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Let K/Q_p be unramified. Inside the Emerton-Gee stack X_2, one can considerthe locus of two-dimensional mod p representations of the absolute Galois groupof K having a crystalline lift with specified Hodge-Tate weights. We study thecase where the Hodge-Tate weights are irregular, which is an analogue forGalois representations of the partial weight one condition for Hilbert modularforms. We prove that if the gap between each pair of weights is bounded by p(the irregular analogue of a Serre weight), then this locus is irreducible. Wealso establish various inclusion relations between these loci.

Irregular loci in the Emerton-Gee stack for GL_2