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Journal article
Anderson localization at the boundary of a two-dimensional topological superconductor
PHYSICAL REVIEW B, v 107(7), 75417
13 Feb 2023
Abstract
A one-dimensional boundary of a two-dimensional topological superconductor can host a number of topo-logically protected chiral modes. Combining two topological superconductors with different topological indices, it is possible to achieve a situation when only a given number of channels (m) are topologically protected, while others are not and therefore are subject to Anderson localization in the presence of disorder. We study transport properties of such quasi-one-dimensional quantum wires with broken time-reversal and spin-rotational symmetries (class D) and calculate the average conductance, its variance and the third cumulant, as well as the average shot noise power. The results are obtained for arbitrary wire length, tracing a crossover from the diffusive Drude regime to the regime of strong localization where only m protected channels conduct. Our approach is based on the nonperturbative treatment of the nonlinear supersymmetric sigma model of symmetry class D with two replicas developed in our recent publication [D. S. Antonenko et al., Phys. Rev. B 102, 195152 (2020)]. The presence of topologically protected modes results in the appearance of a topological Wess-Zumino-Witten term in the sigma-model action, which leads to an additional subsidiary series of eigenstates of the transfer-matrix Hamiltonian. The developed formalism can be applied to study the interplay of Anderson localization and topological protection in quantum wires of other symmetry classes.
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Details
- Title
- Anderson localization at the boundary of a two-dimensional topological superconductor
- Publication Details
- PHYSICAL REVIEW B, v 107(7), 75417
- Publisher
- AMER PHYSICAL SOC; COLLEGE PK
- Grant note
- We are grateful to E. J. K?nig for valuable discussions. This work was partially supported by the Russian Science Foundation under Grant No. 20-12-00361.
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Drexel University
- Web of Science ID
- WOS:000972005400003
- Scopus ID
- 2-s2.0-85148331748
- Other Identifier
- 991021861309604721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Materials Science, Multidisciplinary
- Physics, Applied
- Physics, Condensed Matter