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Z_{3} Parafermionic Zero Modes without Andreev Backscattering from the 2/3 Fractional Quantum Hall State
Yahya Alavirad1, David Clarke1, Amit Nag1
1Department of Physics, Condensed Matter Theory Center and the Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA.
Physical Review Letters
|December 9, 2017
Summary
Parafermionic zero modes, exotic excitations with non-Abelian statistics, can be realized using superconducting quantum dots on fractional quantum Hall edges. This approach offers a pathway beyond challenging crossed Andreev reflection methods.
Area of Science:
- Condensed matter physics
- Quantum information science
- Topological quantum computation
Background:
- Parafermionic zero modes exhibit non-Abelian statistics, richer than Majorana modes.
- They are theoretically predicted at the interface of fractional quantum Hall edge states and superconductors.
- Current experimental efforts face challenges with realizing the necessary crossed Andreev reflection.
Purpose of the Study:
- To propose an alternative experimental platform for realizing parafermionic zero modes.
- To investigate the potential of superconducting quantum dot arrays on fractional quantum Hall edges.
- To overcome the limitations of existing methods for generating these exotic excitations.
Main Methods:
- Utilizing a superconducting quantum dot array structure integrated with a fractional quantum Hall edge.
- Leveraging coherent superconducting forward scattering, a phenomenon already experimentally demonstrated.
- Analyzing the interaction between a spin-singlet superconductor and spin-unpolarized 2/3 fractional quantum Hall edge loops.
Main Results:
- The proposed structure facilitates the generation of parafermionic zero modes via forward scattering.
- Systematic tuning into parafermionic degeneracy is achievable with a modest array size (around 10 elements).
- This method circumvents the difficulties associated with crossed Andreev reflection.
Conclusions:
- Superconducting quantum dot arrays offer a viable and experimentally accessible route to realizing parafermionic zero modes.
- This work provides a promising direction for advancing topological quantum computation.
- The findings pave the way for exploring novel quantum phenomena in condensed matter systems.
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