Analysis and Research on EEG Signals Based on HHT Algorithm

Liu, Zhuofu; Ying, Qiongmei; Luo, Zhongming; Fan, Yingying

doi:10.1109/imccc.2016.185

“…However, Sr 2 RuO 4 lacks the frustrated inter-band interactions favorable for the formation of the complex multi-band order parameter. Nevertheless, given the difficulties in reconciling chiral p-wave pairing [9][10][11]31 and the strict experimental upper bounds placed on the edge current, [32][33][34][35] as well as the indications of Pauli limiting effect in this material, 43,44 it might be instructive to investigate the possibility of alternative TRSB superconductivity which does not necessarily involve chiral p-wave pairing.Finally, although our discussions are focused on Sr 2 RuO 4 , the analyses are suitable for studying the nature of multi-band superconductivity in other systems. …”

mentioning

confidence: 99%

“…Finally, although there is strong evidence for the timereversal symmetry breaking (TRSB) chiral p-wave superconductivity in Sr 2 RuO 4 , [26][27][28][29][30] difficulties remain in reconciling the expectations for this order and a few key experiments, including the puzzling absence [31][32][33][34] (or smallness 35 ) of spontaneous edge current (although recent years have seen numerous attempts to explain the absence of edge current [36][37][38][39][40][41][42] ), the anomalous suppression of the in-plane upper critical field H c2 43 and indications of a first order transition for in-plane H c2 at low temperatures 44 (see Ramires et al 45 for a recent attempt to explain this). It is thus tempting to ask whether Sr 2 RuO 4 could in fact support an alternative TRSB oddparity superconducting order, made possible by the multiband nature, 46 analogous to what has been discussed in the context of MgCNi 3 , 47 some iron-based superconductors, [48][49][50] and SrPtAs.…”

mentioning

confidence: 99%

Leggett modes and multiband superconductivity inSr2RuO4

Huang

¹

,

Scaffidi²,

Sigrist

³

et al. 2016

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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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“…However, Sr 2 RuO 4 lacks the frustrated inter-band interactions favorable for the formation of the complex multi-band order parameter. Nevertheless, given the difficulties in reconciling chiral p-wave pairing [9][10][11]31 and the strict experimental upper bounds placed on the edge current, [32][33][34][35] as well as the indications of Pauli limiting effect in this material, 43,44 it might be instructive to investigate the possibility of alternative TRSB superconductivity which does not necessarily involve chiral p-wave pairing.…”

Section: Discussionmentioning

confidence: 99%

“…Finally, although there is strong evidence for the timereversal symmetry breaking (TRSB) chiral p-wave superconductivity in Sr 2 RuO 4 , [26][27][28][29][30] difficulties remain in reconciling the expectations for this order and a few key experiments, including the puzzling absence [31][32][33][34] (or smallness 35 ) of spontaneous edge current (although recent years have seen numerous attempts to explain the absence of edge current [36][37][38][39][40][41][42] ), the anomalous suppression of the in-plane upper critical field H c2 43 and indications of a first order transition for in-plane H c2 at low temperatures 44 (see Ramires et al 45 for a recent attempt to explain this). It is thus tempting to ask whether Sr 2 RuO 4 could in fact support an alternative TRSB oddparity superconducting order, made possible by the multiband nature, 46 analogous to what has been discussed in the context of MgCNi 3 , 47 some iron-based superconductors, [48][49][50] and SrPtAs.…”

mentioning

confidence: 99%

Leggett modes and multi-band superconductivity in Sr2RuO4

Huang,

Scaffidi,

Sigrist

et al. 2016

Preprint

View full text Add to dashboard Cite

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 αand 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.

show abstract