Little-Parks oscillations with half-quantum fluxoid features in Sr2RuO4 microrings

Abstract

In a microring of a superconductor with a spin-triplet equal-spin pairing state, a fluxoid, a combined object of magnetic flux and circulating supercurrent, can penetrate as half-integer multiples of the flux quantum. A candidate material to investigate such half-quantum fluxoids is Sr 2 RuO 4 . We fabricated Sr 2 RuO 4 microrings using single crystals and measured their resistance behavior under magnetic fields controlled with a three-axis vector magnet. Proper Little-Parks oscillations in the magnetovoltage as a function of an axially applied field, associated with fluxoid quantization, are clearly observed using bulk single-crystalline superconductors. We then performed magnetovoltage measurements with additional in-plane magnetic fields. By carefully analyzing both the voltages V + (V − ) measured at positive (negative) current, we find that, above an in-plane threshold field of about 10 mT, the magnetovoltage maxima convert to minima. We interpret this behavior as the peak splitting expected for the half-quantum fluxoid states. DOI: 10.1103/PhysRevB.96.180507 Recently, it has been recognized that Majorana particles, which have unusual equivalence to their own antiparticles and have been long sought in elementary particle physics, can be realized as quasiparticle excitation in condensed-matter systems such as topological superconductors [1]. In particular, Majorana zero modes (MZMs), the zero-energy states of the Majorana branch, have attracted much attention since MZMs do not obey ordinary Abelian statistics and can be utilized for quantum computing [2,3]. Thus, direct detection of MZMs has become a holy grail of current condensed-matter physics [4,5]. Half-quantum fluxoid (HQF) [6] in a spin-triplet superconductor or a superfluid is known to host such MZMs [7,8].An additional phase degree of freedom in a superconducting wave function is the key ingredient for the realization of HQF states. For a spin-singlet superconducting ring with wave function ψ S = | S |e iθ , the single-valuedness of ψ S requires quantization = n 0 [integer-quantum fluxoid (IQF)] inside a closed path. Here, n is an integer, is the fluxoid, and 0 = h/2e is the flux quantum with h the Planck constant and e the elementary charge. Note that, in a superconductor smaller than the penetration depth, the fluxoid, which contains an integration of the supercurrent along a closed path, is quantized, rather than the flux. For a spin-triplet equal-spin pairing (ESP) superconductor, the wave function ψ T = | T |(−e iθ ↑ |↑↑ + e iθ ↓ |↓↓ ) has two phase degrees of freedom. In an ESP ring, half-integer quantization = n 0 with n = ±1/2, ± 3/2, . . . is allowed even under the constraint of the single-valuedness of the wave function. Such a fluxoid state is called the HQF state.One of the materials that can host the HQF is Sr 2 RuO 4 , which is a leading candidate spin-triplet ESP superconductor [9,10]. This oxide has a layered perovskite structure and exhibits superconductivity below 1.5 K. Various experiments have provided firm evidence for the sp...

Properties of the H−T phase diagram of the 3−K phase in eutectic Sr2Kaneyasu1, Enokida2, Nomura3 et al. 2019Phys. Rev. B7190View full textAdd to dashboardCite

“…However, Josephson tunneling experiments such as the test of selection rules and superconducting quantum interface device (SQUID) experiments connecting an s-wave superconductor with junctions on opposite in-plane faces of SRO support odd-parity pairing symmetry [24][25][26]. Moreover, the observation of half-flux quanta in micrometer-sized loops of SRO [27][28][29] is readily interpreted in terms of an odd-parity state through the additional degree of freedom of the d-vector orientation [30,31].…”

Observation of half-quantum flux in the unconventional superconductor β-Bi 2 Pd

“…1D. A broadening of the transition width (∼ 1.5 K) as compared to that of the as-grown films (< 0.2 K) is typical for devices in similar dimensions that have undergone nanofabrication processes [7,8,37,9,17]. The Little-Parks effect can be observed when the sample is placed at a fixed temperature within the superconducting transition regime, where the variation of the T c manifests as a fluctuation of the resistance [5].…”

Spontaneous emergence of Josephson junctions in homogeneous rings of single-crystal Sr2RuO4

“…For this, we compare the data from Ring A with those of Ring C (Sample B in ref. [20]), where the transition is considerably broader ( Fig. 6e).…”

“…The rings were heated up to above 5 K between each magnetic field. Data for panels (b) and (e) are adopted from [20].…”