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We present a symmetry-based analysis of competition between different gapped states that have been proposed in bilayer graphene (BLG), which are all degenerate on a mean field level. We classify the states in terms of a hidden SU(4)…
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.…
We numerically study the quantum Hall effect in biased bilayer graphene based on a tight-binding model in the presence of disorder. Integer quantum Hall plateaus with quantized conductivity $\sigma_{xy}=\nu e^2/h$ (where $\nu$ is any…
By numerical exact diagonalization techniques, we obtain the quantum phase diagram of the lattice fractional quantum Hall (FQH) systems in the presence of quenched disorder. By implementing an array of local potential traps representing the…
There are known two distinct types of the integer quantum Hall effect. One is the conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems, and the other is its relativistic counterpart recently observed in…
A partially filled Landau level (LL) hosts a variety of correlated states of matter with unique properties. The ability to control these phases requires tuning the effective electron interactions within a LL, which has been difficult to…
Electron-electron interactions play an important role in graphene and related systems and can induce exotic quantum states, especially in a stacked bilayer with a small twist angle. For bilayer graphene where the two layers are twisted by a…
Synthetic quantum Hall bilayer (SQHB), realized by optically driven monolayer graphene in the quantum Hall regime, provides a flexible platform for engineering quantum Hall phases as discussed in [Phys. Rev. Lett. 119, 247403]. The coherent…
The realization of fractional Chern insulators in moir\'e materials has sparked the search for further novel phases of matter in this platform. In particular, recent works have demonstrated the possibility of realizing quantum anomalous…
We present measurements of quantized conductance in electrostatically induced quantum point contacts in bilayer graphene. The application of a perpendicular magnetic field leads to an intricate pattern of lifted and restored degeneracies…
We demonstrate theoretically that quantum dots in bilayers of graphene can be realized. A position-dependent doping breaks the equivalence between the upper and lower layer and lifts the degeneracy of the positive and negative momentum…
We discuss the quantum Hall effect of bilayer graphene with finite gate voltage where the Fermi energy exceeds the interlayer hopping energy. We calculated magnetic susceptibility, diagonal and off-diagonal conductivities in…
Using the first principles calculations, we show that mechanically tunable electronic energy gap is realizable in bilayer graphene if different homogeneous strains are applied to the two layers. It is shown that the size of energy gap can…
Remarkable recent experiments have observed fractional quantum anomalous Hall (FQAH) effects at zero field and unusually high temperatures in twisted semiconductor bilayer $t$MoTe$_2$. Intriguing observations in these experiments such as…
The relativistic-like behavior of electrons in graphene significantly influences the interaction properties of these electrons in a quantizing magnetic field, resulting in more stable fractional quantum Hall effect states as compared to…
Berry curvature is analogous to magnetic field but in momentum space and is commonly present in materials with non-trivial quantum geometry. It endows Bloch electrons with transverse anomalous velocities to produce Hall-like currents even…
Electrostatic confinement of charge carriers in bilayer graphene provides a unique platform for carbon-based spin, charge or exchange qubits. By exploiting the possibility to induce a band gap with electrostatic gating, we form a versatile…
We derive the low-energy theory of semi-quantized quantum Hall states, a recently observed class of gapless bilayer fractional quantum Hall states. Our theory shows these states to feature gapless quasiparticles of fractional charge coupled…
Controllable point junctions between different quantum Hall phases are a necessary building block for the development of mesoscopic circuits based on fractionally-charged quasiparticles. We demonstrate how particle-hole duality can be…
We report experimental observation of the reentrant integer quantum Hall effect in graphene, appearing in the N$=$2 Landau level. Similar to high-mobility GaAs/AlGaAs heterostructures, the effect is due to a competition between…