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We study the recently observed graphene fractional quantum Hall state at a filling factor $\nu_G=1/3$ using a four-component trial wave function and exact diagonalization calculations. Although it is adiabatically connected to a 1/3…
The quantum Hall effect (QHE) is a topologically protected phenomenon which has been observed in various systems. In experiments, the size of Hall bar device to realize the QHE is generally much larger than the phase coherence length, in…
We have analyzed the breakdown of the quantum Hall effect in 1 micrometer wide Hall devices fabricated from an exfoliated monolayer graphene transferred on SiOx. We have observed that the deviation of the Hall resistance from its quantized…
The interplay between quantum Hall states and Cooper pairs is usually hindered by the suppression of the superconducting state due to the strong magnetic fields needed to observe the quantum Hall effect. From this point of view graphene is…
Quantum Hall effect in 1,2-layer graphene is analyzed. The transverse and longitudinal resistivity are found to be universal functions of the filling factor and temperature. At fixed magnetic field mode the magneto-transport problem is…
Graphene is a model system for the study of electrons confined to a strictly two-dimensional layer1 and a large number of electronic phenomena have been demonstrated in graphene, from the fractional2, 3 quantum Hall effect to…
In a twisted graphene on hexagonal Boron Nitride, the presence of a gap and the breaking of the symmetry between carbon sublattices leads to multicomponent fractional quantum Hall effect (FQHE) due to the electrons correlation. We report on…
We numerically study the quantum Hall effect in biased bilayer graphene based on a tight-binding model in the presence of disorder. Integer quantum Hall plateaus with quantized conductivity $\sigma_{xy}=\nu e^2/h$ (where $\nu$ is any…
The integer quantum Hall states at fillings $\nu = 0$ and $|\nu| = 1$ in monolayer graphene have drawn much attention as they are generated by electron-electron interactions. Here we explore aspects of the $\nu = 0$ and $|\nu| = 1$ quantum…
We propose realizing the quantum anomalous Hall effect by proximity coupling graphene to an antiferromagnetic insulator that provides both broken time-reversal symmetry and spin-orbit coupling. We illustrate our idea by performing ab initio…
We use a lowest Landau level model to study the recent observation of an anomalous Hall effect in twisted bilayer graphene. This effective model is rooted in the occurrence of Chern bands which arise due to the coupling between the graphene…
The miniaturization of quantum Hall resistance standards (QHRS) using epitaxial graphene on silicon carbide necessitates understanding how device dimensions impact performance. This study reveals a pronounced scale-dependent carrier density…
We simulate a hybrid superconductor-graphene device in the quantum Hall regime to identify the origin of downstream resistance oscillations in a recent experiment [Zhao et. al. Nature Physics 16, (2020)]. In addition to the previously…
The quantum Hall effect is a remarkable manifestation of quantized transport in a two-dimensional electron gas. Given its technological relevance, it is important to understand its development in realistic nanoscale devices. In this work we…
Perturbations of the two dimensional carbon lattice of graphene, such as grain boundaries, have significant influence on the charge transport and mechanical properties of this material. Scanning tunneling microscopy measurements presented…
We examine the photonic spin Hall effect (SHE) in a graphene-substrate system with the presence of external magnetic field. In the quantum Hall regime, we demonstrate that the in-plane and transverse spin-dependent splittings in photonic…
This short theoretical review deals with some essential ingredients for the understanding of the quantum Hall effect in graphene in comparison with the effect in conventional two-dimensional electron systems with a parabolic band…
We report on the stability of the quantum Hall plateau in wide Hall bars made from a chemically gated graphene film grown on SiC. The $\nu=2$ quantized plateau appears from fields $B \simeq 5$ T and persists up to $B \simeq 80$ T. At high…
We argue that by inducing superconductivity in graphene via the proximity effect, it is possible to observes the "quantum valley Hall effect". In the presence of magnetic field, supercurrent causes "valley pseudospin" to accumulate at the…
Low-energy transport measurements in Quantum Hall systems have been argued to be governed by emergent modular symmetries whose predictions are robust against many of the detailed microscopic dynamics. We propose the recently-observed…