Nicolás Legnazzi and Omar Osenda
Instituto de Física Enrique Gaviola (CONICET) and Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, Argentina

Nanowires of Bi₂Se₃ show topological states localized near the surface of the material [1-4]. The topological nature of these states can be analyzed using well-known quantities [5-9]. We calculate the topological entropy suggested by Kitaev and Preskill [10] for these states together with a new entropy based on a reduced density matrix that we propose as a measure to distinguish topological one-electron states. Our results show that the topological entropy is a constant independent of the parameters that characterize a topological state as its angular momentum, longitudinal wave vector, and radius of the nanowire. The new entropy is always larger for topological states than for normal ones, allowing the identification of the topological ones. We show how the reduced density matrices associated with both entropies are constructed from the pure state using positive maps [11,12] and explicitly obtaining the Krauss operators.

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