Borel-Padé analysis of the critical exponent of Anderson transition in Bogoliubov-de Gennes symmetry classes

  Disorder and the associated localization phenomenon are ubiquitous in physical systems. The realization of quantum kicked rotor model in chaotic atom-optic system [1] opened up the possibility of direct observation of dynamic localization in higher dimensions. The scaling theory and universality classes of Anderson transition are at the heart of the study of disordered systems. In this study, we apply Borel-Padé resummation to the β-function [2] of four Boguliubov-de Gennes symmetry classes corresponding to disordered superconductors. From the approximated β-function we derive the critical conductance and critical exponent of each symmetry class in different dimensions. We compare our three-dimensional results with a recent numerical study [3]. We also discuss the applicability of Borel-Padé resummation to the epsilon-expansion of critical exponent.

[1] Julien Chabé et al, Phys. Rev. Lett. 101, 255702 (2008)

[2] Yoshiki Ueoka and Keith Slevin, J. Phys. Soc. Jpn. 83, 084711 (2014) and J. Phys. Soc. Jpn. 86, 094707 (2017).

[3] Tong Wang et al, Phys. Rev. B 104, 014206 (2021).