Anderson Critical Metal Phase in Trivial States Protected by Average Magnetic Crystalline Symmetry

TL;DR

This paper discovers a scale-invariant critical metal phase in trivial states protected by average magnetic crystalline symmetry, arising during transitions between obstructed atomic insulators under certain disorder conditions.

Contribution

It introduces the concept of a critical metal phase in magnetic crystalline symmetric systems and constructs explicit models demonstrating this phenomenon.

Findings

Critical metal phase is scale-invariant under specific disorder.

Models respecting average magnetic symmetries show this phase.

Mapping to percolation explains the underlying mechanism.

Abstract

Transitions between distinct obstructed atomic insulators (OAIs) protected by crystalline symmetries, where electrons form molecular orbitals centering away from the atom positions, must go through an intermediate metallic phase. In this work, we find that the intermediate metals will become a scale-invariant critical metal phase (CMP) under certain types of quenched disorder that respect the magnetic crystalline symmetries on average. We explicitly construct models respecting average $C_{2z}T$, $m$, and $C_{4z}T$ and show their scale-invariance under chemical potential disorder by the finite-size scaling method. Conventional theories, such as weak anti-localization and topological phase transition, cannot explain the underlying mechanism. A quantitative mapping between lattice and network models shows that the CMP can be understood through a semi-classical percolation problem. Ultimately, we systematically classify all the OAI transitions protected by (magnetic) groups $Pm$, $P2'$, $P4'$, and $P6'$ with and without spin-orbit coupling, most of which can support CMP.