Efros-Shklovskii Law at the Thinnest Limit of a Material

For a half-century, the Efros-Shklovskii (ES) law has been a powerful framework for describing conduction in disordered systems featuring a Coulomb gap. Here, we examined the validity of the ES law at the ultimate 2D thickness limit by investigating the low-temperature transport of three single-atom-thick crystalline systems based on the √3×√3-Au reconstruction on a Si(111) surface. Structural disorder was represented by three distinct configurations: (i) random network of domain walls (α-Au phase), (ii) inhomogeneous Au-Cu solid solution, and (iii) random 2D gas of Tl adatoms atop the crystalline layer. We found that only the domain-wall-disordered α-Au phase exhibits temperature dependence of the conduction described by the ES law. In contrast, the other two configurations display typical metallic behavior.