Spontaneous polarization of composite fermions in the $n=1$ Landau level of graphene

Abstract

Motivated by recent experiments that reveal expansive fractional quantum Hall states in the $n=1$ graphene Landau level and suggest a nontrivial role of the spin degree of freedom [Amet {\em et al.}, Nat. Common. {\bf 6}, 5838 (2014)], we perform accurate quantitative study of the the competition between fractional quantum Hall states with different spin polarizations. We find that the fractional quantum Hall effect is well described in terms of composite fermions, but the spin physics is qualitatively different from that in the $n=0$ Landau level. In particular, for the states at filling factors $n/(2n\pm 1)$, both exact diagonalization and the composite fermion theory show that the ground state is fully spin polarized and supports a robust spin wave mode even in the limit of vanishing Zeeman coupling. Thus, even though composite fermions are formed, a mean field description that treats them as weakly interacting particles breaks down, and the exchange interaction between them is strong enough to cause a qualitative change in the behavior by inducing full spin polarization. We also verify that the fully spin polarized composite fermion Fermi sea has lower energy than the paired Pfaffian state at the relevant half fillings in the $n=1$ graphene Landau level, indicating a lack of fractional quantum Hall effect at half filling in the $n=1$ graphene Landau level.

13 pages, 13 figures, published version

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Cited by in corpus (43)

• Even denominator fractional quantum Hall states in higher Landau levels of graphene
• The nature of composite fermions and the role of particle hole symmetry: A microscopic account
• Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
• Higher-Spin Theory of the Magnetorotons
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Fractional Quantum Hall Effect at $\nu =2+6/13$: The Parton Paradigm for the Second Landau Level
• Fermi wave vector for the non-fully spin polarized composite-fermion Fermi sea
• Fractional Quantum Hall Effect at $\nu =2+4/9$
• A non-Abelian parton state for the $\nu =2+3/8$ fractional quantum Hall effect
• Quench dynamics of collective modes in fractional quantum Hall bilayers
• ${\mathbb{Z}}_n$ superconductivity of composite bosons and the $7/3$ fractional quantum Hall effect
• Transitions from Abelian composite fermion to non-Abelian parton fractional quantum Hall states in the zeroth Landau level of bilayer graphene
• Positions of the magnetoroton minima in the fractional quantum Hall effect
• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
• Unconventional ${\mathbb{Z}}_n$ parton states at $\nu =7/3$: The role of finite width
• Fractional quantum Hall effect with unconventional pairing in monolayer graphene
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Widely Tunable Quantum Phase Transition from Moore-Read to Composite Fermi Liquid in Bilayer Graphene
• Geometric Fluctuation of Conformal Hilbert Spaces and Multiple Graviton Modes in Fractional Quantum Hall Effect
• Composite fermion pairing induced by Landau level mixing
• Origin of the $\nu =1/2$ fractional quantum Hall effect in wide quantum wells
• Local density of states and particle entanglement in topological quantum fluids
• Revisiting excitation gaps in the fractional quantum Hall effect
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Valley Stoner Instability of the Composite Fermi Sea
• Prediction of non-Abelian fractional quantum Hall effect at $\nu =2+\frac{4}{11}$
• Landau level quantization for massless Dirac fermions in the spherical geometry: graphene fractional quantum Hall effect on the Haldane sphere
• Fractional quantum Hall coexistence phases in higher Landau levels of graphene
• Incompressible Even Denominator Fractional Quantum Hall States in the Zeroth Landau Level of Monolayer Graphene
• Spin and valley ordering of fractional quantum Hall states in monolayer graphene
• Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene
• Entanglement scaling and charge fluctuations in a Fermi liquid of composite fermions
• Bubble phase at $\nu =1/3$ for a spinless hollow-core interaction
• Disorder-induced topological superconductivity in a spherical quantum-Hall--superconductor hybrid
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Fractional quantum Hall effects in graphene on a h-BN substrate
• $2{\mathbf{k}}_{\mathbf{F}}$ Density Wave Instability of Composite Fermi Liquid
• Dispersion of collective modes in spinful fractional quantum Hall states on the sphere
• Anomalous Transport Gaps of Fractional Quantum Hall Phases in Graphene Landau Levels are Induced by Spin-Valley Entangled Ground States
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor
• Composite fermions and parton wavefunctions in twisted graphene on hexagonal boron nitride
• Dipole representation of composite fermions in graphene quantum Hall systems