Quantum anomalous Hall (QAH) insulator is a topological phase which exhibits chiral edge states in the absence of magnetic field. The celebrated Haldane model is the first example of QAH effect, but difficult to realize. Here, we predict the two-dimensional single-atomic-layer V2O3 with a honeycomb-Kagome structure is a QAH insulator with a large band gap (large than 0.1 eV) and a high ferromagnetic Curie temperature (about 900 K). Combining the first-principle calculations with the effective Hamiltonian analysis, we find that the spin-majority dxy and dyz orbitals of V atoms on the honeycomb lattice form a massless Dirac cone near the Fermi level which becomes massive when the on-site spin-orbit coupling is included. Interestingly, we find that the large band gap is caused by a cooperative effect of electron correlation and spin-orbit coupling. Both first-principle calculations and the effective Hamiltonian analysis confirm that 2D V2O3 has a non-zero Chern number (i.e., one). Our work paves a new direction towards realizing the QAH effect at room temperature.

The two-dimensional electron gas in a graphene bilayer in the Bernal stacking supports a variety of uniform broken-symmetry ground states in Landau level N = 0 at integer filling factors ν ∈ [−3,4]. When an electric potential difference (or bias) is applied between the layers at filling factors ν = 1,3, the ground state evolves from an interlayer coherent state at small bias to a state with orbital coherence at higher bias, where electric dipoles associated with the orbital pseudospins order spontaneously in the plane of the layers. In this paper, we show that, by further increasing the bias at these two filling factors, the two-dimensional electron gas goes first through an electron crystal with an orbital pseudospin texture at each site and then into a helical state where the pseudospins rotate in space. The pseudospin textures in the electron crystal and the helical state are due to the presence of a Dzyaloshinskii-Moriya interaction in the effective pseudospin Hamiltonian when orbital coherence is present in the ground state. We study in detail the electronic structure of the helical and electron crystal states as well as their collective excitations and then compute their electromagnetic absorption.

A graphene bilayer in a transverse magnetic field has a set of Landau levels with energies E = ± N (N + 1)ℏω * c where ω * c is the effective cyclotron frequency and N = 0, 1, 2, ... All Landau levels but N = 0 are four times degenerate counting spin and valley degrees of freedom. The Landau level N = 0 has an extra degeneracy due to the fact that orbitals n = 0 and n = 1 both have zero kinetic energies. At integer filling factors, Coulomb interactions produce a set of broken-symmetry states with partial or full alignement in space of the valley and orbital pseudospins. These quantum Hall pseudo-ferromagnetic states support topological charged excitations in the form of orbital and valley Skyrmions. Away from integer fillings, these topological excitations can condense to form a rich variety of Skyrme crystals with interesting properties. We study in this paper different crystal phases that occur when an electric field is applied between the layers. We show that orbital Skyrmions, in analogy with spin Skyrmions, have a texture of electrical dipoles that can be controlled by an in-plane electric field. Moreover, the modulation of electronic density in the crystalline phases are experimentally accessible through a measurement of their local density of states 73.22.Gk,78.70.Gq

We have analyzed the crucial role the Coulomb interaction strength plays on the even and odd denominator fractional quantum Hall effects in a two-dimensional electron gas (2DEG) in the ZnO heterointerface. In this system, the Landau level gaps are much smaller than those in conventional GaAs systems. The Coulomb interaction is also very large compared to the Landau level gap even in very high magnetic fields. We therefore consider the influence of higher Landau levels by considering the screened Coulomb potential in the random phase approximation. Interestingly, our exact diagonalization studies of the collective modes with this screened potential successfully explain recent experiments of even and odd denominator fractional quantum Hall effects, in particular, the unexpected absence of the 5/2 state and the presence of 9/2 state in ZnO.Discovery of the odd-denominator fractional quantum Hall effects (FQHE) in GaAs heterojunctions in 1982 [1] and its subsequent explanation by Laughlin [2,3], has remained the 'gold standard' for novel quantum states of correlated electrons in a strong magnetic field. These effects also have been observed in 'Dirac materials' such as graphene [4,5,9]. and are expected to be present in other graphene-like materials [6][7][8] with novel attributes. The FQHE states in monolayer and bilayer graphene were investigated theoretically [9][10][11][12] and experimentally [13,14]. For example, in bilayer graphene the application of a bias voltage results in some Landau levels (LLs) a phase transition between incompressible FQHE and compressible phases [11,12]. The FQHE in silicene and germanene indicated that because of the strong spinorbit interaction present in these materials as compared to graphene, the electron-electron interaction and the FQHE gap are significantly modified [15]. The puckered structure of phosphorene exhibits a lower symmetry than graphene. This results in anisotropic energy spectra and other physical characteristics of phosphorene, both in momentum and real space in the two-dimensional (2D) plane [16,17]. The anisotropic band structure of phosphorene causes splitting of the magnetoroton mode into two branches with two minima. For long wavelengths, we also found a second mode with upward dispersion that is clearly separated from the magnetoroton mode and is entirely due to the anisotropic bands [18].In 1987, a discovery of the quantum Hall state at the LL filling factor ν = 5 2 , the first even-denominator state observed in a single-layer system [19] added to the mystery of the FQHE. It soon became clear that this state must be different from the FQHE in predominantly odd-denominator filling fractions [1]. Understanding this enigmatic state has remained a major challenge in all these years [20,21]. At this half-filled first excited LL, a novel state described by a pair wave function involving a Pfaffian [12,22], where the low-energy excitations obey non-Abelian exchange statistics, has been the strongest * Tapash.Chakraborty@umanitoba.ca candidate.The field of FQHE has...