Real space computational approaches for exploring charge/spin/thermal transport in materials with billions of atoms
1Catalan Institute of Nanoscience Nanotechnology, Campus UAB, Bellaterra, Spain
2ICREA, Institució Catalana de Recerca i Estudis Avancats, Spain
I will overview two decades of development of real space developments of quantum transport methodologies which have allowed simulations of bulk charge/thermal and spin transport in model systems of remarkable complexity, including all sort of disorder (static and vibrational), varying dimensionality and system sizes reaching the experimental and technology relevant scales (for technical details read ). After some introduction of the scope of those methods, I will focus on most recent developments on quantum Hall (spin) conductivities which have allowed the exploration of unprecedented transport features in disordered Dirac Matter, including our recent exploration of spin dynamics in graphene and topological insulators which demonstrate the brute force capability of such methods as unrivaled tools for new fundamental discoveries [2,3].
 L. E. F. Foa Torres, S. Roche, and J. C. Charlier, Introduction to Graphene-Based Nanomaterials: From Electronic Structure to Quantum Transport (Cambridge University Press, Cambridge, 2014).
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 D. Van Tuan et al., Nature Physics 10, 857–863 (2014); D. Van Tuan et al., Scientific Reports 6, 21046 (2016); A.W. Cummings and S. Roche, Phys. Rev. Lett. 116, 086602 (2016). A. Cresti, D. Van Tuan, D. Soriano, A. W. Cummings, S. Roche, Phys. Rev. Lett. 113, 246603 (2014). D. Van Tuan and S. Roche, Phys. Rev. Lett. 116, 106601 (2016). D. Van Tuan, J. M. Marmolejo-Tejada, X. Waintal, B.K. Nikolic, and S. Roche, arXiv:1603.03870.