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Register a new userResonant generation of $p$-wave Cooper pair in non-Hermitian Kitaev chain at exceptional point
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We investigate a non-Hermitian extension of Kitaev chain by considering imaginary $p$-wave pairing amplitudes. The exact solution shows that the phase diagram consists two phases with real and complex Bogoliubov-de-gens spectra, associated with $mathcal{PT}$-symmetry breaking, which is separated by a hyperbolic exceptional line. The exceptional points (EPs) correspond to a specific Cooper pair state $( 1+c_{k}^{dagger }c_{-k}^{dagger }) leftvert 0rightrangle $ with movable $k$ when the parameters vary along the exceptional line. The non-Hermiticity around EP supports resonant generation of such a pair state from the vacuum state $% leftvert 0rightrangle $ of fermions via the critical dynamic process. In addition, we propose a scheme to generate a superconducting state through a dynamic method.
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We investigate the number-anomalous of the Majorana zero modes in the non-Hermitian Kitaev chain, whose hopping and superconductor paring strength are both imbalanced. We find that the combination of two imbalanced non-Hermitian terms can induce defective Majorana edge states, which means one of the two localized edge states will disappear due to the non-Hermitian suppression effect. As a result, the conventional bulk-boundary correspondence is broken down. Besides, the defective edge states are mapped to the ground states of non-Hermitian transverse field Ising model, and the global phase diagrams of ferromagnetic-antiferromagnetic crossover for ground states are given. Our work, for the first time, reveal the break of topological robustness for the Majorana zero modes, which predict more novel effects both in topological material and in non-Hermitian physics.
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