Related papers: Quantum Hall Effect in Higher Dimensions
We study the quantum Hall states in the lowest Landau level for a single wide quantum well. Due to a separation of charges to opposite sides of the well, a single wide well can be modelled as an effective two level system. We provide…
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…
The quantum Hall effect is usually observed when the two-dimensional electron gas is subjected to an external magnetic field, so that their quantum states form Landau levels. In this work we predict that a new phenomenon, the quantum…
In this work we obtain the Landau levels and the Hall conductivity at zero temperature of a two-dimensional electron gas on a conical surface. We investigate the integer quantum Hall effect considering two different approaches. The first…
We consider the fractional quantum Hall effect at the filling factor $\nu=4/11$, where two independent experiments have observed a well-developed and quantized Hall plateau. We examine the Abelian state described by the "$4\bar{2}1^{3}$"…
The quantum Hall effect emerges when two-dimensional samples are subjected to strong magnetic fields at low temperatures: Topologically protected edge states cause a quantized Hall conductivity in multiples of $e^2/h$. Here we show that the…
To fully appreciate the impacts that the discovery of the quantum Hall effect had on electrical metrology, it may benefit the reader to cultivate a general understanding of the phenomenon. Two-dimensional electron systems can exhibit many…
Developing a non-compact version of the SUSY Hopf map, we formulate the quantum Hall effect on a super-hyperboloid. Based on $OSp(1|2)$ group theoretical methods, we first analyze the one-particle Landau problem, and successively explore…
Physics of two-dimensional electron gases under perpendicular magnetic field often displays three distinct stages when increasing the field amplitude: a low field regime with classical magnetotransport, followed at intermediate field by a…
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…
The single-particle spectral function for an incompressible fractional quantum Hall state in the presence of a scalar short-ranged attractive impurity potential is calculated via exact diagonalization within the spherical geometry. In…
Strong correlation brings a rich array of emergent phenomena, as well as a daunting challenge to theoretical physics study. In condensed matter physics, the fractional quantum Hall effect is a prominent example of strong correlation, with…
We consider the quantum mechanics of a particle on a noncommutative plane. The case of a charged particle in a magnetic field (the Landau problem) with a harmonic oscillator potential is solved. There is a critical point, where the density…
The spectrum of charged particles in translation-invariant systems in a magnetic field is characterized by the Landau levels, which play a fundamental role in the thermodynamic and transport properties of solids. The topological nature and…
We analyze the electronic properties of a simple stacking defect in Bernal graphite. We show that a bound state forms, which disperses as $|\bfk-\bfK|^3$ in the vicinity of either of the two inequivalent zone corners $\bfK$. In the presence…
We discuss quantum Hall effect in the presence of arbitrary pair interactions between electrons. It is shown that irrespective of the interaction strength the Hall conductivity is given by the filling fraction of Landau levels averaged over…
The purpose of these lectures is to describe the basic theoretical structures underlying the rich and beautiful physics of the quantum Hall effect. The focus is on the interplay between microscopic wavefunctions, long-distance effective…
The abelian hierarchy of quantum Hall states accounts for most of the states in the lowest Landau level, and there is evidence of a similar hierarchy of non-abelian states emanating from the {\nu} = 5/2 Moore-Read state in the second Landau…
In this letter, we discuss the recently proposed fractional quantum Hall effect in the absence of Landau levels. It is shown that the parton construction can explain all properties of 1/3 state, including the effective charge of…
It is demonstrated that all observed fractions at moderate Landau level fillings for the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…