by Dr Naba Prakash Nayak, IIT Bombay

Abstract:

Sublattice-symmetric localization problems in lower-dimensional (quasi-1D and 2D) systems exhibit a rich variety of physical phenomena, including resilience to Anderson localization at the band center, critical metallic phases, and wavefunction freezing with multifractal characteristics. In quasi-1D systems, these phases host localized band insu- lators separated by delocalized Dyson critical points, which serve as boundaries between insulating states. In the full 2D limit, the system transitions from a finite-conductivity critical metal to a localized phase at a critical termination point [1]. The 1D winding number in these systems displays quantization that persists beyond bulk gap closures, with robust invariants being carried entirely by localized states [2]. In the 2D limit, despite lacking strong topological invariants, these systems realize weak topological phases constructed from lower-dimensional strong topological states. This weak topology fundamentally influences Anderson criticality. Furthermore, recent studies reveal that vacancy defects in bipartite lattices, such as graphene, enhance quantum metric measurements attributed to multifractal behavior with long-range correlations [3]. These findings highlight the interplay of localization, topology, and quantum geometry in lower-dimensional quantum systems.

 

[1] N. P. Nayak, S. Sarkar, K. Damle, and S. Bera, Band-center metal-insulator transition in bond-disordered graphene, Phys. Rev. B 109, 035109 (2024).
[2] I. Mondragon-Shem, T. L. Hughes, J. Song, and E. Prodan, Topological criticality in the chiral-symmetric aiii class at strong disorder, Phys. Rev. Lett. 113, 046802 (2014).
[3] Q. Marsal and A. M. Black-Schaffer, Enhanced quantum metric due to vacancies in graphene, Phys. Rev. Lett. 133, 026002 (2024).