Anisotropy and strong-coupling effects on the collective mode spectrum of chiral superconductors: application to Sr2RuO41

Sauls, J. A.; Wu, Hao; Chung, Suk Bum

doi:10.3389/fphy.2015.00036

Cited by 17 publications

(16 citation statements)

References 36 publications

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“…Here we demonstrate that the signatures of bosonic spectral evolution inherent to nematic SCs can be directly captured through the microwave power absorption spectrum, P(ω) = dQRe[ j(Q, ω) · E * (Q, ω)], that is, the Joule losses of the electric field (E) and current ( j) within the penetration depth Λ = mc 2 /4πne 2 [24,[26][27][28][29]. The charge current density is obtained from the diagonal quasiclassical propagator of Eq.…”

Section: Selection Rules and Em Absorption Spectramentioning

confidence: 92%

Chiral Higgs Mode in Nematic Superconductors

et al. 2019

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Nematic superconductivity with spontaneously broken rotation symmetry has recently been reported in doped topological insulators, M x Bi 2 Se 3 (M=Cu, Sr, Nb). Here we show that the electromagnetic (EM) response of these compounds provides a spectroscopy for bosonic excitations that reflect the pairing channel and the broken symmetries of the ground state. Using quasiclassical Keldysh theory, we find two characteristic bosonic modes in nematic superconductors: the nematicity mode and the chiral Higgs mode. The former corresponds to the vibrations of the nematic order parameter associated with broken crystal symmetry, while the latter represents the excitation of chiral Cooper pairs. The chiral Higgs mode softens at a critical doping, signaling a dynamical instability of the nematic state towards a new chiral ground state with broken time reversal and mirror symmetry. Evolution of the bosonic spectrum is directly captured by EM power absorption spectra. We also discuss contributions to the bosonic spectrum from sub-dominant pairing channels to the EM response.Introduction. Spontaneous symmetry breaking is an important concept that spreads across the diverse fields of modern physics. The recent discovery of two-fold rotation symmetry in superconducting compounds, M x Bi 2 Se 3 (M = Cu, Sr, Nb), has stimulated an intense discussion of superconductivity with a new class of spontaneous symmetry breaking [1][2][3][4][5][6][7][8][9][10][11]. The rotation symmetry breaking in the basal plane is compatible with odd-parity time-reversal invariant pairing belonging to the two-dimensional irreducible representation (E u ) of the D 3d symmetry, which exhibits twofold symmetric gap anisotropy (Fig. 1). The anisotropy is represented by a nematic order parameter [12]. The odd-parity superconductor (SC) M x Bi 2 Se 3 has also attracted much attention as a prototype of DIII topological SCs that host helical Majorana fermions [13][14][15][16][17][18][19][20][21].

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Section: Selection Rules and Em Absorption Spectramentioning

confidence: 92%

Chiral Higgs Mode in Nematic Superconductors

et al. 2019

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“…In principle, the clapping modes also manifest as resonances in optical spectroscopies. 62,63,65,66 However, they do not couple to the Raman A 1g channel, 65 thus distinguishing them from the Leggett modes.…”

Section: Leggett Modes and Their Detection In Raman Spectroscopymentioning

confidence: 99%

“…These modes originate from relative phase oscillations between the two components of the chiral order parameter (thus belonging to angular momentum 2 fluctuations) and are characterized by an excitation gap √ 2∆ 0 for a two dimensional isotropic chiral p-wave superconductor. [63][64][65][66] The excitation energy may become smaller for anisotropic superconductors. 66,67 Note that by symmetry orthogonal order parameter components from different bands do not couple, so that one can treat the Leggett and clapping modes separately.…”

Section: Leggett Modes and Their Detection In Raman Spectroscopymentioning

confidence: 99%

“…[63][64][65][66] The excitation energy may become smaller for anisotropic superconductors. 66,67 Note that by symmetry orthogonal order parameter components from different bands do not couple, so that one can treat the Leggett and clapping modes separately. In principle, the clapping modes also manifest as resonances in optical spectroscopies.…”

Section: Leggett Modes and Their Detection In Raman Spectroscopymentioning

confidence: 99%

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Leggett modes and multiband superconductivity inSr2RuO4

Huang

Scaffidi²,

Sigrist

et al. 2016

Phys. Rev. B

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Sr2RuO4 is a prototypical multi-band superconductor with three bands crossing the Fermi level. These bands exhibit distinct dimensional characteristics, with one quasi-2D γ-band and two quasi-1D α-and β-bands. This leads to the expectation that the superconductivity on the γ-band may be only weakly Josephson-coupled to that on the other two bands. Based on an explicit microscopic weak coupling calculation appropriate for Sr2RuO4, we study the collective Leggett modes associated with the relative phase oscillations between the bands and show that a relatively soft Leggett mode exists due to the comparatively weaker inter-band Josephson coupling. These calculations also provide insight into why the superconducting gap magnitudes may be comparable on all three bands, despite the noticeable differences between the γ and α/β bands. The analyses can be readily applied to other multi-band superconductors.Multi-band superconductors possess physical properties that are not present in single-band superconductors. Depending on the nature of the interactions driving the Cooper pairing and the orbital character of the bands, the superconducting order parameter may not be dominated by one band with only much weaker induced superconductivity on the other bands. This is particularly so in multi-band systems with unconventional pairing symmetry, where the correlations underlying the superconductivity often involve electrons on different bands strongly interacting with each other. These inter-band interactions give rise to effective Josephson couplings between the superconducting order parameters of the different bands 1 . As a consequence, in the ground state, the multiple order parameters are locked in a configuration with a particular set of relative phases and magnitudes.Under external perturbations or at finite temperatures, the relative phase between the multiple order parameters can fluctuate, costing a finite amount of energy that is determined by the inter-band couplings. These collective excitations are commonly referred to as Leggett modes.1 They respond to electromagnetic fields in a peculiar manner, and are unlike the usual global U(1) phase fluctuations which are pushed up to the plasma frequency due to Coulomb interactions. 2 The putative chiral p-wave superconductor Sr 2 RuO 4 3-5 is a prototypical multi-band system, with three bands crossing the Fermi energy -two quasi one dimensional (1D) α/β-bands and one quasi two dimensional (2D) γ-band (Fig. 1). 9The quasi-1D bands originate primarily from the hybridized 4d xz and yz-orbitals, while the γ-band is dominated by the xy-orbital. These orbitals are further mixed by spin-orbit coupling. [6][7][8] The exact superconducting gap structure in this material is an ongoing debate. [9][10][11] In spite of this, a few things can be said regarding the effective interactions between the low energy fermions on the three Fermi surfaces. Firstly, the intraband Cooper pair scattering on the quasi-1D bands may be markedly different from that on the quasi-2D band. This could lead ...

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“…[22] Half-domain walls are more common and appear as OP suppression in the boundary regions of unconventional superconductors, [23,24] or when a singlet superconductor is in contact with a strong ferromagnet. [25] Collective modes in unconventional superconductors with broken momentum-space symmetries have been studied in d-wave materials [26]; UPt 3 and UBe 13 [27][28][29]; Sr 2 RuO 4 [30,31]. Superfluid 3 He feature many collective modes.…”

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confidence: 99%

Bound collective modes in nonuniform superconductors

Hammer

Vorontsov

2016

Phys. Rev. B

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We study dynamics of a superconducting condensate in the presence of a domain wall defect in the order parameter. We find that broken translation and reflection symmetries result in new collective excitations, bound to the domain wall region. Two additional amplitude/Higgs modes lie below the bulk pairbreaking edge 2∆; one of them is a Goldstone mode with vanishing excitation energy. Spectrum of bound collective modes is related to the topological structure and stability of the domain wall. The 'unbound' bulk collective modes and transverse gauge field mostly propagate across the domain wall, but the longitudinal component of the gauge field is completely reflected. Softening of the amplitude mode suggests reduced damping and possible route to its detection in geometrically confined superfluids or in superconductor-ferromagnetic heterostructures.

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Anisotropy and strong-coupling effects on the collective mode spectrum of chiral superconductors: application to Sr2RuO41

Cited by 17 publications

References 36 publications

Chiral Higgs Mode in Nematic Superconductors

Chiral Higgs Mode in Nematic Superconductors

Leggett modes and multiband superconductivity inSr2RuO4

Bound collective modes in nonuniform superconductors

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