Related papers: Quantum Hall effect in momentum space
Hall conductivity for the intrinsic anomalous quantum Hall effect in homogeneous systems is given by the topological invariant composed of the Green function depending on momentum of quasiparticle. This expression reveals correspondence…
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…
We show how the weakly trapped Harper-Hofstadter model can be mapped onto a Harper-Hofstadter model in momentum space. In this momentum-space model, the band dispersion plays the role of the periodic potential, the Berry curvature plays the…
Hall conductivity for the intrinsic quantum Hall effect in homogeneous systems is given by the topological invariant composed of the Green function depending on momentum of quasiparticle. This expression reveals correspondence with the…
The von Neumann lattice representation is a convenient representation for studying several intriguing physics of quantum Hall systems. In this formalism, electrons are mapped to lattice fermions. A topological invariant expression of the…
A bosonic analogue of the fractional quantum Hall eff ect occurs in rapidly rotating trapped Bose gases: There is a transition from uncorrelated Hartree states to strongly correlated states such as the Laughlin wave function. This physics…
We derive an efficient formula for Z$_2$ topological invariants characterizing the quantum spin Hall effect. It is defined in a lattice Brillouin zone, which enables us to implement numerical calculations for realistic models even in three…
Electrons moving through a noncoplanar magnetic texture acquire a Berry phase, which can be described as an effective magnetic field. This effect is known as the topological Hall effect and has been observed in topological spin textures.…
We investigate spontaneous interlayer phase coherence and the occurrence of the quantum Hall effect in triple-layer electron systems. Our work is based on a simple tight-binding model that greatly facilitates calculations and whose accuracy…
The Berry curvature is a geometrical property of an energy band which acts as a momentum space magnetic field in the effective Hamiltonian describing single-particle quantum dynamics. We show how this perspective may be exploited to study…
Quantum Hall Dynamics is formulated on von Neumann lattice representation where electrons in Landau levels are defined on lattice sites and are treated systematically like lattice fermions. We give a proof of the integer Hall effect, namely…
We consider the problem of magnetic charges in $(2+1)$ dimensions for a torus geometry in real-space, subjected to an inverted Lorentz force due to an external electric field applied normal to the surface of the torus. We compute the Hall…
The quantum Hall effect is generally understood for free electron gases, in which topologically protected edge states between Landau levels (LLs) form conducting channels at the edge of the sample. In periodic crystals, the LLs are…
We study transport properties and topological phase transition in two-dimensional interacting disordered systems. Within dynamical mean-field theory, we derive the Hall conductance, which is quantized and serves as a topological invariant…
We consider spin-polarized electrons in a single Landau level on a torus. The quantum Hall problem is mapped onto a one-dimensional lattice model with lattice constant $2\pi/L_1$, where $L_1$ is a circumference of the torus (in units of the…
A theory of integer quantum Hall effect(QHE) in realistic systems based on von Neumann lattice is presented. We show that the momentum representation is quite useful and that the quantum Hall regime(QHR), which is defined by the propagator…
We present an experimental evidence of \emph{topological} Hall-effect in an all-optical third-order nonlinear optical process via spatial symmetry-breaking in pseudo-spin textures created by a spatially-structured pump laser beam. The…
By breaking the time-reversal-symmetry in three-dimensional topological insulators with introduction of spontaneous magnetization or application of magnetic field, the surface states become gapped, leading to quantum anomalous Hall effect…
Here, we elaborate on and develop the geometrical approach introduced in K. Le Hur, Physics Reports 1104 1-42 (2025) between the magnetic monopole created from a radial field, quantum physics and topological lattice models through quantum…
The quintessential two-dimensional lattice model that describes the competition between the kinetic energy of electrons and their short-range repulsive interactions is the repulsive Hubbard model. We study a time-reversal symmetric variant…