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We present a microscopic theory to give a physical picture of the formation of quantum anomalous Hall (QAH) effect in graphene due to a joint effect of Rashba spin-orbit coupling $\lambda_R$ and exchange field $M$. Based on a continuum…
In two-dimensional (2D) electron systems under strong magnetic fields, interactions can cause fractional quantum Hall (FQH) effects. Bringing two 2D conductors to proximity, a new set of correlated states can emerge due to interactions…
We observed broken-symmetry quantum Hall effects and level crossings between spin- and valley- resolved Landau levels (LLs) in Bernal stacked trilayer graphene. When the magnetic field was tilted with respect to sample normal from…
We study the optical response of bilayer graphene with a kink potential composed of a domain wall separating two AB regions with opposite interlayer bias. The band structure and the local optical conductivity in real space are investigated…
Monolayer staggered materials of the graphene family present intrinsic spin-orbit coupling and can be driven through several topological phase transitions using external circularly polarized lasers, and static electric or magnetic fields.…
In the presence of a perpendicular magnetic field, ABC-stacked trilayer graphene's chiral band structure supports a 12-fold degenerate N=0 Landau level (LL). Along with the valley and spin degrees of freedom, the zeroth LL contains…
The non-interacting energy spectrum of graphene and its bilayer counterpart consists of multiple degeneracies owing to the inherent spin, valley and layer symmetries. Interactions among charge carriers are expected to spontaneously break…
We investigate the emergence of topological valley Hall and kink states in a two-dimensional topolectrical (TE) model as a result of broken chiral and reflection symmetries. The TE system consists of two segments hosting distinct…
The electronic properties of graphene are described by a Dirac Hamiltonian with a fourfold symmetry of spin and valley. This symmetry may yield novel fractional quantum Hall (FQH) states at high magnetic field depending on the relative…
Graphene is a two-dimensional carbon material with a honeycomb lattice and Dirac-type low-energy spectrum. In a strong magnetic field, where Coulomb interactions dominate against disorder broadening, quantum Hall ferromagnetic states…
Semimetals exhibit intriguing characteristics attributed to the coexistence of both electrons and holes. In rhombohedral multilayer graphene, a strong trigonal warping effect gives rise to a semi-metallic state near the Fermi surface,…
Bilayer graphene in a magnetic field supports eight zero-energy Landau levels, which, as a tunable band gap develops, split into two nearly-degenerate quartets separated by the band gap. A close look is made into the properties of such an…
In graphene superlattices, bulk topological currents can lead to long-range charge-neutral flow and non-local resistance near Dirac points. A ballistic version of these phenomena has never been explored. Here, we report transport properties…
Here we study the evolution of local electronic properties of a twisted graphene bilayer induced by a strain and a high curvature. The strain and curvature strongly affect the local band structures of the twisted graphene bilayer; the…
In a graphene Landau level (LL), strong Coulomb interactions and the fourfold spin/valley degeneracy lead to an approximate SU(4) isospin symmetry. At partial filling, exchange interactions can spontaneously break this symmetry, manifesting…
We investigate an effective model of proximity modified graphene (or symmetrylike materials) with broken time-reversal symmetry. We predict the appearance of quantum anomalous Hall phases by computing bulk band gap and Chern numbers for…
A number of quantum Hall isospin ferromagnetic (QHIFM) states have been predicted in the relativistic zero Landau level (LL) of graphene monolayer. These states, especially the states at LL filling factor v = 0 of charge-neutral graphene,…
The quantum valley Hall effect (QVHE) is characterized by the valley Chern number (VCN) in a way that one-dimensional (1D) chiral metallic states are guaranteed to appear at the domain walls (DW) between two domains with opposite VCN for a…
The observation of large nonlocal resistances near the Dirac point in graphene has been related to a variety of intrinsic Hall effects, where the spin or valley degrees of freedom are controlled by symmetry breaking mechanisms. Engineering…
A variational ground state for insulating bilayer graphene (BLG), subject to quantizing magnetic fields, is proposed. Due to the Zeeman coupling, the layer anti-ferromagnet (LAF) order parameter in fully gapped BLG gets projected onto the…