Low-dimensional superconductor serves as an excellent platform for investigating emergent superconductingquantum oscillation phenomena. The low-dimensional natures of these materials, originating from the finite sizewhich is comparable with the superconducting coherence length, indicate that the corresponding physicalproperties will be constrained by quantum confinement effects. Importantly, some of the frontiers and hot issuesin low-dimensional superconductors, including the anomalous metal state during the superconductor-insulatortransition, spin-triplet pairing mechanism in superconductors, thermal-excited and electrical current-excitedvortex dynamics in superconductors, and the " charge-vortex duality" in quantum dot materials andsuperconducting nanowires, are strongly correlated with the superconducting quantum oscillation effects. Inrecent years, all the above-mentioned topics have achieved breakthroughs based on the studies ofsuperconducting quantum oscillation effects in low-dimensional superconductors. Generally, the periodicity andamplitude of the oscillation can clearly demonstrate the relation between the geometric structure ofsuperconductors and various superconducting mechanisms. In particular, superconducting quantum oscillationphenomena are always correlated with the quantization of magnetic fluxoids and their dynamics, the pairingmechanism of superconducting electrons, and the excitation and fluctuation of superconducting systems.ICI-V 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-Bohmeffect, whose phase, amplitude and period are all helpful in studying superconductivity: the phase reflects thepairing 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 bythermal fluctuation or electrical current, and the corresponding oscillation phenomena show distincttemperature-dependent amplitudes compared with the Little-Parks effect. c) The Weber blockade effectoriginates from the magnetic flux moving across the superconducting nanowire, and such an effect provides aunique nonmonotonic critical current under a magnetic field in characteristics. The prospects of theabove-mentioned quantum oscillation effects of low-dimensional superconductors for applications are alsodiscussed at the end of this review, including quantum computing, device physics and low-temperature physics
