Odd-frequency superconducting pairing in multiband superconductors

Black‐Schaffer, Annica M.; Balatsky, Alexander V.

doi:10.1103/physrevb.88.104514

Cited by 141 publications

(205 citation statements)

References 49 publications

(70 reference statements)

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“…Recently, an intriguing possibility of bulk odd-ω pairing was proposed for model two-band superconductors. Here an odd parity in the band index of the Cooper pair induces an odd-ω dependence [23,24]. We demonstrate odd-ω superconductivity in Sr 2 RuO 4 arising from a similar odd parity in the orbital index.…”

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confidence: 80%

Odd-Frequency Superconductivity in Sr2RuO4 Measured by Kerr Rotation

Komendová

Black‐Schaffer

2017

Phys. Rev. Lett.

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We establish the existence of bulk odd-frequency superconductivity in Sr2RuO4 and show that an intrinsic Kerr effect is a direct evidence of this state. We use both general two-and three-orbital models, as well as a realistic tight-binding description of Sr2RuO4 to demonstrate that odd-frequency pairing arises due to finite hybridization between different orbitals in the normal state, and is further enhanced by finite inter-orbital pairing.The layered perovskite strontium ruthenate Sr 2 RuO 4 hosts an exotic superconducting state at low temperatures [1], with experiments having established both spintriplet pairing [2,3] and broken time-reversal symmetry [4,5]. The strongest candidate for the spatial symmetry is chiral p-wave order, with d-vector d = ∆ 0ẑ (k x ± ik y ) [6,7], although the exact gap structure is still disputed [8][9][10][11]. For example, spontaneous edge currents, associated with chiral p-wave pairing, have so far not been found [12]. The situation is further complicated by the Fermi surface consisting of three bands originating from three hybridizing Ru 4d orbitals; electron-like γ-(from xy orbital) and β-bands (xz, yz orbitals) and hole-like α-band (xz and yz orbitals).In this work we establish that the multi-orbital nature of Sr 2 RuO 4 hosts bulk odd-frequency (odd-ω) superconductivity. Odd-ω superconductivity is a dynamical phenomenon where the fermionic nature of the Cooper pair is preserved due to an oddness in frequency (or equivalently time) [13,14]. It is well established to exist in superconductor-ferromagnet junctions [15][16][17][18][19] and also predicted for superconductor-normal metal junctions [20][21][22]. However, odd-ω superconductivity has remained elusive in bulk materials without external magnetic fields. Recently, an intriguing possibility of bulk odd-ω pairing was proposed for model two-band superconductors. Here an odd parity in the band index of the Cooper pair induces an odd-ω dependence [23,24]. We demonstrate odd-ω superconductivity in Sr 2 RuO 4 arising from a similar odd parity in the orbital index.Importantly, we also show that a finite Kerr rotation angle in clean Sr 2 RuO 4 is direct evidence of odd-ω superconductivity. Detecting the Kerr effect in superconducting Sr 2 RuO 4 was instrumental for establishing timereversal symmetry breaking [4]. Recently, it has also been shown that inter-orbital processes are needed for a finite Kerr rotation [25][26][27][28], unless invoking extrinsic impurity effects [29,30]. We find odd-ω superconductivity and Kerr rotation emerging from the same finite hybridization between different orbitals and supplemented by possible finite inter-orbital pairing.Two-orbital superconductor.-To establish odd-ω superconductivity in Sr 2 RuO 4 and its connection to the Kerr effect we start by studying a minimal two-orbital model. The general Bogoliubov-de Gennes Hamiltonian reads k Ψ † kĤ k Ψ k , wherêand Ψ † k = (c † k↑1 c † k↑2 c −k↓1 c −k↓2 ) for orbitals 1 and 2. The normal and superconducting parts of the Hamiltonian are, respectively,We...

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confidence: 80%

Odd-Frequency Superconductivity in Sr2RuO4 Measured by Kerr Rotation

Komendová

Black‐Schaffer

2017

Phys. Rev. Lett.

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“…Here the 2 center-of-mass angular momentum of the vortex can be transferred into the orbital angular momentum of the chiral d-wave state and the d-wave state can thus appear in the vortex core [148,149,150]. By this process the intrinsic chiral d-wave state in graphene has been shown to be significantly strengthened in the core of a doubly quantized s-wave superconducting vortex [151]. Due to the circular geometry of the vortex, the proximity effect is in this case significantly enhanced compared to linear Josephson junctions.…”

Section: Superconducting Proximity Effectsmentioning

confidence: 99%

“…Hence no strong predictions can be made. Interestingly, some work has shown that the chiral d-wave state in graphene can be enhanced by proximity effect to external superconductors [135,151]. This might thus offer a promising alternative approach to an experimental discovery of chiral d-wave superconductivity in graphene.…”

Section: Summary and Perspectivementioning

confidence: 99%

Chirald-wave superconductivity in doped graphene

Black‐Schaffer

Honerkamp

2014

J. Phys.: Condens. Matter

171

176

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Abstract. A highly unconventional superconducting state with a spin-singlet d x 2 −y 2 ± id xy -wave, or chiral d-wave, symmetry has recently been proposed to emerge from electron-electron interactions in doped graphene. Especially graphene doped to the van Hove singularity at 1/4 doping, where the density of states diverges, has been argued to likely be a chiral d-wave superconductor. In this review we summarize the currently mounting theoretical evidence for the existence of a chiral d-wave superconducting state in graphene, obtained with methods ranging from mean-field studies of effective Hamiltonians to angle-resolved renormalization group calculations. We further discuss multiple distinctive properties of the chiral d-wave superconducting state in graphene, as well as its stability in the presence of disorder. We also review means of enhancing the chiral d-wave state using proximity-induced superconductivity. The appearance of chiral d-wave superconductivity is intimately linked to the hexagonal crystal lattice and we also offer a brief overview of other materials which have also been proposed to be chiral d-wave superconductors.

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“…Notably, there are no zero-energy or subgap states, otherwise often associated with oddfrequency pairing. 43,48,49,[56][57][58][59] Recent works have pointed out that zero-energy states do not always accompany odd-frequency pairing, 41,54,60,61 and odd-frequency, oddinterband pairing provides another example when this happens.…”

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confidence: 99%

“…Still, it was recently pointed out, using symmetry arguments and simple mean-field BCS calculations, that superconducting pairing which is odd in both frequency and band index can be ubiquitous in multiband superconductors, although the explicit frequency dependence was never found. 41 The fermionic nature of the superconducting wave function usually renders a division into spin-singlet evenparity (i.e. s-, d-wave) or spin-triplet odd-parity (p-wave) superconductors, but it can also be even or odd under time, or equivalently frequency.…”

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confidence: 99%