The discovery of the halo phenomenon has changed the traditional understanding of nuclear structure and opened up a new frontier in nuclear physics. The resonant states are thought to play a critical role at the formation of a halo. In this paper, we adopt the complex momentum representation method to explore the single-particle resonances for several slightly heavier nuclei than those halo nuclei found in experiment. The single particle bound and resonant levels and their evolution with the quadruple deformation beta(2) are obtained and accompanied by a clear shell structure. The configuration occupations and density distributions of valence nucleon support the existence of halo structure. Namely, an s-wave halo may be formed in the range of -0.06 <= beta(2) <= 0.13 (-0.12 <= beta(2) <= 0.12) in Fe-77 (Cr-75), and a p-wave halo may be formed in the range of 0.09 <= beta(2) <= 0.13 in Ar-53. This prediction is of referential value for the exploration of heavier halo nuclei in experiment.
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