The noncommutative Kubo Formula: Applications to Transport in Disordered Topological Insulators with and without Magnetic Fields

Abstract

The non-commutative theory of charge transport in mesoscopic aperiodic systems under magnetic fields, developed by Bellissard, Shulz-Baldes and collaborators in the 90's, is complemented with a practical numerical implementation. The scheme, which is developed within a $C^{\ast }$-algebraic framework, enable efficient evaluations of the non-commutative Kubo formula, with errors that vanish exponentially fast in the thermodynamic limit. Applications to a model of a 2-dimensional Quantum spin-Hall insulator are given. The conductivity tensor is mapped as function of Fermi level, disorder strength and temperature and the phase diagram in the plane of Fermi level and disorder strength is quantitatively derived from the transport simulations. Simulations at finite magnetic field strength are also presented.

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Cited by in corpus (8)

• Real-space calculation of the conductivity tensor for disordered topological matter
• Real-space representation of winding number for one-dimensional chiral-symmetric topological insulator
• Quantum criticality at the Chern-to-normal insulator transition
• Effect of Strong Disorder on 3-Dimensional Chiral Topological Insulators: Phase Diagrams, Maps of the Bulk Invariant and Existence of Topological Extended Bulk States
• A Non-Commutative Formula for the Isotropic Magneto-Electric Response
• Disordered Crystals from First Principles II: Transport Coefficients
• Conformal energy currents on the edge of a topological superconductor
• Regularized universal topological markers for Dirac systems