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The even denominator fractional quantum Hall effect has been experimentally observed in graphene in the fourth Landau level ($n = 3$). This paper is motivated by recent studies regarding the possibility of pairing and the nature of the…
Bilayer graphene exhibits a rich phase diagram in the quantum Hall regime, arising from a multitude of internal degrees of freedom, including spin, valley, and orbital indices. The variety of fractional quantum Hall states between filling…
We study the fractional quantum Hall effect in the central Landau level of bilayer graphene. By tuning the external applied magnetic field and the electric bias between the two layers one can access a regime where there is a degeneracy…
Broken symmetry ground states with uniform electron density are common in quantum Hall systems when two Landau levels simultaneously approach the chemical potential at integer filling factor $\nu$. The close analogy between these…
A magnetic field applied perpendicularly to the chiral two-dimensional electron gas (C2DEG)\ in a Bernal-stacked bilayer graphene quantizes the kinetic energy into a discrete set of Landau levels $N=0,\pm 1,\pm 2,...$ While Landau level…
We point out that the zero-energy Landau level of Dirac fermions in graphene can be, in the presence of a repulsive electron-electron interaction, split into two (levels) associated with a "bond ordering" formation having a "Kekule…
We have investigated the fractional quantum Hall states for the Dirac electrons in a graphene layer in different Landau levels. The relativistic nature of the energy dispersion relation of the electrons in the graphene significantly…
A number of quantum Hall isospin ferromagnetic (QHIFM) states have been predicted in the relativistic zero Landau level (LL) of graphene monolayer. These states, especially the states at LL filling factor v = 0 of charge-neutral graphene,…
Using transport measurements, we investigate multicomponent quantum Hall (QH) ferromagnetism in dual-gated rhombohedral trilayer graphene (r-TLG), in which the real spin, orbital pseudospin and layer pseudospins of the lowest Landau level…
The rich phase diagram of quantum spin-ladder systems has attracted much attention in the theoretical literature. The progress in experimental realisations of this fascinating physics however has been much slower. While materials with a…
Topological and crystalline orders of electrons both benefit from enhanced Coulomb interactions in partially filled Landau levels. In bilayer graphene (BLG), the competition between fractional quantum Hall liquids and electronic crystals…
Synthetic quantum Hall bilayer (SQHB), realized by optically driven monolayer graphene in the quantum Hall regime, provides a flexible platform for engineering quantum Hall phases as discussed in [Phys. Rev. Lett. 119, 247403]. The coherent…
We consider the zero-filled quantum-Hall ferromagnetic state of bilayer graphene subject to a kink-like perpendicular electric field, which generates domain walls in the electronic state and low-energy collective modes confined to move…
The most celebrated property of the quantum spin Hall effect is the presence of spin-polarized counter-propagating edge states. This novel edge state configuration has also been predicted to occur in graphene when spin-split electron- and…
A graphene bilayer in a transverse magnetic field has a set of Landau levels with energies $E=\pm \sqrt{N(N+1)}\hslash \omega_{c}^{\ast}$ where $\omega_{c}^{\ast}$ is the effective cyclotron frequency and $% N=0,1,2,...$ All Landau levels…
The stability of the zero-energy Landau levels in bilayer graphene against the chiral symmetric disorder is examined in the presence of the trigonal warping. Based on the tight-binding lattice model with a bond disorder correlated over…
The recent discovery of fractional quantum Hall states in graphene raises the question of whether the physics of graphene and its bilayer offers any advantages over GaAs-based materials in exploring strongly-correlated states of…
We discuss monolayer and bilayer quantum Hall systems in which each layer is a half-filled Landau level (LL) system. In the mean field approximation of the Son's formalism there is a common pairing structure that underlines the…
Charge neutral bilayer graphene has a gapped ground state as transport experiments demonstrate. One of the plausible such ground states is layered antiferromagnetic spin density wave (LAF) state, where the spins in top and bottom layers…
We consider the fractional quantum Hall effect (FQHE) at the filling factor $8/17$, where signatures of incompressibility have been observed in the zeroth Landau level of bilayer graphene. We propose an Abelian state described by the…