The theory of the qhe is built largely around the special properties of singleparticle freeelectron. Experimental observation of the quantum hall effect and berrys phase in graphene. Landau levels play a role in the explanation of the integer and fractional quantum hall effect 1, which is treated in another proseminar. Pdf quantum hall effect a brief introduction researchgate. 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. Landau level spectra and the quantum hall effect of. Quantum hall effect an overview sciencedirect topics. The landau levels are invariant subspaces of b, b and since not only aa but also bb has a. Pdf quantum hall effect and landau levels in the 3d. Afterwards, haldane proposed the qhe without landau levels, showing nonzero chern number c1, which has been experimentally observed at relatively low temperatures. Mar 02, 2019 as a result, there are no landau levels, edge states, or quantum hall effect on one surface. But two surfaces can support a complete cyclotron motion and the quantum hall effect.
Pdf fractional quantum hall effect in the absence of. Generationrecombination noise due to localisation in spin. Aoki, in comprehensive semiconductor science and technology, 2011. Jul 12, 2011 the fractional quantum hall effect occurs when electrons move in landau levels. The first four chapters require only basic quantum mechanics. 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. 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 quantum hall effect qhe is the remarkable observation of quantized transport in two dimensional electron gases placed in a transverse magnetic field. Pdf landau levels and quantum hall effect in graphene. They were attributed to generation recombination processes involving localised states in the tails of the spinsplit landau levels.
The basics are described well but theres nothing about chernsimons theories or the importance of the edge modes. Fractional quantum hall effect without landau levels. Noise was measured under integral quantum hall con ditions in the filling factor range 2 hall voltage at least two lorentzians could be distinguished. There occurs an analogous phenomenon, the quantum spin hall effect, where a spin current flows instead of a charge current. Landau level mixing and the fractional quantum hall effect arxiv.
Quantum hall effect and landau levels in the 3d topological insulator hgte. The spacing of these levels is proportional to the classical cyclotron frequency. In 1988, it was proposed that there was quantum hall effect without landau levels. A twodimensional condensedmatter lattice model is presented which exhibits a nonzero quantization of the hall conductance. The integer quantum hall effect is a singleparticle phenomenon. Model for a quantum hall effect without landau levels f. In this letter i show how, in principle, a qhe may also result from breaking of timereversal. An odd integer number of the filling factor means that. The fractional quantum hall effect occurs when electrons move in landau levels. Landau levels, cyclotron frequency, degeneracy strength, flux quantum.
Landau level spectra and the quantum hall effect of multilayer graphene mikito koshino1 and edward mccann2 1department of physics, tohoku university, sendai 9808578, japan 2department of physics, lancaster university, lancaster la1 4yb, united kingdom received 5 january 2011. 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 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. Magnetotransport in 2deg the levels are degenerate since the energy of 2deg depends only on one variable, n. Two prominent ones are prange and girvin, the quantum hall e. 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. The qh effect without landau levels is referred to as the quantum anomalous hall effect. The quantization of electron orbits in a magnetic field results. The fictitious magnetic field is an emergent phenomenon, an effective interaction that emerges from. Here we show the theoretical discovery of the fractional quantum hall effect in the absence of landau levels in. 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. Quantum hall effects world scientific publishing company. We assume that the chemical potential is in between two landau levels at positive energies, shown by the dashed line in fig.
For emerging physics and lowpowerconsumption electronics. Lecture notes on quantum hall effect a work in progress. Grayson eecs, nu the workshop on semiconductors, electronic materials, thin films and photonic materials tel aviv university february 2225, 2015. Theory of quantum hall effect and high landau levels modern.
Fractional quantum hall effect in the absence of landau levels. The phenomena are typically divided into two classes, the integer quantum hall effect iqhe. Under some circumstances of weak but nonzero disorder, quantized hall plateaus appear which are characterized by simple rational fractional. 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 structure of fractional quantum hall effect data is similar to that for the integer effect, and can be understood according to a. Experimental observation of the quantum hall effect and. In this study, using a theoretical flatband lattice model, the fractional quantum hall effect is observed in the. Quantum mechanics told us, once we have a periodic motion with angular momentum. Integer quantum hall effect, which is the hall effect quantized into integer times e 2 h e. From landau levels to quantum hall effects by bertrand i.
The landau level structure shows two zeroenergy modes. Here we study the landau levels and edge states of surface dirac fermions. Experimental observation of the quantum hall effect and berry. This quantum hall effect is referred to as the quantum anomalous hall qah effect. As a result, there are no landau levels, edge states, or quantum hall effect on one surface. 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. Noise was measured under integral quantum hall con ditions in the filling factor range 2 quantum hall effect. There are surprisingly few dedicated books on the quantum hall e. Model for a quantum hall effect without landau levels. The quantum hall effect landau levels quantum mechanics of. Quantum hall effects in graphene 55, 56 have been studied intensively.
The high landau level filling fractions 52, 73 and 83 are understood by this model. Haldane eugene higgins professor in princeton university nobel laureate of 2016 this paper has been cited 1500 times. As a result, the charged particles can only occupy orbits with discrete energy values, called landau levels. There are surprisingly few dedicated books on the quantum hall effect. Highchernnumber and hightemperature quantum hall effect without landau levels preprint pdf available july 2019 with 110 reads how we measure reads.
We derive effective hamiltonians for the fractional quantum hall effect in n 0 and n 1. Nov 10, 2005 experimental observation of the quantum hall effect and berrys phase in graphene. The two surfaces are connected by the weyl nodes, which are higherdimensional singularities. The high landau level filling fractions 52, 73 and 83 are understood by.
What is important is that the quantum states of the electrons in all these cases belong to discrete energy eigenvalues. 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. 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. The zeeman effect, which we discussed in some detail in sect. Readers are referred to chapter 4 for the basic concepts of quantum hall effects in semiconductors, e. Pdf fractional quantum hall effect in the absence of landau. They are typical phenomena on the topological insulator. Here we show the theoretical discovery of the fractional quantum hall effect in the absence of landau levels in an interacting fermion model. Magnetotransport in 2deg landau quantization reminder from qm magnetic field is described by the vector potential, we will use the so called landau gauge. Edge states and integer quantum hall effect in topological. When the magnetic field is at b0, only the lowest three landau levels will be populated. The eigenwavefunctions and eigenenergy for this hamiltonian are very simple.
Pdf highchernnumber and hightemperature quantum hall. Landau quantization in quantum mechanics is the quantization of the cyclotron orbits of charged particles in magnetic fields. Landau levels that account perturbatively for landau level mixing by. 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. From landau levels to quantum hall effects landau congress. To see this, we can return to the simple definition 1. Then some aspects about landau quantization will be covered. Generally speaking, the iqhe in graphene has the same underlying mechanism as that in the semiconductor 2deg. Experimentally this effect is often observed in atomic gases but can also manifest itself with bound electrons in semiconductors and dielectrics. The angular momentum model which couples the spin and charge is discussed as a possible theory of the quantum hall effect. This is a course on the quantum hall effect, given in tifr, mumbai.
760 615 1168 1341 9 925 483 1187 581 1622 853 1010 998 964 1530 520 226 296 188 1593 969 52 588 773 248 1514 1340 1289 1614 595 915 33 1445 328 410 679