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When electrons are confined in two dimensions and subjected to strong magnetic fields, the Coulomb interactions between them become dominant and can lead to novel states of matter such as fractional quantum Hall liquids. In these liquids…
We review the basic aspects of electrons in graphene (two-dimensional graphite) exposed to a strong perpendicular magnetic field. One of its most salient features is the relativistic quantum Hall effect the observation of which has been the…
Quantum Hall effect (QHE), the ground to construct modern conceptual electronic systems with emerging physics, is often much influenced by the interplay between the host two-dimensional electron gases and the substrate, sometimes predicted…
Graphene and its multilayers have attracted considerable interest owing to the fourfold spin and valley degeneracy of their charge carriers, which enables the formation of a rich variety of broken-symmetry states and raises the prospect of…
The recent discovery of fractional quantum Hall states in graphene raises the question of whether the physics of graphene and its bilayer offers any advantages over GaAs-based materials in exploring strongly-correlated states of…
The quantum Hall effect is a remarkable manifestation of quantized transport in a two-dimensional electron gas. Given its technological relevance, it is important to understand its development in realistic nanoscale devices. In this work we…
We investigate transport in a gate-defined graphene quantum point contact in the quantum Hall regime. Edge states confined to the interface of p and n regions in the graphene sheet are controllably brought together from opposite sides of…
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…
Using graphene resonator, we perform electromechanical measurements in quantum Hall regime to probe the coupling between a quantum Hall (QH) system and its mechanical motion. Mechanically perturbing the QH state through resonance modifies…
Since the ground-breaking discovery of the quantum Hall effect, half-quantized quantum Hall plateaus have been some of the most studied and sought-after states. Their importance stems not only from the fact that they transcend the composite…
Graphene's honeycomb lattice structure underlies much of the remarkable physics inherent in this material, most strikingly through the formation of two ``flavors'' of Dirac cones for each spin. In the quantum Hall regime, the resulting…
Graphene is a two-dimensional carbon material with a honeycomb lattice and Dirac-like low-energy excitations. When Zeeman and spin-orbit interactions are neglected its Landau levels are four-fold degenerate, explaining the $4 e^2/h$…
The quantum Hall effect is widely used for the investigation of fundamental phenomena, ranging from topological phases to composite fermions. In particular, the discovery of a room temperature resistance quantum in graphene is significant…
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…
Trilayer graphene allows systematic control of its electronic structure through stacking sequence and twist geometry, providing a versatile platform for correlated states. Here we report magnetotransport in alternating twisted trilayer…
This work investigates the coexistence of distinct topologically ordered phases within a single setup. We demonstrate this concept through tensor network simulations of the Hofstadter-Bose-Hubbard model under a spatially modulated chemical…
There is an increasing interest in the electronic properties of few layer graphene as it offers a platform to study electronic interactions because the dispersion of bands can be tuned with number and stacking of layers in combination with…
The rise of graphene opens a new door to qubit implementation, as discussed in the recent proposal of valley pair qubits in double quantum dots of gapped graphene (Wu et al., arXiv: 1104.0443 [cond-mat.mes-hall]). The work here presents the…
The observed quantization of the Hall conductivity in graphene at high magnetic fields is explained as being due to the dynamically generated spatial modulation of either the electron spin or the density, as decided by the details of…
Strongly interacting topological matter exhibits fundamentally new phenomena with potential applications in quantum information technology. Emblematic instances are fractional quantum Hall states, where the interplay of magnetic fields and…