相关论文: Geometric construction of the Quantum Hall Effect …

The fractional quantum Hall effect (FQHE) stands as a quintessential manifestation of an interacting two-dimensional electron system. One of FQHE's most fundamental characteristics is the energy gap separating the incompressible ground…

We present a novel fundamental effect that for the matter waves the space-averaging free-fall point of quantum particles undergoes a spin-dependent transverse shift in the gravitational field of Earth. This effect is similar to the…

The quantum Hall effect (QHE) is traditionally considered a purely two-dimensional (2D) phenomenon. Recently, a three-dimensional (3D) version of the QHE has been reported in the Dirac semimetal ZrTe5. It was proposed to arise from a…

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…

A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…

We have generalized recent results of Cappelli, Trugenberger and Zemba on the integer quantum Hall effect constructing explicitly a ${\cal W}_{1+\infty}$ for the fractional quantum Hall effect such that the negative modes annihilate the…

The quantum geometry has significant consequences in determining transport and optical properties in quantum materials. Here, we use a semiclassical formalism coupled with perturbative corrections unifying the nonlinear anomalous Hall…

Following recent work on the quantum Hall effect on $S^4$, we solve the Landau problem on the complex projective spaces ${\bf C}P^k$ and discuss quantum Hall states for such spaces. Unlike the case of $S^4$, a finite spatial density can be…

The quantum Hall (QH) effect, quantized Hall resistance combined with zero longitudinal resistance, is the characteristic experimental fingerprint of Chern insulators - topologically non-trivial states of two-dimensional matter with broken…

The quantum even-dimensional balls are defined as the $C^*$-algebras generated by certain graphs. We exhibit a polynomial algebra for each even-dimensional quantum ball, and classify the irreducible representations of it.

These lecture notes yield an introduction to quantum Hall effects both for non-relativistic electrons in conventional 2D electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief…

For a particle confined to the two-dimensional helical surface embedded in four-dimensional (4D) Euclidean space, the effective Hamiltonian is deduced in the thin-layer quantization formalism. We find that the gauge structure of the…

In homogeneous cosmologies, quantum geometry effects lead to a resolution of the classical singularity without having to invoke special boundary conditions at the singularity or introduce ad-hoc elements such as unphysical matter. The same…

We demonstrate the emergence of the quantum Hall (QH) hierarchy in a 2D model of coupled quantum wires in a perpendicular magnetic field. At commensurate values of the magnetic field, the system can develop instabilities to appropriate…

Using a mapping of a layered three-dimensional system with significant inter-layer tunneling onto a spin-Hamiltonian, the phase diagram in the strong magnetic field limit is obtained in the semi-classical approximation. This phase diagram,…

We construct an algebraic description for the ground state and for the static response of the quantum Hall plateaux with filling factor $\nu=N/(2N+1)$ in the large $N$ limit. By analyzing the algebra of the fluctuations of the shape of the…

In this thesis, I will present studies on the collective modes of the fractional quantum Hall states, which are bulk neutral excitations reflecting the incompressibility that defines the topological nature of these states. It was first…

Quantum Hall effect wavefunctions corresponding to the filling factors 1/2p+1, 2/2p+1,..., 2p/2p+1, 1, are shown to form a basis of irreducible cyclic representation of the quantum algebra U_q(sl(2)) at q^{2p+1}=1. Thus, the wavefunctions…

We study the quantum Hall effect inside a gravitational field. First, we review the influence of the gravitational field of the Earth on the quantum Hall effect. Taking the gravitational field of the Earth to be uniform along the vertical…

An intriguing observation on the quantum anomalous Hall effect (QAHE) in magnetic topological insulators (MTIs) is the dissipative edge states, where quantized Hall resistance is accompanied by nonzero longitudinal resistance. We…