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The puzzling appearance of a large resistance peak in the superconducting state near T, of mesoscopic superconducting wires is analyzed. It is shown that this resistance anomaly can be explained in terms of thermal Buctuations producing phase slips of the superconducting order parameter in quasi-one-dimensional wires. Good quantitative agreement with the experimental observations is obtained within the framework of the modified Langer-Ambegaokar and McCumber-Halperin models.A typical resistive transition into the superconducting state, R(T), is usually described as a slow but monotonic decrease of the resistance due to fluctuations of the superconducting order parameter alt above T" followed by a sharp drop at the transition temperature T = T,. Recent experiments on mesoscopi c superconducting samples revealed, however, a surprising R(T) behavior characterized by the presence of an anomalous resistance peak in the vicinity of T,. 2 The measured resistance typically becomes 10 to 20% higher than the normal-state resistance value B"which is extracted &om the plateau in the R(T) curve above T,. In an attempt to understand the origin of this phenomenon, Santhanam et al. , as well as Vloeberghs et oL, suggested several physical mechanisms based on the ideas discussed in Refs. 3 -5 which, however, failed to explain quantitatively the experimental observations.In this paper we show that the anomalous resistance peak in mesoscopic superconducting samples, with a width m much smaller than the temperature-dependent coherence length ((T) and the charge imbalance relaxation length Aq(T), s is related to intrinsic resistive Huctuations which can be analyzed within the framework of the Langer-Ambegaokar (LA) and McCumber-Halperins (MH) models. These models have to be modified to take into account the confinement of the superconducting current by the extremely narrow lines forming a mesoscopic sample.Typical experimental zero-field R(T) curves, clearly showing a resistance peak above T"are plotted for different transport currents I in Fig. 1. These data were obtained on a 1 x 1 pm2 square mesoscopic Al loop having a thickness t = 25 nm and a width m = 0.15 pm (see Fig. 1 inset). The details of the sample preparation and characterization have been described in detail elsewhere. ' Different samples all have a sheet resistance ranging between 1.5 and 2.0 0/U at 4.2 K, indicating a well-defined metallic character. These values are nearly 4 orders of magnitude smaller than the typical sheet resistance R~h/4e 6.45 kQ/CI for which electron localization phenomena become important.Therefore, the existence of the anomalous R(T) peak above T, ( Fig. 1) cannot be related to a resistance increase due to a pronounced granularity or disorder-induced effects.

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The superconducting field (H)-temperature ( T ) phase boundary has been measured in mesoscopic AI samples of different topology: lines, open and filled squares, which were made under the same conditions from the same material. These samples clearly show different superconducting H-T phase boundaries which are nicely reproducing the predictions of the theoretical calculations made for their particular confinement geometries. The confinement of the flux lines by the lattice of the submicrometer holes has been studied in the Pb/Ge multilayers. A substantial enhancement of the critical current j , has been achieved. Sharp integer and rational matching peaks in the j,(H) curve are observed. The possibility of the "quantum design" of the superconducting critical parameters (H,(T) and j c ( T , H)) of the mesoscopic and nanostructured superconductors by optimizing the confinement geometry for the superconducting condensate and for the flux lines has been demonstrated.