Fractional quantum Hall effect with unconventional pairing in monolayer graphene

Abstract

Motivated by the observation of even denominator fractional quantum Hall effect in the $n=3$ Landau level of monolayer graphene [Y. Kim $\text{et al.}$, Nature Physics $\text{15}$, 154 (2019)], we consider a Bardeen-Cooper-Schrieffer variational state for composite fermions and find that the composite-fermion Fermi sea in this Landau level is unstable to an $f$-wave pairing. Analogous calculation suggests the possibility of a $p$-wave pairing of composite fermions at half filling in the $n=2$ graphene Landau level, whereas no pairing instability is found at half filling in the $n=0$ and $1$ graphene Landau levels. The relevance of these results to experiments is discussed.

arXiv comment13 pages, 7 figures

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• High-Resolution Tunneling Spectroscopy of Fractional Quantum Hall States
• Composite fermion pairing induced by Landau level mixing
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Prediction of non-Abelian fractional quantum Hall effect at $\nu =2+\frac{4}{11}$
• Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene
• Unlocking new regimes in fractional quantum Hall effect with quaternions
• Phase diagram of compressible and paired states in the quarter-filled Landau level
• Magnetic field effect on tunneling through triple barrier in AB bilayer graphene
• Energy minimization of paired composite fermion wave functions in the spherical geometry
• Numerical demonstration of Abelian fractional statistics of composite fermions in the spherical geometry
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Topological pairing of composite fermions via criticality
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
• 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