Events in Physics
Aires Ferreira, York
Critical delocalization of chiral zero energy modes in disordered graphene
Graphene subjected to chiral disorder is believed to host zero energy modes resilient to localisation, as dictated the renormalisation group analysis of the underlying effective field theory [1]. For “C-z” chiral disorder—such as vacancies and bond disorder—a line of fixed points with conductivity ~e2/h is predicted. Such an unconventional quantum transport regime is found at variance with recent numerical works, however, which report the localisation of all states, including the zero energy modes [2]. In this talk, I introduce an exact expansion of response functions in terms of Chebyshev polynomials, whose implementation in large memory machines allows to tackle non-interacting systems with in excess of 109 atoms and fine meV resolutions [3,4]. Its application to the honeycomb lattice with random dilute vacancy defects (orthogonal chiral class, BDI) reveals a remarkably robust metallic state at the band’s centre. The Kubo conductivity of zero energy modes is found to match graphene’s universal ballistic conductivity—4e2/(pi h) —within 1% accuracy, regardless of the vacancies’ concentration [4]. These results testify to the power of the new Chebyshev polynomial method, and provide strong evidence that the field-theoretical picture is valid well beyond its “controlled” weak-coupling regime.
[1] F. Evers and A.D. Mirlin, Rev. Mod. Phys. 80, 1355 (2008); P.M. Ostrovsky et al., Phys. Rev. Lett. 105, 266803 (2010); S. Gattenlohner et al., Phys. Rev. Lett. 112, 026802 (2014)
[2] G.T. de Laissardiere and D. Mayou, Phys. Rev. Lett. 111, 146601 (2013); A. Cresti et al., Phys. Rev. Lett. 110, 196601 (2013); Z. Fan et al., Phys. Rev. B 89, 245422 (2014)
[3] A. Ferreira, unpublished
[4] A. Ferreira, and E. Mucciolo, Phys. Rev. Lett. 115, 106601 (2015)
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