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arXiv · 2304.09674

Band-center metal-insulator transition in bond-disordered graphene

Naba P. Nayak·Surajit Sarkar·Kedar Damle·Soumya Bera
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Abstract

We study the transport properties of a tight-binding model of non-interacting fermions with random hopping on the honeycomb lattice. At the particle-hole symmetric chemical potential, the absence of diagonal disorder (random onsite potentials) places the system in the well-studied chiral orthogonal universality class of disordered fermion problems, which are known to exhibit both a critical metallic phase and a dimerization-induced localized phase. Here, our focus is the behavior of the two-terminal conductance and the Lyapunov spectrum in quasi-1D geometry near the dimerization-driven transition from the metallic to the localized phase. For a staggered dimerization pattern on the square and honeycomb lattices, we find that the renormalized localization length $ξ/M$ ($M$ denotes the width of the sample) and the typical conductance display scaling behavior controlled by a crossover length-scale that diverges with exponent $ν\approx 1.05(5)$ as the critical point is approached. However, for the plaquette dimerization pattern, we observe a relatively large exponent $ν\approx 1.55(5)$ revealing an apparent non-universality of the delocalization-localization transition in the BDI symmetry class.

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Naba P. Nayak, Surajit Sarkar, Kedar Damle, Soumya Bera. 2024-02-28. Band-center metal-insulator transition in bond-disordered graphene. https://doi.org/10.1103/physrevb.109.035109

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