For emerging physics and lowpowerconsumption electronics. Here we show the theoretical discovery of the fractional quantum hall effect in the absence of landau levels in an interacting fermion model. Quantum hall effects in graphene 55, 56 have been studied intensively. Aoki, in comprehensive semiconductor science and technology, 2011. Model for a quantum hall effect without landau levels. Fractional quantum hall effect in the absence of landau levels. In 1988, it was proposed that there was quantum hall effect without landau levels. Lecture notes on quantum hall effect a work in progress.
They are typical phenomena on the topological insulator. Jun 06, 2011 the quantum hall effect qhe is the remarkable observation of quantized transport in two dimensional electron gases placed in a transverse magnetic field. In this study, using a theoretical flatband lattice model, the fractional quantum hall effect is observed in the. The landau levels are invariant subspaces of b, b and since not only aa but also bb has a. Quantum hall effect an overview sciencedirect topics. Model for a quantum hall effect without landau levels f. An odd integer number of the filling factor means that. There are surprisingly few dedicated books on the quantum hall e. In this letter i show how, in principle, a qhe may also result from breaking of timereversal. Magnetotransport in 2deg the levels are degenerate since the energy of 2deg depends only on one variable, n. From landau levels to quantum hall effects landau congress.
A twodimensional condensedmatter lattice model is presented which exhibits a nonzero quantization of the hall conductance. The zeeman effect, which we discussed in some detail in sect. We derive effective hamiltonians for the fractional quantum hall effect in n 0 and n 1. The quantum hall effect qhe is the remarkable observation of quantized transport in two dimensional electron gases placed in a transverse magnetic field. Two prominent ones are prange and girvin, the quantum hall e. Theory of quantum hall effect and high landau levels modern. The integer quantum hall effect is a topological state of quantum matter in two dimensions, and has recently been observed in threedimensional topological insulator thin films.
This quantum hall effect is referred to as the quantum anomalous hall qah effect. The first four chapters require only basic quantum mechanics. Pdf landau levels and quantum hall effect in graphene. Experimentally this effect is often observed in atomic gases but can also manifest itself with bound electrons in semiconductors and dielectrics. What is important is that the quantum states of the electrons in all these cases belong to discrete energy eigenvalues. Mar 02, 2019 as a result, there are no landau levels, edge states, or quantum hall effect on one surface.
As a result, there are no landau levels, edge states, or quantum hall effect on one surface. The basics are described well but theres nothing about chernsimons theories or the importance of the edge modes. Pdf quantum hall effect and landau levels in the 3d. Readers are referred to chapter 4 for the basic concepts of quantum hall effects in semiconductors, e. Noise was measured under integral quantum hall con ditions in the filling factor range 2 quantum hall effect. Quantum hall effect and landau levels in the 3d topological insulator hgte. From landau levels to quantum hall effects by bertrand i.
Magnetotransport in 2deg landau quantization reminder from qm magnetic field is described by the vector potential, we will use the so called landau gauge. The quantum hall effect landau levels quantum mechanics of. Here we study the landau levels and edge states of surface dirac fermions. Edge states and integer quantum hall effect in topological.
The qh effect without landau levels is referred to as the quantum anomalous hall effect. Jul 12, 2011 the fractional quantum hall effect occurs when electrons move in landau levels. Landau levels, cyclotron frequency, degeneracy strength, flux quantum. Quantum hall effects world scientific publishing company. Highchernnumber and hightemperature quantum hall effect without landau levels preprint pdf available july 2019 with 110 reads how we measure reads. By contrast, the fractional quantum hall effect is a collective phenomenon for which coulomb interactions between electrons are essential. The landau levels are degenerate, with the number of electrons per level directly proportional to the strength of the applied magnetic field. In metals and in the conduction band of semiconductors, on the other hand, the energy levels of electrons belong to the continuum spectrum, and in some instances, electrons can even be treated as free particles.
The landau level structure shows two zeroenergy modes. Pdf quantum hall effect a brief introduction researchgate. The phenomena are typically divided into two classes, the integer quantum hall effect iqhe. Pdf fractional quantum hall effect in the absence of landau. The high landau level filling fractions 52, 73 and 83 are understood by. The general argument so far is great in that it applies to virtually any complicated electron system with interactions and in a real material, but we would probably feel better if we could calculate the hall conductance directly for some simple system. Haldane eugene higgins professor in princeton university nobel laureate of 2016 this paper has been cited 1500 times. The quantum hall effect qhe with quantized hall resistance of he2 starts the research on topological quantum states and lays the foundation of topology in physics. But two surfaces can support a complete cyclotron motion and the quantum hall effect. The quantization of electron orbits in a magnetic field results. The fractional quantum hall effect is also understood as an integer quantum hall effect, although not of electrons but of chargeflux composites known as composite fermions.
The structure of fractional quantum hall effect data is similar to that for the integer effect, and can be understood according to a. Pdf fractional quantum hall effect in the absence of. Afterwards, haldane proposed the qhe without landau levels, showing nonzero chern number c1, which has been experimentally observed at relatively low temperatures. We assume that the chemical potential is in between two landau levels at positive energies, shown by the dashed line in fig.
Landau levels that account perturbatively for landau level mixing by. The fictitious magnetic field is an emergent phenomenon, an effective interaction that emerges from. Experimental observation of the quantum hall effect and berry. To see this, we can return to the simple definition 1. The quantum hall effect qhe in twodimensional 2d electron systems is usually associated with the presence of a uniform externally generated magnetic field, which splits the spectrum of electron energy levels into landau levels. Landau level mixing and the fractional quantum hall effect arxiv. Here we show the theoretical discovery of the fractional quantum hall effect in the absence of landau levels in. Landau quantization in quantum mechanics is the quantization of the cyclotron orbits of charged particles in magnetic fields. There are surprisingly few dedicated books on the quantum hall effect. Landau levels play a role in the explanation of the integer and fractional quantum hall effect 1, which is treated in another proseminar.
Landau levels within landau levels so fractional quantized hall states are understood as filled landau levels of particles in a fictitious magnetic field, within a partiallyfull landau level of the true magnetic field. The theory of the qhe is built largely around the special properties of singleparticle freeelectron. It is well known that the topological phenomena with fractional excitations, the fractional quantum hall effect, will emerge when electrons move in landau levels. The angular momentum model which couples the spin and charge is discussed as a possible theory of the quantum hall effect. Generally speaking, the iqhe in graphene has the same underlying mechanism as that in the semiconductor 2deg. Nov 10, 2005 experimental observation of the quantum hall effect and berrys phase in graphene. They were attributed to generation recombination processes involving localised states in the tails of the spinsplit landau levels. In quantizing magnetic fields, the electron spectrum splits into landau levels and, at low temperatures, a 2deg demonstrates the quantum hall effect, which manifests itself in zero longitudinal resistance r l and quantized hall resistance r h h2e 2 n, where n is the number of filled landau levels. Pdf highchernnumber and hightemperature quantum hall.
The quantum hall effect qhe refers to a set of phenomena and associated phases of matter found in twodimensional electron gases subjected to a large perpendicular magnetic. The two surfaces are connected by the weyl nodes, which are higherdimensional singularities. Grayson eecs, nu the workshop on semiconductors, electronic materials, thin films and photonic materials tel aviv university february 2225, 2015. This is a course on the quantum hall effect, given in tifr, mumbai. The high landau level filling fractions 52, 73 and 83 are understood by this model. The fractional quantum hall effect occurs when electrons move in landau levels. The spacing of these levels is proportional to the classical cyclotron frequency.
The integer quantum hall effect is a singleparticle phenomenon. As a result, the charged particles can only occupy orbits with discrete energy values, called landau levels. Under some circumstances of weak but nonzero disorder, quantized hall plateaus appear which are characterized by simple rational fractional. When the magnetic field is at b0, only the lowest three landau levels will be populated. Then some aspects about landau quantization will be covered. There occurs an analogous phenomenon, the quantum spin hall effect, where a spin current flows instead of a charge current.
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