It is essential to understand to what extent the protected edge states of topological insulators (TIs) can survive against the degradation of the ubiquitous disorders in realistic devices. From a different perspective, disorders can also help to enrich the applications by modulation of the phases in TIs. In this work, the phases and phase transitions in stanene, a two-dimensional TI, have been investigated via the statistical approach based on the random matrix theory. Using a tight binding model with Aderson disorder term and the Landauer-Büttiker formalism, we calculated the conductance of realistic stanene ribbons of tens of nanometers long with random disorders. The calculated phase diagram presents TI in the gap, metal in high energy and ordinary insulator in large disorder region. Increasing the width of the ribbon can significantly enhance the robustness of TI phase against disorders. Due to different underlying symmetries, the metallic phase can be further categorized into unitary and orthogonal classes according to the calculated universal conductance fluctuations. The local density of states is calculated, showing characteristic patterns, which can facilitate the experimental identification of the phases. It is found that different phases have distinguishing statistical distribution of conductance. Whereas at the phase boundary the distribution exhibits intermediate features to show where the phase transition occurs. To reveal the phase evolution process, we further studied the effects of the disorders on respective transmission channels. It is found that when phase transition takes place, the major transmission channels of the old phase are fading and the new channels of the new phase are emerging.
Keywords: conductance; disordered; fluctuations; phase transitions; stanene.
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