Pdf integer quantum hall effect in a lattice model. Metrology and microscopic picture of the integer quantum hall. Experimental observation of the quantum hall effect and. Theory of the integer and fractional quantum hall effects. Unconventional integer quantum hall effect in graphene. We also show that strained superlattices can be used to open significant energy gaps. It is a collective quantum e ect, like superconductivity. Theory of the integer and fractional quantum hall effects arxiv. In contrast, when we come to discuss the fractional quantum hall effect in section 3, the interactions between electrons will play a key role.
Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. The phenomenon is demonstrated by a twodimensional electron gas 2deg under a constant magnetic eld that is perpendicular to the 2d plane. A simple physical realization of an integer quantum hall state of interacting two dimensional bosons is provided. The quantum hall effects remains one of the most important subjects to have emerged in condensed matter physics over the past 20 years. Basic physics underlying the phenomenon is explained, along with diverse. So far the applicability and measurements of the berry phase were mostly limited. The integer quantum hall effect concerns the transport properties of a 2 dimensional electron system in the. This is similar to the hall conductivity of a massless dirac fermion with timereversal symmetry broken by a mass term m.
Theory of the integer and fractional quantum hall effects shosuke sasaki. In fact, this means that the dc conductivity is entirely determined by the 2d interface layer. Topological invariants for fractional quantum hall states v. Energy gaps and a zerofield quantum hall effect in graphene. Percolation, quantum tunnelling and the integer hall effect j t chalker and p d coddington physics department. 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 is a topological state of quantum matter in two dimensions and has recently been observed in threedimensional topological insulator thin films.
A generic theory of the integer quantum hall effect. Center for advanced high magnetic field science, graduate school of science, osaka university, 11 machikaneyama, toyonaka, osaka 5600043, japan. The main experimental devices hall bar and corbino disk are described and the basic experimental facts underlying the quantum hall effect are presented. 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 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 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. 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. The hall resistance in the classical hall effect changes continuously with applied magnetic field. 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. Pdf integer quantum hall effect in trilayer graphene.
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. Quantum hall effect and topological insulators joint. Feb 09, 2012 integer quantum hall effect in a lattice model revisited. Edge states and integer quantum hall effect in topological. It is known that the integer v is the topological invariant of. 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. This causes a gap to open between energy bands, and. We will consider the integer quantum hall effect beginning with the classical one. A generic sequence by which the iqhe plateaus disappear is. 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. 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. 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. Devices used for observing the quantum hall effect.
Likewise, the supercurrent in the quantum hall effect qhe is due to the existence of an energy gap. 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. The integer quantum hall effect universitat zu koln. 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. 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. The quantum hall effect is a phenomenon occurring in a 2dimensional electron gas. The focus is on the interplay between microscopic wavefunctions, longdistance effective chernsimons theories, and the modes which live on the boundary. The integer quantum hall effect iqhe is usually modeled by a galilean or rotationally invariant hamiltonian. The quantum hall effect is referred to as the integer or fractional quantum hall effect depending on whether is an integer or fraction, respectively.
Electronic quantum optics beyond the integer quantum hall effect. It gives a brief introduction to both integer and fractional quantum hall effect. The purpose of these lectures is to describe the basic theoretical structures underlying the rich and beautiful physics of the quantum hall effect. International centre for theoretical sciences 3,262 views. The main experimental devices hall bar and corbino disk are described and the basic experimental facts underlying the. This chapter starts with concepts of metal physics which are necessary for the understanding and description of metal behaviour in high magnetic fields. The discovery of the integer quantum hall effect in twodimensional electron gas opens a window to explore topological phases in quantum matter 1,2. The common feature of these systems is that the bulk has a. So far the applicability and measurements of the berry phase were mostly limited to. Originally, it was observed using a metaloxidesemiconductor transistor mosfet. 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. The quantum hall effect is referred to as the integer or fractional quantum hall effect depending on whether. Conclusion the quantum hall effect, due to a magnetic. Electronic quantum optics beyond the integer quantum hall.
A pronounced integer quantum hall effect is observed in these heterostructures with direct current. Jul 04, 2019 introduction to integer quantum hall effect by ganpathy murthy. The many electrons inside an ultrathin layer construct a quasitwodimensional quasi2d. Quantum hall effect an overview sciencedirect topics. In a mosfet, the electrons are trapped at the interface between silicon, which is a semiconductor, and silicon oxide, an. The integer quantum hall effect is derived for a finite rectangular sample and rather general boundary conditions using a kubo formula approach. The disappearance of integer quantum hall effect iqhe at strong disorder and weak magnetic field is studied in a lattice model. Dynamical quantum hall effect in the parameter space pnas. The quantisation of the conductivity happens for dirty, manyparticle mesoscopic systems. Introduction to integer quantum hall effect by ganpathy murthy duration. Introduction to integer quantum hall effect by ganpathy. Iqhe phases actually, the states with different integer quantum hall conductivity are different phases of matter at t0. The calculations and the explanations are terse, but provide a. 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.
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. Sep 27, 2009 we suggest realistic ways of creating this quantum state and observing the pseudomagnetic quantum hall effect. Topological invariants for fractional quantum hall states. Integer quantum hall effect in a lattice model revisited. A model is introduced for anderson localisation in the integer quantum hall regime. Percolation, quantum tunnelling and the integer hall effect. This results in a sequence of singleparticle quantum hall states at filling factor.
The diagonal elements of the conductivity tensor are only nonzero within the transitional ranges, i. The striking feature of the integer quantum hall effect is the persistence of the quantization i. 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. The quantum hall qh effect is one of the most remarkable phenomena discovered in the last century. Berry phase, aharonovbohm effect, nonabelian berry holonomy. The localized states dont contribute to conductance, and the quantization can be found with either. Southampton university, southampton so9 5nh, uk received 16 october 1987 abstract. 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.
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. In the quantum hall effect the longitudinal conductance vanishes while the hall conductance. Electronhole asymmetric integer and fractional quantum hall. Adiabatic transport, nonabelian statistics and the fusion algebra in incompressible systems the fractional quantum hall effect fqhe 3, i. Lecture 12 the integer quantum hall effect continued. One of the best known examples is the berry phase m.
References home university of waterloo university of. Mar 03, 2015 introduction to integer quantum hall effect by ganpathy murthy duration. Note that just above and below the zero energy landau level, the hall conductivity e22h. The situation with highfrequency conductivity of these heterostructures at low temperatures is quite different. 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. 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. Topological insulators generic form of a twoband hamiltonian. Introduction to the quantum hall effect and topological phases.
Electronhole asymmetric integer and fractional quantum. To study this phenomenon, scientists apply a large magnetic field to a 2d sheet semiconductor. In the iqhe this energy gap is that between the landau levels. Integer quantum hall effect, which is the hall effect quantized into integer times e 2 h e.
Integer quantum hall effect fractional quantum hall effect discovery. Pdf quantum hall effect a brief introduction researchgate. Pdf the classical hall effect, the integer quantum hall effect and the fractional quantum hall effect. Kubo formalism article pdf available in journal of applied physics 1124 february 2012 with 191 reads how we measure reads. Introduction to integer quantum hall effect by ganpathy murthy. Majorana quantization and halfinteger thermal quantum hall. Classical hall effect consider a quasi2dimensional sample of conducting material metal with length l in the xdirection and width w in the ydirection and. We know the basic phenomenology of the quantum hall effect qhe.
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