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[3] A. Ferreira, unpublished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)