In this work we explore 1+1-dimensional p-wave superconductors using the probe D-brane construction. Specifically, we choose three intersecting D-brane models: D1/D5, D2/D4, and D3/D3 systems. According to the dilaton running behavior, we denote the former two systems as nonconformal models and the last system as conformal. We find that all three models are qualitatively similar in describing superconducting condensate as well as some basic features (such as the gap formation and DC superconductivity) of superconducting conductivity. There also exist some differences among the three models as far as the AC conductivity is concerned. Specifically, for D3/D3 model there is no peak at nonzero frequency for the imaginary part of the conductivity, which is present in the nonconformal models; their asymptotic behaviors are different-for D1/D5 the real part of the AC conductivity approaches one at large frequency limit, for D2/D4 it slowly goes to a certain nonzero constant smaller than one, and for D3/D3 it goes to zero. We find that the profile of the AC conductivity for the D1/D5 system is very similar to that of higher dimensional p-wave superconductors.
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