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The phase diagram of an interacting two-dimensional electron system in a high magnetic field is enriched by the varying form of the effective Coulomb interaction, which depends strongly on the Landau level index. While the fractional…
We report on transport measurements of dual-gated, single-layer graphene devices in the quantum Hall regime, allowing for independent control of the filling factors in adjoining regions. Progress in device quality allows us to study…
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…
Helical trilayer graphene realizes a versatile moir\'e system for exploring correlated topological states emerging from high Chern bands. Motivated by recent experimental observations of anomalous Hall effects at fractional fillings of…
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…
In condensed matter physics, the study of electronic states with SU(N) symmetry has attracted considerable and growing attention in recent years, as systems with such a symmetry can often have a spontaneous symmetry-breaking effect giving…
The microscopic quantum theory of nonlinear stimulated scattering of chiral particles in doped $AB$ stacked bilayer graphene on Coulomb field of charged impurities in the presence of strong coherent electromagnetic radiation is presented.…
We investigate the chemisorptions of oxygen molecules on bilayer graphene (BLG) and its electrically modified charge-doping effect using conductivity measurement of the field effect transistor channeled with BLG. We demonstrate that the…
In this article we review the quantum Hall physics of graphene based two-dimensional electron systems, with a special focus on recent experimental and theoretical developments. We explain why graphene and bilayer graphene can be viewed…
Landau level bending near the edge of graphene, described using 2d Dirac equation, provides a microscopic framework for understanding the quantum Hall Effect (QHE) in this material. We review properties of the QHE edge states in graphene,…
Electron wavefunctions in twisted bilayer graphene may have a strong single layer character or be intrinsically delocalized between layers, with their nature often determined by how energetically close they are to the Dirac point. In this…
We report on our studies of interacting electrons in bilayer graphene in a magnetic field. We demonstrate that the long range Coulomb interactions between electrons in this material are highly important and account for the band asymmetry in…
With the two-band continuum model, we study the broken inversion and time-reversal symmetry state of electrons with finite-range repulsive interactions in bilayer graphene. With the analytical solution to the mean-field Hamiltonian, we…
Trilayer graphene in the fractional Quantum Hall Effect regime displays a set of unique interaction-induced transitions that can be tuned entirely by the applied bias voltage. These transitions occur near the anti-crossing points of two…
We consider the impact of Berry phase on the Wigner crystal (WC) state of a two-dimensional electron system. We consider first a model of Bernal bilayer graphene with a perpendicular displacement field, and we show that Berry curvature…
We study the influence of the quantum geometry on the magnetic responses of quadratic band crossing semimetals. More explicitly, we examine the Landau levels, quantum Hall effect, and magnetic susceptibility of a general two-band…
Magnetic fields quench the kinetic energy of two dimensional electrons, confining them to highly degenerate Landau levels. In the absence of disorder, the ground state at partial Landau level filling is determined only by Coulomb…
The effect of an Aharonov-Bohm (AB) pseudo magnetic field on a two dimensional electron gas in graphene is investigated. We consider it modeled as in the usual AB effect but since such pseudo field is supposed to be induced by elastic…
When electrons are confined in two dimensions and subjected to strong magnetic fields, the Coulomb interactions between them become dominant and can lead to novel states of matter such as fractional quantum Hall liquids. In these liquids…
Semiconductor double-layers in the quantum Hall regime tend to have superfluid exciton condensate ground states when the total filling factor is an odd integer, provided that the Landau orbitals at the Fermi level in the two layers have the…