We review some recent developments in the field of quasi-one-dimensional superconductivity. We demonstrate that low temperature properties of superconducting nanowires are essentially determined by quantum fluctuations. Smooth (Gaussian) fluctuations of the superconducting phase (also associated with plasma modes propagating along a wire) may significantly affect the electron density of states in such nanowires and induce persistent current noise in superconducting nanorings. Further interesting phenomena, such as nonvanishing resistance and shot noise of the voltage in current-biased superconducting nanowires, are caused by non-Gaussian fluctuations of the order parameter — quantum phase slips (QPSs). Such phenomena may be interpreted in terms of the tunneling of fluxons playing the role of effective quantum 'particles' dual to Cooper pairs and obeying complicated full counting statistics, which reduces to the Poissonian one in the low frequency limit. We also demonstrate that QPS effects may be particularly pronounced in the thinnest wires and rings, where quantum phase slips remain unbound and determine a nonperturbative length scale L_c, beyond which the supercurrent gets suppressed by quantum fluctuations. Accordingly, for T→ 0, such nanowires should become insulating at scales exceeding L_c, whereas at shorter length scales they may still exhibit superconducting properties. We argue that certain nontrivial features associated with quantum fluctuations of the order parameter may be sensitive to a specific circuit topology and may be observed in structures like a system of capacitively coupled superconducting nanowires.

Keywords: superconductivity, low-dimensional systems, quantum fluctuations, quantum phase slips PACS: 74.25.F−, 74.40.−n, 74.78.Na (all) DOI: 10.3367/UFNe.2021.04.038962 URL: https://ufn.ru/en/articles/2022/9/a/ 001099189500001 2-s2.0-85108789686 2022PhyU...65..883S Citation: Semenov A G, Zaikin A D "Superconducting quantum fluctuations in one dimension" Phys. Usp. 65 883–919 (2022) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 24th, August 2020, revised: 5th, March 2021, accepted: 7th, April 2021 Оригинал: Семенов А Г, Заикин А Д «Сверхпроводящие квантовые флуктуации в одном измерении» УФН 192 945–983 (2022); DOI: 10.3367/UFNr.2021.04.038962