Related papers: Quantum Hall Effect and Noncommutative Geometry
The quantum anomalous Hall effect refers to the quantization of Hall effect in the absence of applied magnetic field. The quantum anomalous Hall effect is of topological nature and well suited for field-free resistance metrology and…
We explore the consequences of introducing a complex conductivity into the quantum Hall effect. This leads naturally to an action of the modular group on the upper-half complex conductivity plane. Assuming that the action of a certain…
We derive semiclassical equations of motion for an accelerated wavepacket in a two-band system. We show that these equations can be formulated in terms of the static band geometry described by the quantum metric. We consider the specific…
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…
The Quantum Hall Effects in all even dimensions are uniformly constructed. Contrary to some recent accounts in the literature, the existence of Quantum Hall Effects does not {\it crucially} depend on the existence of division algebras. For…
By considering N_e-electrons and N_h-holes together in uniform external magnetic and electric fields, we end up with a total Hall conductivity \sigma_{H}^{tot}, which is depending to the difference between N_e and N_h and becomes null when…
Using the correlation function of chiral vertex operators of the Coulomb gas model, we find the Laughlin wavefunctions of quantum Hall effect, with filling factor $\nu =1/m$, on Riemann sufaces with Poincare metric. The same is done for…
One of the most celebrated accomplishments of modern physics is the description of fundamental principles of nature in the language of geometry. As the motion of celestial bodies is governed by the geometry of spacetime, the motion of…
A square lattice model which exhibits a nonzero quantized Hall conductance in a zero net magnetic field at certain values of the parameters is presented. The quantization is due to the existence of a topological winding number that…
We study a generic two-dimensional hopping model on a honeycomb lattice with strong spin-orbit coupling, without the requirement that the half-filled lattice be a Topological Insulator. For quarter-(or three-quarter) filling, we show that a…
When a conduction electron couples with a non-coplanar localized magnetic moment, the realspace Berry curvature is exerted to cause the geometrical Hall effect, which is not simply proportional to the magnetization. So far, it has been…
This paper provides an examination of how are prediction of standard quantum mechanic (QM) affected by introducing a noncommutative (NC) structure into the configuration space of the considered system (electron in the Coulomb potential in…
We propose a formula constructed out of elementary functions that captures many of the detailed features of the transverse resistivity $\rho_{xy}$ for the integer quantum Hall effect. It is merely a phenomenological formula in the sense…
We establish a universal theory to understand quasiparticle Hall effects and transverse charge-carrier transport in organic semiconductors. The simulations are applied to organic crystals inspired by rubrene and cover multiple transport…
The Hall conductivity of an electron gas on the surface of constant negative curvature (the Lobachevsky plane) in the presence of an orthogonal magnetic field is investigated. It is shown that the effect of the surface curvature is to…
The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. Existence of the quantum Hall effect requires breaking of the time reversal symmetry caused by an external…
We study the quantum Hall effect in the surface states of topological insulator in the presence of a perpendicular magnetic field in the framework of edge states. Motion of Dirac fermions will form descrete Landau levels, among which a…
Up to almost the last two decades all the experimental results concerning the quantum Hall effect (QHE), i.e., the observation of plateaux at integer (IQHE) or fractional (FQHE) values of the constant h/e2, were related to quantum-wells in…
Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a modular symmetry group commuting with the renormalization group flow and hence mapping different phases of…
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…