Using the full-band $\mathbf{k}·\mathbf{p}$ Hamiltonian model and the lattice Green's function method combined with the Landauer-Büttiker formula, we investigate the magnetotransport and magnetic-field-dependent electronic structure in monolayer InSe and its nanoribbons. Landau levels of the topmost valence band of the monolayer InSe first vary linearly and then quadratically with increasing magnetic field strength. Interestingly, four edge electronic states emerge for each Landau level as the monolayer InSe is confined to nanoribbons. However, this unusual Landau level will evolve into a conventional one with increasing magnetic field strength, which has two edge electronic states. The evolution of Landau levels with increasing magnetic field strength gives rise to a step transition from $4Q_0$ to $Q_0$ in the charge conductance of the two-terminal InSe nanoribbon. Here $Q_0=2e^2/h$ is the charge conductance quantum, where $h$ is the Planck's constant and $e$ is the elementary charge. Moreover, the intrinsic conducting electronic states in the InSe nanoribbon with a perpendicular magnetic field are verified by analyzing disorder effects and the six-terminal Hall and longitudinal resistance characteristics. Both bulk and edge electronic states contribute to transport as the magnetic field strength is relatively small, whereas only edge electronic states conduct as the field is increased. Meanwhile, a step transition of the Landau level filling factor from 4 to 1 is found as well. These findings provide a deeper understanding of the magnetoelectronic structures and magnetotransport features of electronic systems with Mexican-hat-like dispersion.

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• Edge states
• Hall effect
• Landau levels
• Magnetotransport
• Microstructure