A slab of time-reversal-symmetric Weyl semimetal serves as a realistic material platform for studying Anderson localization (AL) in two-dimensional (2D) systems, as it belongs to the symplectic symmetry class, which is the only 2D system that hosts an AL transition. In the present work, we theoretically explore the features of AL in such a slab induced by conventional white-noise disorder and random surface adsorption. By means of the scaling analysis of the localization length, we find that the surface adsorption can facilitate the AL. Specifically, a higher surface adsorption concentration results in a lower critical disorder strength of white noise. However, the bond energy of surface adsorption hardly influences the AL in the slab, since surface adsorption can equivalently be treated as random surface vacancies at a given concentration. More interestingly, when the slab with surface adsorption enters the localization regime after the AL transition, we observe anomalous near-degeneracy by statistics of the adjacent energy-level spacings of the slab. Through numerical analysis, we find that such an anomaly associated with the random surface adsorption can be justified in terms of weak level repulsion between exotic and intrinsic atoms on the slab surface in the strong localization regime.

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• Anderson localization
• Disordered systems
• Two-dimensional electron system
• Weyl semimetal
• Finite-size scaling
• Tight-binding model