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The Quantum Hall Effect (QHE) is a prototypical realization of a topological state of matter. It emerges from a subtle interplay between topology, interactions, and disorder. The disorder enables the formation of localized states in the…
We report the observation of the quantized Hall effect in suspended graphene probed with a two-terminal lead geometry. The failure of earlier Hall-bar measurements is discussed and attributed to the placement of voltage probes in mesoscopic…
Topological insulators are bulk electronic insulators which possess symmetry protected gapless modes on their surfaces. Breaking the symmetries that underlie the gapless nature of the surface modes is predicted to give rise to exotic new…
The quantum Hall system can be used to study many-body physics owing to its multiple internal electronic degrees of freedom and tunability. While quantum phase transitions have been studied intensively, research on the temperature-induced…
The three-dimensional (3D) topological insulator (TI) is a novel state of matter as characterized by two-dimensional (2D) metallic Dirac states on its surface. Bi-based chalcogenides such as Bi2Se3, Bi2Te3, Sb2Te3 and their combined/mixed…
The helical edge states in a quantum spin Hall insulator are presumably protected by time- reversal symmetry. However, even in the presence of magnetic field which breaks time-reversal symmetry, the helical edge conduction can still exist,…
We engineer quantum anomalous Hall effect in silicene via doping 3d transition metals. We show that there exists a stable quantum anomalous Hall effect in Vanadium doped silicene using both analytical model and Wannier interpolation. We…
The quantum anomalous Hall effect (QAHE) is a fundamental quantum transport phenomenon that manifests as a quantized transverse conductance in response to a longitudinally applied electric field in the absence of an external magnetic field,…
We report the observation of a quantum anomalous Hall effect in twisted bilayer graphene showing Hall resistance quantized to within .1\% of the von Klitzing constant $h/e^2$ at zero magnetic field.The effect is driven by intrinsic strong…
The quantum anomalous Hall effect (QAHE) is a topological state of matter with a quantized Hall resistance. It has been observed in some two-dimensional insulating materials such as magnetic topological insulator films and twisted bilayer…
We theoretically study the correlated insulator states, quantum anomalous Hall (QAH) states, and field-induced topological transitions between different correlated states in twisted multilayer graphene systems. Taking twisted…
We study anisotropic lattice strips in the presence of a magnetic field in the quantum Hall effect regime. At specific magnetic fields, causing resonant Umklapp scattering, the system is gapped in the bulk and supports chiral edge states in…
Superlattice potential modulation can produce flat minibands in Bernal-stacked bilayer graphene. In this work we study how band topology and interaction-induced symmetry-broken phases in this system are controlled by tuning the displacement…
To fully appreciate the impacts that the discovery of the quantum Hall effect had on electrical metrology, it may benefit the reader to cultivate a general understanding of the phenomenon. Two-dimensional electron systems can exhibit many…
Magnetic topological states refer to a class of exotic phases in magnetic materials with their non-trivial topological property determined by magnetic spin configurations. An example of such states is the quantum anomalous Hall (QAH) state,…
Topological insulators host exotic quantum phenomena such as the quantum spin Hall (QSH) effect, which enables dissipationless one-dimensional edge conduction. Realizing such states at room temperature and on a macroscopic scale is…
Transport through edge-channels is responsible for conduction in quantum Hall (QH) phases. Topology dictates quantization of both charge and thermal transport coefficients. These turn out to approach robust quantized values when incoherent…
Four-terminal resistances, both longitudinal and diagonal, of a locally gated graphene device are measured in the quantum-Hall (QH) regime. In sharp distinction from previous two-terminal studies [J. R. Williams \textit{et al.}, Science…
An established way of realizing topologically protected states in a two-dimensional electron gas is by applying a perpendicular magnetic field thus creating quantum Hall edge channels. In electrostatically gapped bilayer graphene…
In Bernal-stacked bilayer graphene (BBG), the Landau levels give rise to an intimate connection between valley and layer degrees of freedom. Adding a moir\'e superlattice potential enriches the BBG physics with the formation of topological…