We develop a manifest non-Hermitian approach of spectral and transport properties of two-dimensional mesoscopic systems in a strong magnetic field. The finite system to which several terminals are attached constitutes an open system that can be described by an effective Hamiltonian. The lifetime of the quantum states expressed by the energy imaginary part depends specifically on the lead-system coupling and makes the difference among three regimes: resonant, integer quantum Hall effect, and superradiant. The discussion is carried on in terms of edge state lifetime in different gaps, channel formation, role of hybridization, and transmission coefficients quantization. A toy model helps in understanding non-Hermitian aspects in open systems.

• Received 19 August 2016
• Revised 28 October 2016

DOI:https://doi.org/10.1103/PhysRevB.94.195431