Efficient linear scaling approach for computing the Kubo Hall conductivity

Frank Ortmann, Nicolas Leconte, Stephan Roche

    Research output: Contribution to journalArticleResearchpeer-review

    10 Citations (Scopus)

    Abstract

    © 2015 American Physical Society. We report an order-N approach to compute the Kubo Hall conductivity for disorderd two-dimensional systems reaching tens of millions of orbitals, and realistic values of the applied external magnetic fields (as low as a few Tesla). A time-evolution scheme is employed to evaluate the Hall conductivity σxy using a wave-packet propagation method and a continued fraction expansion for the computation of diagonal and off-diagonal matrix elements of the Green functions. The validity of the method is demonstrated by comparison of results with brute-force diagonalization of the Kubo formula, using (disordered) graphene as the system of study. This approach to mesoscopic system sizes is opening an unprecedented perspective for so-called reverse engineering in which the available experimental transport data are used to get a deeper understanding of the microscopic structure of the samples. Besides, this will not only allow addressing subtle issues in terms of resistance standardization of large-scale materials (such as wafer scale polycrystalline graphene), but will also enable the discovery of new quantum transport phenomena in complex two-dimensional materials, out of reach with classical methods.
    Original languageEnglish
    Article number165117
    JournalPhysical Review B - Condensed Matter and Materials Physics
    Volume91
    Issue number16
    DOIs
    Publication statusPublished - 10 Apr 2015

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