Theory of Half-Integer Fractional Quantum Spin Hall Insulator Edges

Theory of Half-Integer Fractional Quantum Spin Hall Insulator Edges

4 Mar 2024 | Julian May-Mann, Ady Stern, and Trithep Devakul
The paper by Julian May-Mann, Ady Stern, and Trithop Devakul explores the edges of fractional quantum spin Hall insulators (FQSH) with half-integer spin Hall conductance. These states are symmetric combinations of spin-up and spin-down FQH states, conserving the z-component of spin and time-reversal symmetry. The authors consider both non-Abelian and Abelian FQSH states, including those based on the Pfaffian, anti-Pfaffian, PH-Pfaffian, 221 FQH, and generic Abelian FQH states. They find that for strong enough spin-conserving interactions, all non-Abelian and Abelian edges flow to the same fixed point, characterized by a single pair of charged counter-propagating bosonic modes. If spin-conservation is broken, the Abelian edge can be fully gapped in a time-reversal symmetric manner, while the non-Abelian edge remains gapless due to time-reversal symmetry and can flow to a new fixed point with a helical gapless pair of Majorana fermions. The results have implications for the recent observation of a half-integer edge conductance in twisted MoTe$_2$. The paper also discusses the experimental relevance of these findings, including the quantized two-terminal conductance and thermal transport signatures of the minimal FQSH and FTI edges.The paper by Julian May-Mann, Ady Stern, and Trithop Devakul explores the edges of fractional quantum spin Hall insulators (FQSH) with half-integer spin Hall conductance. These states are symmetric combinations of spin-up and spin-down FQH states, conserving the z-component of spin and time-reversal symmetry. The authors consider both non-Abelian and Abelian FQSH states, including those based on the Pfaffian, anti-Pfaffian, PH-Pfaffian, 221 FQH, and generic Abelian FQH states. They find that for strong enough spin-conserving interactions, all non-Abelian and Abelian edges flow to the same fixed point, characterized by a single pair of charged counter-propagating bosonic modes. If spin-conservation is broken, the Abelian edge can be fully gapped in a time-reversal symmetric manner, while the non-Abelian edge remains gapless due to time-reversal symmetry and can flow to a new fixed point with a helical gapless pair of Majorana fermions. The results have implications for the recent observation of a half-integer edge conductance in twisted MoTe$_2$. The paper also discusses the experimental relevance of these findings, including the quantized two-terminal conductance and thermal transport signatures of the minimal FQSH and FTI edges.
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