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arXiv · 2407.03401

Cheshire qudits from fractional quantum spin Hall states in twisted MoTe$_2$

Rui Wen·Andrew C. Potter
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Abstract

Twisted MoTe$_2$ homobilayers exhibit transport signatures consistent with a fractional quantum spin Hall (FQSH) state. We describe a route to construct topological quantum memory elements, dubbed Cheshire qudits, formed from punching holes in such a FQSH state and using proximity-induced superconductivity to gap out the resulting helical edge states. Cheshire qudits encode quantum information in states that differ by a fractional topological "Cheshire" charge that is hidden from local detection within a condensate anyons. Control of inter-edge tunneling by gates enables both supercurrent-based readout of a Cheshire qudit, and capacitive measurement of the thermal entropy associated with its topological ground-space degeneracy. Additionally, we systematically classify different types of gapped boundaries, Cheshire qudits, and parafermionic twist defects for various Abelian and non-Abelian candidate FQSH orders that are consistent with the transport data, and describe experimental signatures to distinguish these orders.

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Rui Wen, Andrew C. Potter. 2024-07-03. Cheshire qudits from fractional quantum spin Hall states in twisted MoTe$_2$. https://arxiv.org/abs/2407.03401

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