Unequivocal Determination of Spin-Triplet Superconductivity Using Composite Rings Xiaoying Xu1Yufan Li12C. L. Chien13

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Unequivocal Determination of Spin-Triplet Superconductivity

Using Composite Rings

Xiaoying Xu,1Yufan Li,1,2C. L. Chien1,3

1William H. Miller III Department of Physics and Astronomy,

Johns Hopkins University, Baltimore, MD 21218, USA

2Department of Physics, The Chinese University of Hong Kong,

Shatin, Hong Kong SAR, China and

3Department of Physics, National Taiwan University, Taipei, 10617, Taiwan

(Dated: October 18, 2022)

arXiv:2210.08733v1 [cond-mat.supr-con] 17 Oct 2022

Phase-sensitive measurements on a composite ring made of a su-

perconductor of interest connected by a known singlet s-wave su-

perconductor can unambiguously determine its pairing symmetry.

In composite rings with epitaxial β−Bi2Pd and s-wave Nb, we have

observed half-integer quantum ﬂux when Nb is connected to the op-

posite crystalline ends of β−Bi2Pd and integer-quantum ﬂux when

Nb is connected to the same crystalline ends of β−Bi2Pd. These

ﬁndings provide unequivocal evidence of odd-parity pairing state of

the triplet superconductor β−Bi2Pd.

Superconductivity is the result of condensation of Cooper pairs, where the pairing of

two electrons can form either spin singlet with spin 0, or spin triplet with spin 1. To satisfy

Fermi statistics, the spatial part of the pair’s wave function must be of even parity for

spin-singlet, and of odd parity for spin-triplet pairing states. The known superconductors

(SCs) are overwhelmingly singlet-pairing, including the conventional s-wave SCs and the

high-Tcd-wave cuprates. The very rare triplet pairing state has only been conﬁrmed in

3He superﬂuid [1]. The decades-long quest of searching for intrinsic triplet SCs is currently

met with renewed interest as it has been shown that triplet pairing states generally lead to

topological superconductivity, essential for realizing Majorana fermions with non-Abelian

brading statistics that facilitates noise-resilient topological quantum computing [2–4].

By the nature of their pairing states, one can decisively distinguish between singlet and

triplet SCs by the parity symmetry of its wave function via phase-sensitive experiments

[5, 6]. It is ﬁrst proposed by Geshkenbein, Larkin, and Barone (GLB) that a signature

half-integer quantum ﬂux (HQF) can be observed in a composite ring structure, consisting

of a triplet p-wave SC connected by a singlet s-wave SC at the opposite ends [5]. It

is a straightforward testament of the odd parity for triplet pairing as the sign of the

gap function reverses upon the inversion of the momentum, or ∆k=−∆−k. This sign

reversal is experienced at the pair of s−pjunctions with opposite normal directions,

contributing a πphase shift that leads to ﬂuxoid quantization on half-integer quantum

numbers; Φ′=(n+1/2)Φ0where nis an integer.

The ﬁrst experimental demonstrations of the phase-sensitive methods are in fact a

variant of the GLB proposal to reveal the d-wave pairing symmetry in high-Tccuprates

[7]. Two orthogonally oriented crystal planes of a single crystal YBa2Cu3O7are connected

with a Pb thin ﬁlm, constituting a corner SQUID / corner junction geometry [8, 9]. The

sign change of the gap function under 90○rotation results a πphase shift in the Josephson

current-phase relation, thus revealing the dx2−y2gap structure.

The GLB experiment, in its original design and for the proposed purpose of detecting

odd parity symmetry, was carried out in Sr2RuO4-Au0.5In0.5SQUID device to examine

the proposed triplet p-wave pairing of Sr2RuO4[10]. In all the aforementioned studies,

the samples of interest are bulk single crystals. An inherent challenge with this approach

is rooted in the small value of the ﬂux quantum Φ0, approximately 20.7 Gauss-(µm)2.

The large sizes of devices when involving bulk specimen, generally on the 100 µm scale,

lead to small ﬂux quantization periods in terms of magnetic ﬁeld on the order of mGauss

[8, 10]. Extrapolation to identify the zero magnetic ﬁeld is required for establishing the

HQF, thus inevitably leaves room for ambiguity [6, 11].

We instead employ a planar composite ring structure, comprising of thin ﬁlms of epi-

taxial β−Bi2Pd, a triplet p-wave SC candidate and Nb, an s-wave SC. The thin ﬁlm

specimen has the advantage of allowing the device to be deﬁned by electron-beam (E-

beam) lithography. In this study, we fabricated µm-sized composite ring devices with the

Φ0-period on the order of 10 Oe in terms of magnetic ﬁeld. The presence of HQF can

be straightforwardly determined from the Little-Parks eﬀect [12, 13]. The result shows

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UnequivocalDeterminationofSpin-TripletSuperconductivityUsingCompositeRingsXiaoyingXu,1YufanLi,1;2C.L.Chien1;31WilliamH.MillerIIIDepartmentofPhysicsandAstronomy,JohnsHopkinsUniversity,Baltimore,MD21218,USA2DepartmentofPhysics,TheChineseUniversityofHongKong,Shatin,HongKongSAR,Chinaand3DepartmentofPhys...

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Unequivocal Determination of Spin-Triplet Superconductivity Using Composite Rings Xiaoying Xu1Yufan Li12C. L. Chien13

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