∆ 2 sc into the description of superconductivity. This parameter is governed by the pair excitations and is associated with particle-hole asymmetry effects which are important for sufficiently large g. In the fermionic regime, ∆ 2 pg represents the difference between the square of the excitation gap ∆ 2 and that of the superconducting order parameter ∆ 2 sc . The parameter ∆ 2 pg , which is necessarily zero in the BCS (mean field) limit increases monotonically with the strength of the attractive interaction g. It follows that there is a significant physical distinction between this BCS-BEC crossover approach (in which g is the essential variable which determines ∆pg) and the widely discussed (Coulomb-modulated) phase fluctuation scenario in which the plasma frequency is the tuning parameter. Finally, we emphasize that in the strong coupling limit, there are important differences between the composite bosons which arise in crossover theories, and the usual bosons of the (interacting) Bose liquid. Because of constraints imposed on the fermionic excitation gap and chemical potential, in crossover theories, the fermionic degrees of freedom can never be fully removed from consideration.

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“…Finally, it should be noted that, since both Eqs. (41) and (38) have the same poles, the condition Q ′ 22 (Q) = 0 yields the same AB mode dispersion as that determined from Eq. (43).…”

Section: A T = 0 Behavior Of the Ab Mode And Pair Susceptibilitymentioning

confidence: 61%

Pair excitations, collective modes, and gauge invariance in the BCS–Bose-Einstein crossover scenario

et al. 2000

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“…It was then independently formulated in several unrelated papers by Betbeder Matibet and Nozieres [9] and Kulik et al [10] in a more complete form where both phase and amplitude fluctuations are considered. Later on, Zha and Levin [11] revisited it and presented three identities of response functions, which are now known to be part of the WIs for response functions. Recently, it was again proposed in the Keldysh formalism with time-ordered Green's functions in Ref.…”

Section: Introductionmentioning

confidence: 99%

Theories of Linear Response in BCS Superfluids and How They Meet Fundamental Constraints

Guo¹,

Chien²,

He³

2013

J Low Temp Phys

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We address the importance of symmetry and symmetry breaking on linear response theories of fermionic BCS superfluids. The linear theory of a noninteracting Fermi gas is reviewed and several consistency constraints are verified. The challenge to formulate linear response theories of BCS superfluids consistent with density and spin conservation laws comes from the presence of a broken U(1)EM symmetry associated with electromagnetism (EM) and we discuss two routes for circumventing this. The first route follows Nambu's integral-equation approach for the EM vertex function, but this method is not specific for BCS superfluids. We focus on the second route based on a consistent-fluctuation-of-the order-parameter (CFOP) approach where the gauge transformation and the fluctuations of the order parameter are treated on equal footing. The CFOP approach allows one to explicitly verify several important constraints: The EM vertex satisfies not only a Ward identity which guarantees charge conservation but also a Q-limit Ward identity associated with the compressibility sum rule. In contrast, the spin degrees of freedom associated with another U(1)z symmetry are not affected by the Cooper-pair condensation that breaks only the U(1)EM symmetry. As a consequence the collective modes from the fluctuations of the order parameter only couple to the density response function but decouple from the spin response function, which reflects the different fates of the two U(1) symmetries in the superfluid phase. Our formulation lays the ground work for application to more general theories of BCS-Bose Einstein Condensation (BEC) crossover both above and below Tc. PACS numbers: 74.20.Fg,03.75.Ss Here S ↑,↓ = ±1 as in (3). The external field A µ has a different physical meaning from that in the density channel. Since n S is the z component of spin density, the field φ coupled to n S corresponds to B z . J S is the difference between the spin-up and the spin-down currents, i.e., the magnetization current. Therefore the field which couples to it is the magnetizing field A ≡ m. The effective external vector field is thus A µ ≡ (B z , m). The resulting Hamiltonian then describes a generalized spin-magnetic field interaction. The Noether current for the global U(1) z symmetry is J µ S = (n S , J S ), which also satisfies the conservation law ∂ µ J µ S = 0.

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“…The expression (19) of the propagator in Nambu space can be further simplified to a more instructive form. We define the operatorÊ p = γ 0 ( γ · p + m) − µσ 3 − ∆γ 0 iγ 5 σ 1 in Nambu space and also introduce the projectorŝ…”

Section: Several Relativistic Models Of a Two-component Bcs Superfluimentioning

confidence: 99%

“…Gauge invariance of a microscopic linear response theory with respect to an external EM field is made possible by considering the perturbations due to the fluctuations of the order parameter in a consistent fashion. The nonrelativistic version of the CFOP method has been extensively studied [6,18,19] and here we will develop a relativistic version of this method.…”

Section: Gauge-invariant Linear Response Theorymentioning

confidence: 99%

Gauge-invariant linear response theory of relativistic Bardeen-Cooper-Schrieffer superfluids

Guo

Chien

2012

Phys. Rev. D

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We develop a gauge-invariant linear response theory for relativistic Bardeen-Cooper-Schrieffer (BCS) superfluids based on a consistent-fluctuation-of-the orderparameter (CFOP) approach. The response functions from the CFOP approach satisfy important generalized Ward identities. The gauge invariance of the CFOP theory is a consequence of treating the gauge transformation and the fluctuations of the order parameter on equal footing so collective-mode effects are properly included. We demonstrate that the pole of the response functions is associated with the massless Goldstone boson. Important physical quantities such as the compressibility and superfluid density of relativistic BCS superfluids can also be inferred from our approach. We argue that the contribution from the massless Goldstone boson is crucial in obtaining a consistent expression for the compressibility.

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Collective modes and implications forc-axis optical experiments in layered cuprates

Cited by 17 publications

References 26 publications

Pair excitations, collective modes, and gauge invariance in the BCS–Bose-Einstein crossover scenario

Pair excitations, collective modes, and gauge invariance in the BCS–Bose-Einstein crossover scenario

Theories of Linear Response in BCS Superfluids and How They Meet Fundamental Constraints

Gauge-invariant linear response theory of relativistic Bardeen-Cooper-Schrieffer superfluids

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