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Abstract

The quantum Hall effect in three-dimensional Weyl semimetal (WSM) receives significant attention for the emergence of the Fermi loop where the underlying two-dimensional Hall conductivity, namely, sheet Hall conductivity, shows quantized plateaus. In tilt multi-Weyl semimetals (mWSMs) lattice models, we systematically study Landau levels (LLs) and magneto-Hall conductivity both under the parallel and perpendicular magnetic field (referenced to the Weyl node's separation), i.e., B∥z and B∥x, to explore the impact of tilting and nonlinearity in the dispersion. We make use of two (single) node low-energy models to qualitatively explain the emergence of mid-gap chiral (linear crossing of chiral) LLs on the lattice for B∥z (B∥x). Remarkably, we find that the sheet Hall conductivity becomes quantized for B∥z even when two Weyl nodes project onto a single Fermi point in two opposite surfaces, forming a Fermi loop with kz as the good quantum number. On the other hand, the Fermi loop, connecting two distinct Fermi points on two opposite surfaces, with kx being the good quantum number, causes the quantization in sheet Hall conductivity for B∥x. The quantization is almost lost (perfectly remained) in the type-II phase for B∥x (B∥z). Interestingly, the jump profiles between the adjacent quantized plateaus change with the topological charge for both cases. The momentum-integrated three-dimensional Hall conductivity is not quantized; however, it bears the signature of chiral LLs resulting in the linear dependence on μ for small μ. The linear zone (its slope) reduces (increases) as the tilt (topological charge) of the underlying WSM increases.