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Charge-neutral graphene in the quantum Hall regime is an example of a quantum Hall ferromagnet in a complex spin-valley space. This system exhibits a plethora of phases, with the particular spin-valley order parameters chosen by the system…

Spin splitting of the energy spectrum of single-layer graphene on Au/Ni(111) substrate has been recently reported. I show that eigenstates of spin-orbit coupled graphene are polarized in-plane and perpendicular to electron momentum $\bf k$;…

Skyrmions are topologically protected spin textures, characterized by a topological winding number N , that occur spontaneously in some magnetic materials. Recent experiments have demonstrated the capability to grow graphene on top Fe/Ir, a…

We consider magic-angle twisted bilayer graphene (TBG) at filling $\nu=+3$, where experiments have observed a robust quantized anomalous Hall effect. This has been attributed to the formation of a valley- and spin-polarized Chern insulating…

Graphene subject to high levels of shear strain leads to strong pseudo-magnetic fields resulting in the emergence of Landau levels. Here we show that, with modest levels of strain, graphene can also sustain a classical valley hall effect…

Topological and valleytronic materials are promising for spintronic and quantum applications due to their unique properties. Using first principles calculations, we demonstrate that germanene (Ge)-based ferromagnetic heterostructures can…

Valley polarized topological kink states, existing broadly in the domain wall of hexagonal lattices systems, are identified in experiments, unfortunately, only very limited physical properties being given. Using an Aharanov-Bohm…

Electronic properties of bilayer graphene are distinct from both the conventional two dimensional electron gas and monolayer graphene due to its particular chiral properties and excitation charge carrier dispersions. We study the effect of…

We analyze the quantum Hall effect in single layer graphene with bilayer stripe defects. Such defects are often encountered at steps in the substrate of graphene grown on silicon carbide. We show that AB or AA stacked bilayer stripes result…

We reveal that local interactions in graphene allow novel spin liquids between the semi-metal and antiferromagnetic Mott insulating phases, identified with algebraic spin liquid and Z$_{2}$ spin liquid, respectively. We argue that the…

We study charge fractionalization in bilayer graphene which is intimately related to its zero modes. In the unbiased case, the valley zero modes occur in pairs rendering it unsuitable for charge fractionalization. A bias plays the role of a…

Graphene properties can be manipulated by a periodic potential. Based on the tight-binding model, we study graphene under a one-dimensional (1D) modulated magnetic field which contains both a uniform and a staggered component. New chiral…

Motivated by the experiments on double monolayer graphene that observe a variety of fractional quantum Hall states [Liu et al., Nat. Phys. 15, 893 (2019); Li et al., Nat. Phys. 15, 898 (2019)], we study the special setting in which two…

Gapless edge modes hosted by chirally-stacked trilayer graphene display unique features when a bulk gap is opened by applying an interlayer potential difference. We show that trilayer graphene with half-integer valley Hall conductivity…

A finite Hall conductance under zero magnetic field implies time reversal symmetry (TRS) breaking due to magnetic order. In rhombohedral stacked multilayer graphene, the angular momentum that breaks TRS can result from the orbital degree of…

In a magnetic field graphene trilayers support a special multiplet of 12 zero(-energy)-mode Landau levels with a threefold degeneracy in Landau orbitals. A close look is made into such zero-mode levels in ABA-stacked trilayers, with the…

We explore the electronic ground states of Bernal-stacked multilayer graphenes using the Hartree-Fock mean-field approximation and the full-parameter band model. We find that the electron-electron interaction tends to open a band gap in…

The quantum anomalous Hall (QAH) effect, first proposed in the Haldane model, is a paradigmatic example of the application of band topology in condensed matter physics. The recent experimental discoveries of high Chern number QAH effect in…

We show that the valley Chern number of the low energy band in twisted double bilayer graphene can be tuned through two successive topological transitions, where the direct bandgap closes, by changing the electric field perpendicular to the…

Recently, multilayer graphene systems have attracted significant attention due to the discovery of a variety of intriguing phases, particularly quantum anomalous Hall (QAH) states. In rhombohedral pentalayer graphene (RPG), both QAH states…