Spin Order in Paired Quantum Hall States

Abstract

We consider quantum Hall states at even-denominator filling fractions, especially $\nu =5/2$, in the limit of small Zeeman energy. Assuming that a paired quantum Hall state forms, we study spin ordering and its interplay with pairing. We give numerical evidence that at $\nu =5/2$ an incompressible ground state will exhibit spontaneous ferromagnetism. The Ginzburg-Landau theory for the spin degrees of freedom of paired Hall states is a perturbed CP${}^2$ model. We compute the coefficients in the Ginzburg-Landau theory by a BCS-Stoner mean field theory for coexisting order parameters, and show that even if repulsion is smaller than that required for a Stoner instability, ferromagnetic fluctuations can induce a partially or fully polarized superconducting state.

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• Valley Isospin Controlled Fractional Quantum Hall States in Bilayer Graphene
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• Contrasting Behavior of the 5/2 and 7/3 Fractional Quantum Hall Effect in a Tilted Field
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• Quantum Hall Phase Diagram of Second Landau-level Half-filled Bilayers: Abelian versus Non-Abelian States
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• Influence of device geometry on tunneling in ν=5/2 quantum Hall liquid
• Experimental constraints and a possible quantum Hall state at $\nu =5/2$
• Skyrmions in the Moore-Read state at nu=5/2
• Halperin States of Particles and Holes in Ideal Time Reversal Invariant Pairs of Chern Bands and The Fractional Quantum Spin Hall Effect in Moiré MoTe${}_2$
• Localized quasiholes and the Majorana fermion in fractional quantum Hall state at nu=5/2 via direct diagonalization
• Variational Monte Carlo study of spin polarization stability of fractional quantum Hall states against realistic effects in half-filled Landau levels
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• A Particle-Hole-Symmetric Model for a Paired Fractional Quantum Hall State in a Half-filled Landau Level
• Finite-thickness effect and spin polarization of the even-denominator fractional quantum Hall states
• Magnetization and Spin Excitations of Non-Abelian Quantum Hall States
• Charged spin textures over the Moore-Read quantum Hall state