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Quantum Hall admittance in non-Hermitian systems

We propose a pair of the complex Berry curvatures associated with the non-Hermitian Hamiltonian and its Hermitian adjoint to reveal new physics in non-Hermitian systems. We give the complex Berry curvature and Berry phase for the two-dimensional non-Hermitian Dirac model. The imaginary part of the complex Berry phase induces the quantum Hall susceptance such that the quantum Hall conductance is generalized to quantum Hall admittance for non-Hermitian systems, which implies that the non-Hermiticity of systems could induce an intrinsic quantum capacitance or inductance of systems depending on the non-Hermitian parameters. We analyze the complex energy band structures of the two-dimensional non-Hermitian Dirac model and demonstrate the point and line gaps and their closings as the exceptional degeneracy of the energy bands in the parameter space, which are associated with topological phases. In the continuum limit, we obtain the complex Berry phase in the parameter space.