Layer Hall effect, where electrons can deflect to opposite directions in different layers of layered antiferromagnetic materials, is a promising physical phenomenon in future spatial-resolved layertronics application. Here, we demonstrate that multiple layer Hall states including layer-polarized Hall, quantized anomalous layer Hall (QALH), and nearly high-Chern-number QALH effects can be sequentially realized in the ${\text{V}}_2{\text{WS}}_4$ magnetic topological insulator family. First, with applied external electric field and increased field strength to 0.4 V/Å, layer-polarized Hall and QALH effect with fully quantized Hall conductivity plateau ${\sigma }_{xy}=e^2/h$ begins to appear in the ${\text{V}}_2{\text{WS}}_4$ bilayer. Furthermore, by tuning the electric field direction and Fermi level, QALH effect can be effectively switched between layers and the number of peaks in Hall conductivity ${\sigma }_{xy}$ exhibits a pronounced parity-dependent behavior. Remarkably, through synergetic modulation of external magnetic and electric fields, a nearly high-Chern-number QALH effect can be observed in an odd-layer ${\text{V}}_2{\text{WS}}_4$ system. The above findings provide a nearly ideal topological magnet family harboring various layer Hall effects especially with fully quantized-layered transport.

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• Density of states
• Edge states
• Electrical conductivity
• Electronic structure
• Fermi surface
• First-principles calculations
• Magnetism
• Surface states
• Topological materials