Related papers: Interacting Quantum Topologies and the Quantum Hal…
For manifolds $\cal M$ of noncompact type endowed with an affine connection (for example, the Levi-Civita connection) and a closed 2-form (magnetic field) we define a Hilbert algebra structure in the space $L^2(T^*\cal M)$ and construct an…
We consider two ways of introducing minimal Abelian gauge interactions into the model presented in [1]. They are different only if the second central charge of the planar Galilei group is nonzero. One way leads to standard gauge…
The fate of integer quantum Hall effect (IQHE) at weak magnetic field is studied numerically in the presence of {\it correlated} disorders. We find a systematic {\it float-up} and {\it merging} picture for extended levels on the low-energy…
The quantum Hall effect is studied in the topological insulator BiSbTeSe$_2$. By employing top- and back-gate electric fields at high magnetic field, the Landau levels of the Dirac cones in the top and bottom topological surface states can…
The interplay between topology and electronic correlation effects offers a rich avenue for discovering emergent quantum phenomena in condensed matter systems. In this work, starting from the Weyl-Hubbard model, we investigate the quantum…
Topological insulators (TIs) are characterized by the quantum anomalous Hall effect (QAHE) on the topological surface states under time-reversal symmetry breaking. Motivated by recent experiments on the magneto-optical effects induced by…
We provide a characterization of tunneling between coupled topological insulators in 2D and 3D under the influence of a ferromagnetic layer. We explore conditions for such systems to exhibit integer quantum Hall physics and localized…
The two-dimensional quantum anomalous Hall (QAH) effect is direct evidence of non-trivial Berry curvature topology in condensed matter physics. Searching for QAH in 2D materials, particularly with simplified fabrication methods, poses a…
We investigate how a magnetic field induces one-dimensional edge channels when the two-dimensional surface states of three-dimensional topological insulators become gapped. The Hall effect, measured by contacting those channels, remains…
We consider a system of two interacting particles with like but unequal charges in a magnetic field in the planar geometry. We construct a complete basis of states compatible with both the axial symmetry and magnetic translations. The basis…
It is well known that the quantum Hall conductivity in the presence of constant magnetic field is expressed through the topological TKNN invariant. The same invariant is responsible for the intrinsic anomalous quantum Hall effect (AQHE),…
Using the fiber bundle concept developed in geometry and topology, the fractionally quantized Hall conductivity is discussed in the relevant many--particle configuration space. Electron-magnetic field and electron-electron interactions…
Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2…
Twisted bilayer MoTe$_2$ is a promising platform to investigate the interplay between band topology and many-body interaction. We present a theoretical study of its interaction-driven quantum phase diagrams based on a three-orbital model,…
Composites formed from charged particles and magnetic flux tubes, proposed by Wilczek, are one model for anyons - particles obeying fractional statistics. Here we propose a scheme for realizing charged flux tubes, in which a charged object…
The symplectic geometry of the phase space associated with a charged particle is determined by the addition of the Faraday 2-form to the standard structure on the Euclidean phase space. In this paper we describe the corresponding algebra of…
The quantum Hall effect under the influence of gravity and inertia is studied in a unified way. We make use of an algebraic approach, as opposed to an analytic approach. We examine how both the integer and the fractional quantum Hall…
Electrons living in a two-dimensional world under a strong magnetic field - the so-called fractional quantum Hall effect (FQHE) - often manifest themselves as fractionally charged quasiparticles (anyons). Moreover, being under special…
We consider recent experimental results [W. Pan {\it et al}, Phys. Rev. Lett. {\bf 90}, 016801 (2003)] for occurrence of the fractional quantum Hall effect-FQHE under the perspective of our formulation in terms of {\it fractons}. These…
A topological phase can often be represented by a corresponding wavefunction (exact eigenstate of a model Hamiltonian) that has a higher underlying symmetry than necessary. When the symmetry is explicitly broken in the Hamiltonian, the…