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• W2987204920 abstract "In the theory of Anderson localization, a landscape function predicts where wave functions localize in a disordered medium, without requiring the solution of an eigenvalue problem. It is known how to construct the localization landscape for the scalar wave equation in a random potential, or equivalently for the Schrodinger equation of spinless electrons. Here, we generalize the concept to the Dirac equation, which includes the effects of spin-orbit coupling and allows us to study quantum localization in graphene or in topological insulators and superconductors. The landscape function $u(mathbit{r})$ is defined on a lattice as a solution of the differential equation $stackrel{⎴}{H}u(mathbit{r})=1$, where $stackrel{⎴}{H}$ is the Ostrowski comparison matrix of the Dirac Hamiltonian. Random Hamiltonians with the same (positive-definite) comparison matrix have localized states at the same positions, defining an equivalence class for Anderson localization. This provides for a mapping between the Hermitian and non-Hermitian Anderson model." @default.
• W2987204920 created "2019-11-22" @default.
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• W2987204920 date "2020-02-12" @default.
• W2987204920 modified "2023-09-23" @default.
• W2987204920 title "Localization landscape for Dirac fermions" @default.
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• W2987204920 doi "https://doi.org/10.1103/physrevb.101.081405" @default.
• W2987204920 hasPublicationYear "2020" @default.
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