Non-Superconducting Non-Abelian Statistics in One-Dimensional Topological Insulators
arXiv:1712.07696
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.
References in corpus (17)
- Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
- Wannier90: A Tool for Obtaining Maximally-Localised Wannier Functions
- Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
- WannierTools: An open-source software package for novel topological materials
- Quantized Anomalous Hall Effect in Magnetic Topological Insulators
- Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
- A generic new platform for topological quantum computation using semiconductor heterostructures
- Non-abelian statistics of half-quantum vortices in p-wave superconductors
- Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
- Direct Measurement of the Zak phase in Topological Bloch Bands
- Implementation of universal quantum gates based on nonadiabatic geometric phases
- Non-Adiabatic Holonomic Quantum Computation in Decoherence-Free Subspaces
- Quantum control and process tomography of a semiconductor quantum dot hybrid qubit
- Spin-charge Separated Solitons in a Topological Band Insulator
- Fractional Fermions with Non-Abelian Statistics
- Localized end states in density modulated quantum wires and rings
- Quantum spin Hall insulators and quantum valley Hall insulators of BiX/SbX (X = H, F, Cl, and Br) monolayers with a record bulk band gap