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Topology is a powerful recent concept asserting that quantum states could be globally protected against local perturbations. Dissipationless topologically protected states are thus of major fundamental interest as well as of practical…
We explore the non-equilibrium transport regime in graphene using a large dc current in combination with a perpendicular magnetic field. The strong in-plane Hall field that is generated in the bulk of the graphene channel results in Landau…
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…
Bilayer graphene exhibits a rich phase diagram in the quantum Hall regime, arising from a multitude of internal degrees of freedom, including spin, valley, and orbital indices. The variety of fractional quantum Hall states between filling…
In this study, we determined the chiral direction of the quantum-Hall (QH) edge states in graphene by adopting simple two-terminal conductance measurements while grounding different edge positions of the sample. The edge state with a…
We show that strained or deformed honeycomb lattices are promising platforms to realize fractional topological quantum states in the absence of any magnetic field. The strained induced pseudo magnetic fields are oppositely oriented in the…
Graphene on hexagonal boron nitride (hBN) can exhibit a topological phase via mutual crystallographic alignment. Recent measurements of nonlocal resistance ($R_{nl}$) near the secondary Dirac point (SDP) in ballistic graphene/hBN…
A gate induced insulating behavior at zero magnetic field is observed in a high mobility suspended monolayer graphene near the charge neutrality point. The graphene device initially cleaned by a current annealing technique was undergone a…
Rhombohedral stacked multilayer graphene is an ideal platform to search for correlated electron phenomena, due to its pair of flat bands touching at zero energy and further tunability by an electric field. Furthermore, its valley-dependent…
The discovery of three-dimensional (3D) topological insulators opens a gateway to generate unusual phases and particles made of the helical surface electrons, proposing new applications using unusual spin nature. Demonstration of the…
We study theoretically the two-dimensional topological electric state in a single band semiconductor with strong spin-orbit interactions under harmonic scalar electrostatic potentials. The electronic states described by the spin Landau…
The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in…
We present results from Monte Carlo simulations of a three dimensional fermionic field theory which can be derived from a model of graphene in which electrons interact via a screened Coulomb potential. For our simulations we employ lattice…
The scaling behavior of the quantum phase transition from an insulator to a quantum Hall plateau state has often been examined within systems realizing Landau levels. We study the topological transition in energy band models with nonzero…
Two-dimensional higher-order topology is usually studied in (nearly) particle-hole symmetric models, so that an edge gap can be opened within the bulk one. But more often deviates the edge anticrossing even into the bulk, where corner…
We report on our accurate evaluation of spin polarizations of the ground state and particle-hole gaps for partially-filled lowest Landau level, observed in recent experiments on graphene subjected to ultra-high magnetic fields. We find that…
In contrast to electron (fermion) systems, topological phases of charge neutral bosons have been poorly understood despite recent extensive research on insulating magnets. The most important unresolved issue is how the inevitable…
Topological and crystalline orders of electrons both benefit from enhanced Coulomb interactions in partially filled Landau levels. In bilayer graphene (BLG), the competition between fractional quantum Hall liquids and electronic crystals…
We have studied the fractional quantum Hall states on the surface of a topological insulator thin film in an external magnetic field, where the Dirac fermion nature of the charge carriers have been experimentally established only recently.…
Topological insulators [1-6] is a new quantum phase of matter with exotic properties such as dissipationless transport and protection against Anderson localization [7]. These new states of quantum matter could be one of the missing links…