Quantum oscillation phenomena in low-dimensional superconductors

<sec>Low-dimensional superconductor serves as an excellent platform for investigating emergent superconducting quantum oscillation phenomena. The low-dimensional natures of these materials, originating from the finite size which is comparable with the superconducting coherence length, indicate that the corresponding physical properties will be constrained by quantum confinement effects. Importantly, some of the frontiers and hot issues in low-dimensional superconductors, including the anomalous metal state during the superconductor-insulator transition, spin-triplet pairing mechanism in superconductors, thermal-excited and electrical current-excited vortex dynamics in superconductors, and the “charge-vortex duality” in quantum dot materials and superconducting nanowires, are strongly correlated with the superconducting quantum oscillation effects. In recent years, all the above-mentioned topics have achieved breakthroughs based on the studies of superconducting quantum oscillation effects in low-dimensional superconductors. Generally, the periodicity and amplitude of the oscillation can clearly demonstrate the relation between the geometric structure of superconductors and various superconducting mechanisms. In particular, superconducting quantum oscillation phenomena are always correlated with the quantization of magnetic fluxoids and their dynamics, the pairing mechanism of superconducting electrons, and the excitation and fluctuation of superconducting systems.</sec><sec>In this review article, three types of typical superconducting quantum oscillation effects observed in low-dimensional superconductors will be discussed from the aspects of research methods, theoretical expectations, and experimental results. a) The Little-Parks effect is the superconducting version of the Aharonov-Bohm effect, whose phase, amplitude and period are all helpful in studying superconductivity: the phase reflects the pairing mechanism in superconductors, the amplitude can be used for investigating the anomalous metal state, and the period provides the information about the sample geometry. b) The vortex motion effect is excited by thermal fluctuation or electrical current, and the corresponding oscillation phenomena show distinct temperature-dependent amplitudes compared with the Little-Parks effect. c) The Weber blockade effect originates from the magnetic flux moving across the superconducting nanowire, and such an effect provides a unique nonmonotonic critical current <inline-formula><tex-math id="M1">\begin{document}$ {I}_{\mathrm{C}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20212289_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20212289_M1.png"/></alternatives></inline-formula> under a magnetic field in <inline-formula><tex-math id="M2">\begin{document}$I\text{-}V$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20212289_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20212289_M2.png"/></alternatives></inline-formula> characteristics. The prospects of the above-mentioned quantum oscillation effects of low-dimensional superconductors for applications are also discussed at the end of this review, including quantum computing, device physics and low-temperature physics.</sec>