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A field theory of quantum Hall effects is constructed based on the \CB picture. It is tightly related with the microscopic wave-function theory. The characteristic feature is that the field operator describes solely the physical degrees of…
Graphene is a unique two-dimensional material with rich new physics and great promise for applications in electronic devices. Physical phenomena such as the half-integer quantum Hall effect and high carrier mobility are critically dependent…
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…
Electrons' multiple quantum degrees of freedom can lead to rich physics, including a competition between various exotic ground states, as well as novel applications such as spintronics and valleytronics. Here we report magneto-transport…
Quantum geometry of electronic wavefunctions results in fascinating topological phenomena. A prominent example is the intrinsic anomalous Hall effect (AHE) in which a Hall voltage arises in the absence of an applied magnetic field. The AHE…
A series of measurements using a technique called electrostatic-manipulation scanning tunneling microscopy (EM-STM) were performed on a highly-oriented pyrolytic graphite surface. The electrostatic interaction between the STM tip and the…
A number of strongly correlated heavy fermion compounds, such as samarium (Sm), ytterbium (Yb), plutonium (Pu) hexaboride, are predicted to become topological insulators at low temperatures. These systems support massless Dirac fermions…
We use low-temperature scanning gate microscopy (SGM) to investigate the breakdown of the quantum Hall regime in an exfoliated bilayer graphene flake. SGM images captured during breakdown exhibit intricate patterns of "hotspots" where the…
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…
Probing and controlling the valley degree of freedom in graphene systems by transport measurements has been a major challenge to fully exploit the unique properties of this two-dimensional material. In this theoretical work, we show that…
Rhombohedral multilayer graphene is a physical realization of the chiral two-dimensional electron gas that can host zero-line modes (ZLMs), also known as kink states, when the local ap opened by inversion symmetry breaking potential changes…
This work treats the effects of disorder and interactions in a quantum Hall ferromagnet, which is realized in a two-dimensional electron gas (2DEG) in a perpendicular magnetic field at Landau level filling factor equal one. We study the…
We systematically investigate the emergence of electron crystal phases in rhombohedral multilayer graphene using comprehensive self-consistent Hartree Fock calculations combined with \textit{ab initio} tight binding model. As the carrier…
The low energy charged excitations in quantum Hall ferromagnets are topological defects in the spin orientation known as skyrmions. Recent experimental studies on nuclear magnetic resonance spectral line shapes in quantum well…
The possibility to effect valley splitting of an electronic current in graphene represents the essential component in the new field of valleytronics in such two-dimensional materials. Based on a symmetry analysis of the scattering matrix,…
The quantum Hall effect is the seminal example of topological protection, as charge carriers are transmitted through one-dimensional edge channels where backscattering is prohibited. Graphene has made its marks as an exceptional platform to…
Unlike regular electron spin, the pseudospin degeneracy of Fermi points in graphene does not couple directly to magnetic field. Therefore, graphene provides a natural vehicle to observe the integral and fractional quantum Hall physics in an…
We introduce a generalized Hamiltonian describing not only all topological phases observed experimentally in Kekul\'e graphene (KekGr) but predicting also new ones. These phases show features like a quadratic band crossing point, valley…
Recent experiments on rhombohedral pentalayer graphene flakes with a substrate induced moir\'e potential have identified both Chern insulators and fractional Quantum Hall states in the absence of an applied magnetic field. Surprisingly,…
We theoretically investigate the manipulation of the quantum anomalous Hall effect (QAHE) in graphene by means of the uniaxial strain. The values of Chern number and Hall conductance demonstrate that the strained graphene in presence of…