Two-dimensional (2D) Dirac semimetals possess intriguing properties due to their low-energy excitations behaving like Dirac fermions. A hallmark of these materials is the unconventional integer quantum Hall effect (IQHE), originating from the quantized Berry phase of Dirac fermions. Herein, using symmetry analysis, tight-binding models, and numerical calculations, we reveal 2D Dirac-Weyl fermions in inversion symmetry breaking systems that exhibit tunable unconventional IQHE. These unique 2D fermions are characterized by a pair of helical edge states related by time-reversal symmetry $\mathcal{T}$, which connect the projections of a Dirac point and two separate Weyl nodes, indicating that the Dirac and Weyl points are interconnected as a whole. We show that these 2D Dirac-Weyl fermions exhibit a tunable unconventional IQHE, featuring a Hall plateau sequence shifted by three units of $\frac{2e^2}{h}$. The distance between adjacent quantized Hall plateaus can be adjusted by strain, which is a unique feature that distinguishes from what is observed in graphene. Through first-principles calculations, we identify an ideal candidate material for hosting 2D Dirac-Weyl fermions, offering a promising avenue for experimental verification. Our findings open up a door to exploring unconventional IQHE in condensed-matter systems beyond graphene.

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• Integer quantum Hall effect
• Landau levels
• Symmetry protected topological states
• Tight-binding model
• k dot p method