The Hunt for Non-Abelian Statistics

By Yuli Lyanda-Geller

Department of Physics and Astronomy, Purdue University, West Lafayette, IN

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Search for non-Abelian statistics is driven both by the quest for a deeper understanding of nature and by prospects to eliminate the sensitivity of conventional quantum bits to the environment, opening a path for fault-tolerant quantum computing. The transformation of non-Abelions upon permutation depends only on the topology of the path of permutation and is not sensitive to its stretching, bending or twisting by local interactions, making non-Abelion-based qubits robust to environmental noise. Non-Abelian statistics requires degeneracies in many-body spectrum, and our work is aimed at search of degeneracies leading to non-Abelions in various systems.

One kind of non-Abelions, the Majorana fermions, can emerge as a result of generating topological superconducting order in semiconductors in proximity of conventional superconductors. A serious challenge in its experimental realization, the suppression of topological superconductivity by impurity disorder, led to proposals of disorder-robust platforms. We have found a new system, where topological superconductivity and Majorana fermions appear exclusively due to impurity disorder itself. Creation and control of Majorana fermions often require a symmetry leading to a spectral gap. Disorder introduces in-gap states and enables conductance and proximity-induced superconductivity. This occurs in quantum Hall ferromagnets, where electrostatic gates can induce edge states with opposite spin polarization and helical domain walls. Due to spin-orbit interactions, the spectrum is gapped, but impurities generate topological superconductivity when domain walls are coupled to a conventional superconductor. Disorder-generated topological superconductivity promises gate-manipulated Majorana fermions when superconducting contacts are implemented in recently observed individual domain walls in integer quantum Hall ferromagnet CdMnTe. Domain walls in fractional quantum Hall ferromagnets promise other non-Abelions, such as parafermions and Fibonacci anyons, and universal quantum computing.

The other system that we intensively investigate is the two-dimensional charge carrier hole system. We demonstrate that near degeneracies in hole spectra in a magnetic field, the many-body hole state at half filling of the ground state is the non-Abelian Moore-Read state. Also, charge carrier hole quantum wires are the promising setting for observation of Majorana fermions.

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  • Yuli Lyanda-Geller (2017), "The Hunt for Non-Abelian Statistics,"

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