Related papers: Phenomenological formula for Quantum Hall resistiv…
Despite the extensive literature on the quantum Hall effect (QHE), a direct derivation of the phenomenological formula $\rho_{xy} = h/e^2\nu$ from first principles has remained elusive. In this work, we revisit the Landau and…
In this paper, we present a phenomenological picture based on the composite fermion theory, in responding to the recent discovery by Shahar et al. of a new transport regime near the transition from a $\nu=1$ quantum Hall liquid to a Hall…
In this paper we give a survey of some models of the integer and fractional quantum Hall effect based on noncommutative geometry. We begin by recalling some classical geometry of electrons in solids and the passage to noncommutative…
We constructed a Hall resistance formula for the fractional quantum Hall effect by analyzing the experimental data reported in [J. P. Eisenstein and H. L. Stormer, {Science} {\bf 248}, 1510 (1990)]. The formula is given as a function of…
An analytic form for the conductivity tensor in crossover between two quantum Hall plateaux is derived, which appears to be in good agreement with existing experimental data. The derivation relies on an assumed symmetry between quantum Hall…
We demonstrate that the non-linear field dependence in the Hall effect, often indistinguishable from the anomalous Hall effect, can be realized entirely within the classical mechanism due to the Lorentz force by analyzing multi-valley…
The quantum Hall effect is one of the most important developments in condensed matter physics of the 20th century. The standard explanations of the famous integer quantized Hall plateaus in the transverse resistivity are qualitative, and…
We present a quantum mechanical model which establishes the veracity of the Riemann hypothesis that the non-trivial zeros of the Riemann zeta-function lie on the critical line of $\zeta(s)$.
We have determined the off-diagonal and diagonal conductivities for a quantum Hall effect system at exactly integer filling at finite temperatures and in the presence of weak short ranged disorder potential within the self consistent Born…
The Riemann Hypothesis (RH), one of the most profound unsolved problems in mathematics, concerns the nontrivial zeros of the Riemann zeta function. Establishing connections between the RH and physical phenomena could offer new perspectives…
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 study quantum Hall effect within the framework of a newly proposed approach, which captures the principal results of some proposals. This can be established by considering a system of particles living on the non-commutative plane in the…
We consider the quantum Hall effect in quantum electrodynamics and find a deviation from the quantum mechanical prediction for the Hall conductivity due to radiative antiscreening of electric charge in an external magnetic field. A weak…
We propose an approach based on a generalized quantum mechanics to deal with the basic features of the intrinsic spin Hall effect. This can be done by considering two decoupled harmonic oscillators on the noncommutative plane and evaluating…
The transport properties of the two-dimensional system in HgTe-based quantum wells containing simultaneously electrons and holes of low densities are examined. The Hall resistance, as a function of perpendicular magnetic field, reveals an…
A proof of the Riemann hypothesis using the reflection principle is presented.
We consider the Hall effect in a system of weakly coupled Luttinger chains. We obtain the full conductivity tensor in the absence of dissipation along the chains. We show that while the dependence of the Hall and transverse conductivities…
Integer and fractional quantum Hall effects were studied with different physics models and explained by different physical mechanisms. In this paper, the common physical mechanism for integer and fractional quantum Hall effects is studied,…
An analytic form for the crossover of the conductivity tensor between two Hall plateaux, as a function of the external magnetic field, is proposed. The form of the crossover is obtained from the action of a symmetry group, a particular…
The $\theta$ dependence of the Grassmannian $U(m+n)/U(m)\times U(n)$ non-linear $\sigma$ model is reexamined. This general theory provides an important laboratory for studying the quantum Hall effect, in the special limit $m=n=0$ (replica…