Non-Superconducting Non-Abelian Statistics in One-Dimensional Topological Insulators

Zhigang Song

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arXiv · 1712.07696

Non-Superconducting Non-Abelian Statistics in One-Dimensional Topological Insulators

Zhigang Song

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Abstract

Topological materials are of great interest for applications in quantum computing, providing intrinsic robustness against environmental noises. A popular direction is to look for Majorana modes in integrated systems interfaced with superconducting materials. However, is superconductivity necessary for materials to exhibits non-abelian statistics? Here we predict with strong theoretical and numerical evidences that there exist topologically phases in a class of one-dimensional single crystals, which contain large bandgaps and are within experimental reach. Specifically, the nontrivial Zak phases are associated with gapless boundary states, which provides the non-Abelian statistics required for constructing topologically-protected quantum gates, even without superconductivity and magnetic field. Another anomalous feature of these materials is that the electric polarization is quantized and a transverse field induces a longitudinal polarization. This novel material property provides an experimentally-accessible mechanism for braiding the non-Abelian anyons.

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Zhigang Song. 2017-12-20. Non-Superconducting Non-Abelian Statistics in One-Dimensional Topological Insulators. https://arxiv.org/abs/1712.07696

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