Indeed, a distinctive half integer quantum hall effect has been predicted 3,4,5 theoretically, as has the existence of a nonzero berrys phase a geometric quantum. Theory of the integer and fractional quantum hall effects arxiv. Half integer quantum hall effect in graphene exceptionally high mobility graphene samples allow us to investigate transport phenomena in the magnetic quantum limit where the qhe manifests itself. Integer quantum hall effect, which is the hall effect quantized into integer times e 2 h e. A pronounced integer quantum hall effect is observed in these heterostructures with direct current. In contrast, when we come to discuss the fractional quantum hall effect in section 3, the interactions between electrons will play a key role.
The focus is on the interplay between microscopic wavefunctions, longdistance effective chernsimons theories, and the modes which live on the boundary. This is similar to the hall conductivity of a massless dirac fermion with timereversal symmetry broken by a mass term m. Electronhole asymmetric integer and fractional quantum hall. We know the basic phenomenology of the quantum hall effect qhe. Kubo formalism article pdf available in journal of applied physics 1124 february 2012 with 191 reads how we measure reads. The iqhe is characterized by vanishing of both the diagonal conductivity and the diagonal resistivity, and by the exact quantization of the hall conductivity into integer multiples. This is followed by a selfconsistent interpretation of this phenomenon. Unconventional integer quantum hall effect in graphene. In the iqhe this energy gap is that between the landau levels.
The diagonal elements of the conductivity tensor are only nonzero within the transitional ranges, i. We also show that strained superlattices can be used to open significant energy gaps. Feb 09, 2012 integer quantum hall effect in a lattice model revisited. The situation with highfrequency conductivity of these heterostructures at low temperatures is quite different. The quantum hall qh effect is one of the most remarkable phenomena discovered in the last century. Quantum hall effect an overview sciencedirect topics.
Southampton university, southampton so9 5nh, uk received 16 october 1987 abstract. At the same time, it is now well understood that these topological invariants can be reexpressed in terms of single particle greens functions 4. The integer quantum hall effect universitat zu koln. This results in a sequence of singleparticle quantum hall states at filling factor. Pdf the classical hall effect, the integer quantum hall effect and the fractional quantum hall effect. The quantum hall effect is an example of a phenomenon having topological features that can be observed in certain materials under harsh and stringent laboratory conditions large magnetic field, near absolute zero temperature. Dynamical quantum hall effect in the parameter space pnas.
Halfinteger quantum hall effect in graphene exceptionally high mobility graphene samples allow us to investigate transport phenomena in the magnetic quantum limit where the qhe manifests itself. So far the applicability and measurements of the berry phase were mostly limited. Topological invariants for fractional quantum hall states v. Integer quantum hall effect basics theories for the quantization disorder in qhs berry phase in qhs topology in qhs effect of lattice effect of spin and electron interaction m. Berry phase, aharonovbohm effect, nonabelian berry holonomy. In the quantum hall effect the longitudinal conductance vanishes while the hall conductance. The common feature of these systems is that the bulk has a. Introduction to the quantum hall effect and topological phases. The hall resistance in the classical hall effect changes continuously with applied magnetic field. The many electrons inside an ultrathin layer construct a quasitwodimensional quasi2d. The quantum hall e ect qhe has been a eld of active research since the monumental discovery of the integer case by klitzing et al. In a mosfet, the electrons are trapped at the interface between silicon, which is a semiconductor, and silicon oxide, an. Basic physics underlying the phenomenon is explained, along with diverse.
Electronhole asymmetric integer and fractional quantum. The quantum hall effect qhe is one of the most remark able condensedmatter phenomena discovered in the second half of the 20th century, and our talk is. A simple physical realization of an integer quantum hall state of interacting two dimensional bosons is provided. Topological insulators generic form of a twoband hamiltonian. Originally, it was observed using a metaloxidesemiconductor transistor mosfet. Sep 27, 2009 we suggest realistic ways of creating this quantum state and observing the pseudomagnetic quantum hall effect. Lecture 12 the integer quantum hall effect continued.
Integer quantum hall effect fractional quantum hall effect discovery. The quantum hall effect is a phenomenon occurring in a 2dimensional electron gas. The purpose of these lectures is to describe the basic theoretical structures underlying the rich and beautiful physics of the quantum hall effect. References home university of waterloo university of. Pdf integer quantum hall effect in trilayer graphene. The striking feature of the integer quantum hall effect is the persistence of the quantization i. Integer quantum hall effect in a lattice model revisited. The quantum hall effect is referred to as the integer or fractional quantum hall effect depending on whether. The integer quantum hall effect iqhe is usually modeled by a galilean or rotationally invariant hamiltonian.
The disappearance of integer quantum hall effect iqhe at strong disorder and weak magnetic field is studied in a lattice model. The fractional quantum hall effect, in particular, has opened up a new paradigm in the study of strongly correlated electrons, and it has been shown that new concepts, such as fractional statistics, anyon, chiral luttinger liquid and composite particles, are. Experimental observation of the quantum hall effect and. Jul 04, 2019 introduction to integer quantum hall effect by ganpathy murthy. The thesis discusses some puzzling results of these experiments and presents a coherent picture of mesoscopic effects in quantum hall systems, which accounts for integer and fractional filling factors and ranges from microscopic theory to effective models, and. Mar 03, 2015 introduction to integer quantum hall effect by ganpathy murthy duration. Topological invariants for fractional quantum hall states. Quantum hall effect 55 skipping cyclotron orbits fourterminal sample configuration to measure the hall and longitudinal resistivities quantum hall effect 56 for a given plateau not a perfect conductor. Adiabatic transport, nonabelian statistics and the fusion algebra in incompressible systems the fractional quantum hall effect fqhe 3, i. The localized states dont contribute to conductance, and the quantization can be found with either. Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. It is known that the integer v is the topological invariant of. Electronic quantum optics beyond the integer quantum hall effect. A model is introduced for anderson localisation in the integer quantum hall regime.
Classical hall effect consider a quasi2dimensional sample of conducting material metal with length l in the xdirection and width w in the ydirection and. When the disorder is sufficiently low, the eightfold degeneracy of the lowest ll is lifted by electronelectron interactions, which results in quantum hall states at all integer filling factors 3, 4. The main experimental devices hall bar and corbino disk are described and the basic experimental facts underlying the quantum hall effect are presented. Likewise, the supercurrent in the quantum hall effect qhe is due to the existence of an energy gap. Introduction to integer quantum hall effect by ganpathy. Conclusion the quantum hall effect, due to a magnetic. Introduction to integer quantum hall effect by ganpathy murthy duration. Introduction to integer quantum hall effect by ganpathy murthy. Plotting the hall resistance essentially the reciprocal of the hall conductance of a lowtemperature twodimensional electron gas against the strength of the imposed magnetic field normal to the gas plane, one finds a stairlike quantized sequence of hall conductances very precisely equal to ne 2 h, where n is the integer that characterizes each. Percolation, quantum tunnelling and the integer hall effect. Pdf integer quantum hall effect in a lattice model. The thesis discusses some puzzling results of these experiments and presents a coherent picture of mesoscopic effects in quantum hall systems, which accounts for integer and fractional filling factors and ranges from microscopic theory to effective models, and covers both equilibrium and nonequilibrium phenomena.
The discovery of the integer quantum hall effect in twodimensional electron gas opens a window to explore topological phases in quantum matter 1,2. It is a collective quantum e ect, like superconductivity. These are not generic symmetries for electrons moving in a crystal background and can potentially confuse nontopological quantities with topological ones and identify otherwise distinct geometrical properties. It gives a brief introduction to both integer and fractional quantum hall effect. Essin department of physics, university of colorado, co 80309 boulder, usa received january 24, 20 we calculate a topological invariant, whose value would co incide with the chern number in the case of integer quantum hall effect, for fractional quantum hall states. Devices used for observing the quantum hall effect. Theory of the integer and fractional quantum hall effects. So far the applicability and measurements of the berry phase were mostly limited to. The main experimental devices hall bar and corbino disk are described and the basic experimental facts underlying the. One of the best known examples is the berry phase m. The integer quantum hall effect is derived for a finite rectangular sample and rather general boundary conditions using a kubo formula approach. Percolation, quantum tunnelling and the integer hall effect j t chalker and p d coddington physics department. Theory of the integer and fractional quantum hall effects shosuke sasaki. Energy gaps and a zerofield quantum hall effect in graphene.
Quantum hall effect and topological insulators joint. The integer quantum hall effect concerns the transport properties of a 2 dimensional electron system in the. Plotting the hall resistance essentially the reciprocal of the hall conductance of a lowtemperature twodimensional electron gas against the strength of the imposed magnetic field normal to the gas plane, one finds a stairlike quantized sequence of hall conductances very precisely equal to ne 2 h, where n. A generic theory of the integer quantum hall effect. This is an example of a symmetryprotected topological spt phase which is a generalization of the concept of topological insulators to systems of interacting bosons or fermions. The calculations and the explanations are terse, but provide a. The quantum hall effects remains one of the most important subjects to have emerged in condensed matter physics over the past 20 years. A generic sequence by which the iqhe plateaus disappear is. Note that just above and below the zero energy landau level, the hall conductivity e22h. Iqhe phases actually, the states with different integer quantum hall conductivity are different phases of matter at t0. The quantum hall effect or integer quantum hall effect is a quantum mechanical version of the hall effect, observed in twodimensional electron systems subjected to low temperatures and strong magnetic fields, in which the hall conductance. This causes a gap to open between energy bands, and. Center for advanced high magnetic field science, graduate school of science, osaka university, 11 machikaneyama, toyonaka, osaka 5600043, japan.
In fact, this means that the dc conductivity is entirely determined by the 2d interface layer. Electronic quantum optics beyond the integer quantum hall. Majorana quantization and halfinteger thermal quantum hall. We will consider the integer quantum hall effect beginning with the classical one. Jul 11, 2018 the quantum hall effect in twodimensional electron gases involves the flow of topologically protected dissipationless charge currents along the edges of a sample. To study this phenomenon, scientists apply a large magnetic field to a 2d sheet semiconductor. Edge states and integer quantum hall effect in topological. The quantisation of the conductivity happens for dirty, manyparticle mesoscopic systems. 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. The quantum hall effect is referred to as the integer or fractional quantum hall effect depending on whether is an integer or fraction, respectively. This chapter starts with concepts of metal physics which are necessary for the understanding and description of metal behaviour in high magnetic fields. Localization and the integer quantum hall e ect the aim of this lecture is to explain how disorder which creates a random potential for electrons, thereby destroying translational symmetry is a necessary and su cient condition for the observed plateaus, for noninteracting electrons. The phenomenon is demonstrated by a twodimensional electron gas 2deg under a constant magnetic eld that is perpendicular to the 2d plane. International centre for theoretical sciences 3,262 views.
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