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Aspects of nuclear structure in alpha-conjugate nuclei have long beenassociated with alpha clustering, including the existence of superdeformedbands. In this paper, an alpha-particle inelastic scattering experimentinvestigating the location of $0^+$ states in $^{28}$Si is reported in anattempt to locate possible cluster states. The results are compared to asemi-microscopic model which shows good agreement with the data, and supportsthe assignment of a newly discovered $0^+$ state as the band-head of apreviously observed superdeformed band in $^{28}$Si

Alpha clustering in $^{28}$Si probed through the identification of high-lying $0^+$ states