In 1996, Hatano and Nelson used a non-Hermitian Anderson model to study the pinning (and depinning) of magnetic flux lines in superconductors. A localization-delocalization transition was found in one dimension, which corresponds to the pinning-depinning transition of the flux lines. After that, the distribution of eigenvalues in the complex plane are calculated analytically based on method of Green's function. In this talk, I will briefly introduce the above story, including:

• Anderson localization and delocalization in Hermitian systems, e.g., the edge state of quantum Hall effect and non-linear sigma models [1,2].
• Hatano-Nelson model (non-Hermitian Anderson model) [3,4].
• Distribution of eigenvalues in Hatano-Nelson model [5].

Reference:

1. Xiao-Liang Qi and Shou-Cheng Zhang, "Topological insulators and superconductors", Rev. Mod. Phys. 83, 1057 (2011).
2. Ching-Kai Chiu, Jeffrey C. Y. Teo, Andreas P. Schnyder, and Shinsei Ryu, "Classification of topological quantum matter with symmetries", Rev. Mod. Phys. 88, 035005 (2016).
3. Naomichi Hatano and David R. Nelson, "Localization Transitions in Non-Hermitian Quantum Mechanics", Phys. Rev. Lett. 77, 570 (1996).
4. Naomichi Hatano and David R. Nelson, "Vortex pinning and non-Hermitian quantum mechanics", Phys. Rev. B 56, 8651 (1997).
5. E. Brezin and A. Zee, "Non-hermitean delocalization: Multiple scattering and bounds", Nucl. Phys. B 509, 599 . (1998).