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

Abstract

We report the observation of half-integer magnetic flux quantization in mesoscopic rings of superconducting β-Bi 2 Pd thin films. The half-quantum fluxoid manifests itself as a π phase shift in the quantum oscillation of the critical temperature. This result verifies unconventional superconductivity of β-Bi 2 Pd, in accord with the expectation of a topological superconductor. We also discuss the strong indication that β-Bi 2 Pd is a spin-triplet superconductor. The condensation of Cooper pairs gives rise to superconductivity [1]. A key signature of the electron pairing is the quantization of the magnetic flux through a multiply-connected superconducting body, in discrete units of Φ 0 = hc 2e. Indeed, the observations of the fluxoid quantization served as the first experimental verifications of the BCS theory [2, 3, 4]. Shortly after the initial magnetometry measurements, Little and Parks further demonstrated the oscillatory feature of the superconducting transition temperature T c , as a result of the periodic free energy of the superconducting state as a function of the applied magnetic flux [5]. The minimumof the free energy, or the maximum of the T c , is always achieved when the applied magnetic flux takes Φ = nΦ 0 , where n is an integer number. In the following decades, the Little-Parks effect, as a stringent test for the electron pairing, has been observed in numerous superconducting materials [6,7,8,9]. On the other hand, Geshkenbein, Larkin and Barone (GLB) predicted that

Observation of a gel of quantum vortices in a superconductor at very low magnetic fields

“…This calls for methods to manipulate vortices and entangle their states to search for non-Abelian statistics 18,58 . Superconductors considered are, among others, Fe based materials whose structural properties and superconducting parameters are similar to β−Bi 2 Pd and β−Bi 2 Pd itself [17][18][19][20]59,60 .…”

Spin-Triplet Pairing State Evidenced by Half-Quantum Flux in a Noncentrosymmetric Superconductor

“…[34][35][36]. The background can be well described by a polynominal function (black dashed line) [33]. One may subtract the background and obtain the oscillatory component ∆R versus H as shown in the lower panel of Fig.…”

“…Trapped flux may induce hysteresis behavior and shift an ordinary Little-Parks oscillation to the false appearance of a π phase shift [33]. The Little-Parks oscillation shown in Fig.…”

Reveal the nematic topological superconductivity from the anisotropic unconventional Josephson effect: Theory and application to doped Bi2Se3

“…The Little-Parks effect reflects the oscillation of the free energy of the superconductor as a function of the applied magnetic flux, resulting in a corresponding periodicity of the resistance near the superconducting transition temperature T c [79]. The minimum of the free energy [80,81], as well as the minimum of resistance, is achieved when the applied magnetic flux becomes (n + 1/2)Φ 0 for a superconducting loop containing an odd number of π-junctions [82][83][84][85], instead of nΦ 0 for a conventional s-wave superconducting loop. Here, n is an integer and Φ 0 = h/2e is the magnetic flux quantum with h Planck constant and e the elemental charge [86,87].…”

“…We propose to fabricate a square-shaped loop of Cu x Bi 2 Se 3 with outer dimensions of 800 nm by 800 nm and line width of 100 nm [83,85], which contains a U-shaped Josephson junction with a metal bridge of Au as shown in Figure 9(b). The superconducting gap of Cu x Bi 2 Se 3 is about 0.45 meV [88,89] and the Fermi velocity in the normal region (yellow bridge in Figure 9(b)) is about 1.4 × 10 6 m/s, which results in the junction coherence length ξ ≈ 652 nm.…”