The original, classical hall e ect was discovered in 1879 by edwin hall. 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 realized in twodimensional electron systems. Course on topology in condensed matter 11,068 views. Edge states and integer quantum hall effect in topological. The first four chapters require only basic quantum mechanics. Introduction to the physics of the quantum hall regime. Jan 26, 2015 if you have a 2d confined electron system at very low temperature below the fermi state and affected by a strong magnetic field 10 t. Left the quantum hall effect qhe occurs in a twodimensional electron system under a large applied magnetic field.
Multilayered quantum hall systems have attracted much interest, following the theoretical prediction of the chiral surface state. The quantum hall effect qhe originates from discrete landau levels forming in a. Yoshioka, the quantum hall effect, springer, berlin 2002. The transverse resistance is precisely quantized at h. 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. Although, the conclusive evidence for collective behaviour of electrons in graphene is lacking so far, recently scientists have observed the fractional quantum hall effect fqhe in graphene experimentally. Jain, composite fermions, cambridge university press 2007 introduction. 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 emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum hall effect. Discovery of the quantum hall effect thank you kvk and mpifkf. By contrast, the fractional quantum hall effect is a collective phenomenon for which coulomb interactions between electrons are essential. Right the quantum anomalous hall effect has quantum hall features without an applied field. The birthday of the quantum hall effect qhe can be fixed very accurately. 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.
On the fractional quantum hall effect sciencedirect. In the course of the theoretical investigation of these phenomena, various new concepts and. Introduction to integer quantum hall effect by ganpathy murthy duration. These lecture notes yield an introduction to quantum hall effects both for nonrelativistic electrons in conventional 2d electron gases such as in semiconductor heterostructures and relativistic electrons in graphene. A landauginzburg theory for paired quantum hall states. References home university of waterloo university of. 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. Sorry, we are unable to provide the full text but you may find it at the following locations. Physics the quantum hall effect gets more practical.
This will provide a useful background for our discussion of the quantum hall e ect. The physicist this book will provide a nice starting point for ideas that an experienced solid state physics educator may use for an indepth introduction to the fundamentals of both the integral and fractional quantum hall effect. Aspects of the quantum hall effect institute for nuclear theory. The basics of quantum hall effect systematic setup definitions and terminology classical vs. Then a is always an integer and therefore all rational filling fractions lead to a fric tionless current. Abstract when exposed to a magnetic field b electrons will move in a direction per. Observation of the fractional quantum hall effect in graphene. The quantum hall effect is observed, if the fermi energy is located in the gap of the electronic. The integer quantum hall effect is a singleparticle phenomenon.
If you have a 2d confined electron system at very low temperature below the fermi state and affected by a strong magnetic field 10 t. Today, more than 20 years after the discovery of the quantum hall effect, the. These lecture notes attempt to explain the main ideas of the theory of the quantum hall effect. The quantum hall effect is a typical realization of topological effects in condensed matter physics. The fractional quantum hall effect, in particular, has opened up. The quantum hall effect or integer quantum hall effect is a quantummechanical version of the hall effect, observed in twodimensional electron systems subjected to low temperatures and strong magnetic fields, in which the hall conductance.
The landau level structure shows two zeroenergy modes. Levitov department of physics, massachusetts institute of technology, 77 massachusetts ave, cambridge, ma 029 electron edge states in graphene in the quantum hall e. Lee statistics of quasiparticles and the hierarchy of fractional quantized hall states b. Dimensional reduction, quantum hall effect and layer parity. The quantum hall effect springer series in solidstate sciences book 3 kindle edition by yoshioka, daijiro.
Request pdf on jan 1, 2002, daijiro yoshioka and others published the quantum hall effect find, read and cite all the research you need on researchgate. Novel excitations and broken symmetries, les houches summer school 1998. But in a magnetic eld, a system of charged particles e. This is a course on the quantum hall effect, given in tifr, mumbai. Yoshioka, the quantum hall effect, springer, berlin. Jan 14, 20 quantum hall effect intro by ady stern duration. Yoshioka,quantum hall effect, springer, berlin 2002. In the quantum hall effect the longitudinal conductance vanishes while the hall conductance. Yoshioka, the quantum hall effect, springer 2002 o. The quantum hall effect in a periodic potential 14 e. In the presence of a strong magnetic field, charged particles confined to move in the plane can form a series of new states of matter with bizarre properties. The structure of fractional quantum hall effect data is similar to that for the integer effect, and can be understood according to a. Girvin, the quantum hall e ect 2nd edition, springer 1990 d.
Quantum hall effect in semiconductor superlattice in a tilted. The quantum hall effects remains one of the most important subjects to have emerged in condensed matter physics over the past 20 years. The classical hall voltage current flow pattern in a hall bar how to solve discovery of the quantum hall the role of mobility the 2deg in a mosfet setting up the quantum mechanical hamiltonian effective masses etc oscillation of the fermi level, landau levels group velocity of the eigenstates channels from a contact to another. Pdf quantum hall effect a brief introduction researchgate. In the integer quantum hall effect, the hall resistance, under suitable conditions, is given only by fundamental constants, namely the planck constant h and the elementary charge e, and what is remarkable and astonishing is that it does not depend on the properties of the substance which houses the twodimensional electrons, such as the. The quantum hall e ect as an electrical resistance standard. The longitudinal conductance vanishes in this effect, and hall conductivity is quantized into integral multiples of e 2 h, or a fraction of e 2 h, for the case of the integer quantum hall effect, and the fractional quantum hall effect, respectively.
Fortunately, our understanding of this menagerie is based almost entirely on many body wavefunctions of a rather simple form. Topological insulators generic form of a twoband hamiltonian. Introduction to the quantum hall effect and topological phases. It is known that the integer v is the topological invariant of. The nature of this plateau is still a matter of debate, and active current research.
Pdf the fractional quantum hall effect researchgate. It is a simple consequence of the motion of charged particles in a magnetic eld. In chapter 5, we briefly discuss several multicomponent quantum hall systems, namely the quantum hall ferromagnetism, bilayer systems and graphene that may be viewed as. The discovery of the integer quantum hall effect in twodimensional electron gas opens a window to explore topological phases in quantum matter 1,2. Chapter 4 will describe the breakdown of quantum hall state in graphene. Use features like bookmarks, note taking and highlighting while reading the quantum hall effect springer series in solidstate sciences book 3. Quantum hall effect university of california, berkeley.
The fractional quantum hall effect fqhe is the quintessential collective quantum behaviour of charge carriers confined to two dimensions but it has not yet been observed in graphene, a material. After a brief historical overview in chapter 1, we discuss in detail the kineticenergy quantisation of nonrelativistic and the relativistic electrons. In this monograph daijiro yoshioka has done a marvelous job. A single layer twodimensional electron gas 2deg exhibits the quantum hall effect qhe when it is placed in a strong perpendicular magnetic field. The interaction physics in the extreme quantum limit which is responsible for the fractional quantum hall effect is discussed at length and from an elementary point.
Electronic phasetransition of graphite in a strong. This is they of state considered by yoshioka and lee. Observation of the fractional quantum hall effect in. What is an intuitive explanation of the quantum hall effect. Download it once and read it on your kindle device, pc, phones or tablets. Quantum hall effect in semiconductor superlattice in a. We study the fractional quantum hall effect using the obtained wave function and we find the current, resistance and hall s voltage for the arbitrary n. Halperin magnetoroton theory of collettive excitations in the fractional quantum hall effect g. Ground state of two dimensional electrons in strong magnetic fields and quantized hall effect d.
The calculations and the explanations are terse, but provide a basic. Topological aspects of the quantum hall effect y hatsugaiy department of applied physics, university of tokyo, 731 hongo, bunkyoku, tokyo 1, japan received 12 august 1996, in. We assume that the chemical potential is in between two landau levels at positive energies, shown by the dashed line in fig. Quantized hall plateaus have been found corresponding to a few even denominator fractions. References for halperins lectures on theory of quantum. Ewdin halls hiterto unpublished account, in the hall effect and its applica. The integer quantum hall effect is derived for a finite rectangular sample and rather general boundary conditions using a kubo formula approach. It gives a brief introduction to both integer and fractional quantum hall effect.
The fractional quantum hall effect is one of the most remarkable phenomena in all of condensed matter physics. The integer quantum hall effect iqhe explaining the existence of plateaus 5. Quantum hall e ect and electromechanics in graphene. The quantum hall effect springer series in solidstate.
Chapter 5 will describe the measurements on graphene nems covering the measurement of coe cient of thermal expansion and modal dispersion at low temperatures. Quantum hall effect integer quantum hall effect fractional quantum hall effect conclusion classical hall effect in 1879 by edwin h. Electromechanics of graphene nems in quantum hall regime will be described in chapter 6. Edge state picture of the iqhe the landauer approach is a scattering approach, which is a completely di erent way of. Chapter 3 is devoted to the transport characteristics of the integer quantum hall effect, and the basic aspects of the fractional quantum hall effect are described in chapter 4.
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