Related papers: Integer and fractional quantum anomalous Hall effe…
The quantum anomalous Hall effect (QAHE) in magnetic topological insulators offers great potential to revolutionize quantum electrical metrology by establishing primary resistance standards operating at zero external magnetic field and…
The rapid development of moir\'e quantum matter has recently led to the remarkable discovery of the fractional quantum anomalous Hall effect, and sparked predictions of other novel correlation-driven topological states. Here, we investigate…
Starting from the graphene lattice tight-binding Hamiltonian with an on-site U and long-range Coulomb repulsion, we derive an interacting continuum Dirac theory governing the low-energy behavior of graphene in an applied magnetic field.…
Fractional quantum Hall (FQH) phases emerge due to strong electronic interactions and are characterized by anyonic quasiparticles, each distinguished by unique topological parameters, fractional charge, and statistics. In contrast, the…
Nontrivial interacting phases can emerge in elementary materials. As a prime example, continuing advances in device quality have facilitated the observation of a variety of spontaneous quantum Hall-like states, a cascade of Stoner-like…
Incompressible even denominator fractional quantum Hall states at fillings $\nu = \pm \frac{1}{2}$ and $\nu = \pm \frac{1}{4}$ have been recently observed in monolayer graphene. We use a Chern-Simons description of multi-component…
Monolayer graphene in a strong magnetic field exhibits quantum Hall states at filling fractions $\nu = 0$ and $\nu = \pm 1$ that are not explained within a picture of noninteracting electrons. We propose that these states arise from…
Owing to the spin, valley, and orbital symmetries, the lowest Landau level (LL) in bilayer graphene exhibits multicomponent quantum Hall ferromagnetism. Using transport spectroscopy, we investigate the energy gaps of integer and fractional…
We study the magnetotransport properties of dual-gated graphene bilayers, in which the total density and layer density imbalance are independently controlled. As the bilayer is imbalanced we observe the emergence of a quantum Hall state…
Strong Goos-H\"anchen (GH) effect at a prism-graphene interface in the quantum Hall effect (QHE) condition is reported. Based on the full quantum description of the temperature-dependent surface conductivity of graphene present in the…
Bori\c{c}i-Creutz (\emph{BC}) model describing the dynamics of light quarks in lattice \emph{QCD} has been shown to be intimately linked to the four dimensional extension of 2D graphene refereed below to as four dimensional graphene…
Experiments on the fractional quantized Hall effect in the zeroth Landau level of graphene have revealed some striking differences between filling factors in the ranges 0<|\nu|<1 and 1<|\nu|<2. We argue that these differences can be largely…
We have measured the quantum Hall activation gaps in bilayer graphene at filling factors $\nu=\pm4$ and $\nu=\pm8$ in high magnetic fields up to 30 T. We find that energy levels can be described by a 4-band relativistic hyperbolic…
Quantum anomalous Hall effect (QAH) is induced by substitution of a certain portion, x, of Bi atoms in a BiTe-based insulating parent compound by magnetic ions (Cr or V). We find the density of in-gap states, N(E), emerging as a result of…
The quantum Hall (QH) effect, quantized Hall resistance combined with zero longitudinal resistance, is the characteristic experimental fingerprint of Chern insulators - topologically non-trivial states of two-dimensional matter with broken…
The experimental discovery of fractional quantum anomalous Hall (FQAH) states in tunable moir\'e superlattices has sparked intense interest in exploring the interplay between topological order and symmetry breaking phases. In this paper, we…
We consider an effective model for graphene with interface-induced spin-orbit coupling and calculate the quantum Hall effect in the low-energy limit. We perform a systematic analysis of the contribution of the different terms of the…
We study the role of Zeeman effect in fractional quantum Hall effect (FQHE) on the surface of topological insulators (TIs). We show that the effective pseudopotentials of the Coulomb interaction are reformed due to Zeeman effect, which are…
The recent discovery of robust quantum anomalous Hall (QAH) effect in rhombohedral multilayer graphene (RMG) aligned with hexagonal boron nitride (hBN) has established a highly versatile platform for correlated topological matter. This…
These lecture notes yield an introduction to quantum Hall effects both for non-relativistic electrons in conventional 2D electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief…