Anomalous Transport Gaps of Fractional Quantum Hall Phases in Graphene Landau Levels are Induced by Spin-Valley Entangled Ground States

Abstract

We evaluate the transport gaps in the most prominent fractional quantum Hall states in the $\mathbf{n}=0$ and $\mathbf{n}=1$ Landau Levels of graphene, accounting for the Coulomb interaction, lattice-scale anisotropies, and one-body terms. We find that the fractional phases in the $\mathbf{n}=0$ Landau level are bond-ordered, while those in the $\mathbf{n}=1$ Landau level are spin-valley entangled. This resolves a long-standing experimental puzzle [Amet, $\text{et al.}$, Nat. Comm. $6$, 5838 (2015)] of the contrasting Zeeman dependence of the transport gaps in the two Landau levels. The spin-valley entangled phases host gapless Goldstone modes that can be probed via bulk thermal transport measurements. As a byproduct of our computations, we place strong constraints on the values of the microscopic anisotropic couplings such that these are consistent with all known experimental results.

7 pages, 4 figures, and Supplementary Material

References in corpus (29)

• Electric Field Effect in Atomically Thin Carbon Films
• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Observation of Fractionally Quantized Anomalous Hall Effect
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Spin Filtered Edge States and Quantum Hall Effect in Graphene
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• Collective Modes and Skyrmion Excitations in Graphene SU(4) Quantum Hall Ferromagnets
• Even denominator fractional quantum Hall state in bilayer graphene
• Theory of integer quantum Hall effect in graphene
• Interplay of Coulomb and electron-phonon interactions in graphene
• Visualizing Broken Symmetry and Topological Defects in a Quantum Hall Ferromagnet
• Composite Fermions and Broken Symmetries in Graphene
• SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field
• Imaging tunable quantum Hall broken-symmetry orders in graphene
• Valley Isospin Controlled Fractional Quantum Hall States in Bilayer Graphene
• Fractional Quantum Hall Effect at $\nu =2+4/9$
• Energy gap of the even-denominator fractional quantum Hall state in bilayer graphene
• SU(4) spin waves in the $\nu =\pm 1$ quantum Hall ferromagnet in graphene
• STM in the fractional quantum Hall effect: Spectroscopy of composite-fermion bound states
• Global phase diagram of charge neutral graphene in the quantum Hall regime for generic interactions
• Quarter- and half-filled quantum Hall states and their topological orders revealed by daughter states in bilayer graphene
• Local density of states and particle entanglement in topological quantum fluids
• Fingerprints of Composite Fermion Lambda Levels in Scanning Tunneling Microscopy
• Absence of heat flow in ν = 0 quantum Hall ferromagnet in bilayer graphene
• Theory of broken symmetry quantum Hall states in the $N=1$ Landau level of Graphene
• Vanishing bulk heat flow in the nu=0 quantum Hall ferromagnet in monolayer graphene
• Magnetic and Lattice Ordered Fractional Quantum Hall Phases in Graphene
• Fractional quantum Hall coexistence phases in higher Landau levels of graphene

Cited by in corpus (1)

• Dispersion of collective modes in spinful fractional quantum Hall states on the sphere