Quantum criticality at the Chern-to-normal insulator transition

Abstract

Using the non-commutative Kubo formula for aperiodic solids [1-3] and a recently developed numerical implementation [4], we study the conductivity $\sigma$ and resistivity $\rho$ tensors as functions of Fermi level and temperature, for models of strongly disordered Chern insulators. The formalism enabled us to converge the transport coefficients at temperatures low enough to enter the quantum critical regime at the Chern-to-trivial insulator transition. We find that the ${\rho }_{xx}$-curves at different temperatures intersect each other at one single critical point, and that they obey a single-parameter scaling law with an exponent close to the universally accepted value for the unitary symmetry class. However, when compared with the established experimental facts on the plateau-insulator transition in the Integer Quantum Hall Effect, we find a universal critical conductance ${\sigma }_{xx}^c$ twice as large, an ellipse rather than a semi-circle law, and absence of the quantized Hall insulator phase.

7 figures; minor typos eliminated; references added

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• Disordered Crystals from First Principles I: Quantifying the Configuration Space
• Criticality in amorphous topological matter -- beyond the universal scaling paradigm
• Origin and localization of topological band gaps in gyroscopic metamaterials
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• The scaling behavior of the insulator to plateau transition in topological band model
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• Mapping the Current-Current Correlation Function Near a Quantum Critical Point
• Localization Trajectory and Chern-Simons axion coupling for Bilayer Quantum Anomalous Hall Systems
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• A $C^{\ast }$-algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals
• Disorder-Induced Topological Phases in a Two-Dimensional Chern Insulator with Strong Magnetic Disorder