Random flux is commonly believed to be incapable of driving full metal-insulator transitions in noninteracting systems. Here we show that random flux can after all induce a full metal–band insulator transition in the two-dimensional Su-Schrieffer-Heeger model. Remarkably, we find that the resulting insulator can be an extrinsic higher-order topological insulator with zero-energy corner modes in proper regimes, rather than a conventional Anderson insulator. Employing both level statistics and finite-size scaling analysis, we characterize the metal–band insulator transition and numerically extract its critical exponent as $\nu =2.48\pm 0.08$. To reveal the physical mechanism underlying the transition, we present an effective band structure picture based on the random-flux averaged Green's function.

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• Quantum phase transitions
• Topological phases of matter
• Disordered systems
• Two-dimensional electron system