Superconductors with Magnetic Impurities: Instantons and Sub-gap States

When subject to a weak magnetic impurity potential, the order parameter and quasi-particle energy gap of a bulk singlet superconductor are suppressed. According to the conventional mean-field theory of Abrikosov and Gor'kov, the integrity of the energy gap is maintained up to a critical concentration of magnetic impurities. In this paper, a field theoretic approach is developed to critically analyze the validity of the mean field theory. Using the supersymmetry technique we find a spatially homogeneous saddle-point that reproduces the Abrikosov-Gor'kov theory, and identify instanton contributions to the density of states that render the quasi-particle energy gap soft at any non-zero magnetic impurity concentration. The sub-gap states are associated with supersymmetry broken field configurations of the action. An analysis of fluctuations around these configurations shows how the underlying supersymmetry of the action is restored by zero modes. An estimate of the density of states is given for all dimensionalities. To illustrate the universality of the present scheme we apply the same method to study `gap fluctuations' in a normal quantum dot coupled to a superconducting terminal. Using the same instanton approach, we recover the universal result recently proposed by Vavilov et al. Finally, we emphasize the universality of the present scheme for the description of gap fluctuations in d-dimensional superconducting/normal structures.Comment: 18 pages, 9 eps figure

Observações sobre a ocorrência de Mosca-Negra-dos-Citros, Aleurocanthus woglumi Ashby, 1915 (Hemiptera: Sternorrhyncha: Aleyrodidae) no estado do Amazonas Observation on the occurrence of the citrus blackfly Aleurocanthus woglumi Ashby, 1915 (Hemiptera: Sternorrhyncha: Aleyrodidae) in the Amazonas state

A mosca-negra-dos-citros (Aleurocanthus woglumi Ashby) é uma importante praga dos citros de origem asiática. Foi detectada no Brasil pela primeira vez em Belém-PA em 2001. Este trabalho tem como objetivo registrar a ocorrência de mosca-negra-dos-citros no estado do Amazonas, sua distribuição geográfica e estudos de biologia em condições de laboratório. A mosca-negra encontra-se atualmente disseminada em mais da metade dos municípios paraenses. No Amazonas foi detectada em junho de 2004 em Manaus e atualmente encontra-se disseminada em toda a área urbana deste município, ocorrendo também em Itacoatiara, Rio Preto da Eva e Iranduba. Em observações feitas em condições de laboratório em Manaus-AM, foi verificado que o ciclo de ovo-adulto foi de 71,76±2,07 dias, caracterizando como uma espécie multivoltina.<br>The citrus blackfly Aleurocanthus woglumi Ashby, pest of citrus in Asian is considered important pest. It was detected for the first time in Belém, PA in 2001. The objective of this work was to report occurrence of the citrus blackfly in Amazon state. Nowadays is found in the majority of the oriental amazon counties. In Manaus, Amazonas was detected in June 2004, actually disseminated in the urban area and in Itacoatiara, Rio Preto da Eva and Iranduba counties. In observations in laboratory in Manaus-AM, was verified that the egg-adult cycle belonged to 71,76±2,07 days, characterizing as a multivoltin species