The quantized Hall response of Landau levels (LLs) provides a paradigmatic mechanism for the quantum Hall effect, where successive LLs contribute chiral edge channels. Pseudo Landau levels (pLLs), generated by strain in Dirac materials, faithfully mimic the LL spectrum but are widely believed to be incapable of supporting a quantized Hall conductivity because the associated pseudomagnetic field preserves time-reversal symmetry and the Hall response at the two valleys cancel. A natural question is whether pLLs can induce a quantum Hall effect without requiring a real magnetic field. By introducing a modified Haldane term, we lift the valley degeneracy of the pLL ladders without distorting the pLL quantization. As a result, multiple pLL branches with the same chirality induce a quantized Hall effect with high plateaus at zero magnetic flux. We establish this mechanism using an analytically solvable Fock-state lattice model and demonstrate its robustness in a strained honeycomb tight-binding lattice. Furthermore, we propose a feasible implementation in a cavity quantum electrodynamics platform, where strain and synthetic gauge fields can be programmably engineered.

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• Chern number
• Electrical conductivity
• Integer quantum Hall effect
• Landau levels
• Dirac semimetal