The quantum hall qh effect is one of the most remarkable phenomena discovered in the last century. Here h is the plancks constant and e is the charge of the electron. Mobility and not conductivity fixes the hall angle for metals pure cu, ag at low temp. We assume that the chemical potential is in between two landau levels at positive energies, shown by the dashed line in fig. A buildup of charge at the sides of the conductors will balance this magnetic influence, producing a measurable. Quantum hall effect by michael stone quantum hall effect by michael stone this book is a compilation of major reprint articles on one of the most intriguing phenomena in modern physics. Generalized longitudinal and hall resistances 2deg patterned into a multirpobe conductor. Together with a detailed introduction by the editor, this volume serves as a stimulating and valuable reference for students and research workers in condensed matter physics and for those with a particle physics background. Introduction to the physics of the quantum hall regime. Institute for theoretical physics events xwrcaldesc. Quantum hall effect in electrondoped black phosphorus.
References home university of waterloo university of. Spin hall effect tip for scanning tunneling microscopy experiments. After the discoverer of the effect the quantity h e. Phenomenology of the quantum spin hall effect one key element that was instrumental in arriving at the theoretical prediction of the qsh state is the prediction of the intrinsic spin hall sh effect in doped semiconductors 15, 16. In recent years, the quantum anomalous hall effect was proposed. This book is a compilation of major reprint articles on one of the most intriguing phenomena in modern physics.
But lets start from the classical hall effect, the famous phenomenon by which a current flows perpendicular to an applied voltage, or vice versa a voltage develops perpendicular to a flowing current. Halfinteger quantum hall effect singlelayer graphene. The quantum hall effect qhe is one of the most fascinating and beautiful phenomena in all branches of physics. The nature of this plateau is still a matter of debate, and active current research. 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. The quantum hall effect is a quantummechanical version of the hall effect, observed in twodimensional electron systems subjected to low temperatures and.
In addition, the hall resistivity is proportional to the magnetic field b and inversely proportional to the carrier density n. Pdf quantum hall effect of haldane model under magnetic field. The landau level structure shows two zeroenergy modes. Many of the physical phenomena observed in quantum materials. 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. 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 emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum hall effect. Chapter 5 will describe the measurements on graphene nems covering the measurement of coe cient of thermal expansion and modal dispersion at low temperatures. 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. Chapter 4 will describe the breakdown of quantum hall state in graphene. The sh effect can be thought of as the spin counterpart to the classical charge hall effect. 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. One of the best known examples is the berry phase m. Hall resistances opens the possibility to combine these resistances to.
Qhe plateaus observed at landau level spectrum with very high cyclotron energy k bilayer novoselov et al, 2005, zhang et al, 2005 manifestation of relativistic dirac electron properties 42x2 spin and valley degeneracy recently. It is a simple consequence of the motion of charged particles in a magnetic. Zerofield quantum anomalous hall metrology as a step. Quantized hall plateaus have been found corresponding to a few even denominator fractions.
This is most evident in a thin flat conductor as illustrated. Quantum hall effects an introduction 1 quantum hall effects an introduction m. Quantum hall effect of haldane model under magnetic field article pdf available in epl europhysics letters 1051 december 20 with 649 reads how we measure reads. Quantum hall effect and topological insulators joint. 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. Conclusion the quantum hall effect, due to a magnetic.
Together with a detailed introduction by the editor, this volume serves as a stimulating and valuable. Physics the quantum hall effect gets more practical. The most important applications of the quantum hall effect qhe are in. Supporting information quantum hall effect in electrondoped black phosphorus field effect transistors fangyuan yang 1,4,5, zuocheng zhang, nai zhou wang2,3,4, guo jun ye2,3,4, wenkai lou6,7, xiaoying zhou 6,7, kenji watanabe 8, takashi taniguchi, kai chang, xian hui chen2,3,4 and yuanbo zhang1,4,5 1state key laboratory of surface physics and department.
In 1880, hall undertook the classical experiment which led to the socalled hall effect. Costato il nuovo cimento b 19711996 volume 109, pages 211 212 1994cite this article. Pdf quantum hall effect a brief introduction researchgate. Ppt quantum hall effects an introduction powerpoint. Right the quantum anomalous hall effect has quantum hall features without an applied field. Yet, there are strong anomalies seen in other properties, such as the surface acoustic wave velocity. Tremendous theoretical and experimental developments are still being made in this sphere. Hsinzon tsai raymond co university of california, berkeley may 4th 2011 the basics of quantum hall effect systematic setup definitions and terminology classical vs. Pepper discovered the quantized hall effect 1, that is, a. Despite jains obvious bias towards promoting his own perspective, i think this book remains the best introduction to the physics of the quantum hall effect. Developments in the quantum hall effect philosophical. Electromechanics of graphene nems in quantum hall regime will be described in chapter 6.
This is a course on the quantum hall effect, given in tifr, mumbai. Nov 10, 2005 indeed, a distinctive halfinteger quantum hall effect has been predicted3,4,5 theoretically, as has the existence of a nonzero berrys phase a geometric quantum phase of the electron. Quantum hall e ect and electromechanics in graphene. Quantum hall effect university of california, berkeley. The noncommutative geometry of the quantum hall effect. Here e is the electron charge whereas h is planck s constant.
The quantum spin hall effect goteborgs universitet. The merger of a noble metal doped with few strong spin orbit coupled. The quantum hall e ect as an electrical resistance standard. The localized states dont contribute to conductance, and the quantization can be found with either. Quantum spin hall effect in twodimensional transition metal dichalcogenides xiaofeng qian,1 junwei liu,2 liang fu,2 ju li1 quantum spin hall qsh effect materials feature edge states that are topologically protected from backscattering.
At charge neutrality, the ensuing ground state is a quantum hall ferromagnet with two filled states of identical spin polarization and an edge dispersion that exhibits two counterpropagating, spinfiltered helical edge channels fig. Experimental observation of the quantum hall effect and berry. So there is still something very strange occurring. In the conventional quantum hall effect, a twodimensional electronic system in the presence of a magnetic field forms metallic conduction paths at. Introduction on the topological aspects of quantum hall effect topological quantum numbers ground state degeneracy chiral edge excitations bulkedge correspondence quasiparticles and fractional and nonabelian statistics recent experiments on the 52 fqh state geometrical aspects of quantum hall effect example. 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. Exchange bias and quantum anomalous nomalous hall effect. The unexpected discovery of the quantum hall effect was the result of basic research on silicon field effect transistors combined with my experience in metrology, the science of measurements. These lecture notes attempt to explain the main ideas of the theory of the quantum hall effect. Pdf this article was done as a term paper for the course. However, the small band gap in materials that have been identified as qsh insulators limits. Clustered states in the fractional quantum hall effect. A topological dirac insulator in a quantum spin hall phase.
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. The quantum hall effects remains one of the most important subjects to have emerged in condensed matter physics over the past 20 years. Course on topology in condensed matter 4,618 views. The quantum hall effect in a periodic potential 14 e. This will provide a useful background for our discussion of the quantum hall e. The fractional quantum hall effect is a variation of the classical hall effect that occurs when a metal is exposed to a magnetic. More recently, the quantum anomalous hall effect was observed for the surface dirac state in magnetic topological insulator thin films 5, 6. To study this phenomenon, scientists apply a large magnetic field to a 2d sheet semiconductor. Quantum spin hall effect in twodimensional transition. We now move on to the quantum hall effect, the mother of all topological effects in condensed matter physics. 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. The quantum anomalous hall effect is a novel manifestation of topological structure in manyelectron systems and may have potential applications in future electronic devices.
It is a simple consequence of the motion of charged particles in a magnetic eld. 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. Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. A typical example is an unusual halfinteger quantum hall effect qhe 2, 3 that is observable even at room temperature in graphene. The quantum hall effect phenomenon can be summarized as follows. 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. The quantum anomalous hall effect is defined as a quantized hall effect realized in a system without an external magnetic field.
The quantum hall effect and the emergence of the value of he2 is found to be understood within five steps. Magnetotransport studies on critical behavior in the quantum hall. The quantum anomalous hall qah effect is a topological phenomenon characterized by quantized hall resistance and zero longitudinal resistance 14. Color online quantum hall effect in graphene as a function of chargecarrier concentration.
This effect is known as the classical hall effect, which is discovered by edwin h. The following link displays the result of a measurement made with a sample of this type gif, 140 kbyte. Different from the conventional quantum hall effect, the qah effect is induced by the interplay between spinorbit coupling soc and magnetic exchange coupling and thus can. The original, classical hall e ect was discovered in 1879 by edwin hall. Ewdin halls hiterto unpublished account, in the hall effect and its applica. Dynamical quantum hall effect in the parameter space pnas. 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. In the quantum anomalous hall effect, the edge states of a ferromagnetically doped topological. Integer quantum hall effect, which is the hall effect quantized into integer times e 2 h e. 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. The strain described by 2 and its crystallographic alignment are shown in fig. Observation of the fractional quantum hall effect in graphene.
Quantum hall effect integer quantum hall effect fractional quantum hall effect conclusion classical hall effect in 1879 by edwin h. Stormer, the fractional quantum hall effect, nobel lecture, december 8, 1998 r. The integer quantum hall effect is derived for a finite rectangular sample and rather general boundary conditions using a kubo formula approach. Helical quantum hall phase in graphene on srtio3 science. If an electric current flows through a conductor in a magnetic field, the magnetic field exerts a transverse force on the moving charge carriers which tends to push them to one side of the conductor. To expand potential application of such a distinct quantum. Quantum hall effect an overview sciencedirect topics. Springerverlag, new york, berlin, heidelberg, london, 1990. This will provide a useful background for our discussion of the quantum hall e ect. Quantum hall effect in a bulk antiferromagnet eumnbi2 with. Under some circumstances of weak but nonzero disorder, quantized hall plateaus appear which are characterized by simple rational fractional. Pdf the complete and the correct interpretation of all of the fractions found in the quantum hall effect of algaasgaas heterostructures is presented. Energy gaps and a zerofield quantum hall effect in. What is an intuitive explanation of the quantum hall effect.
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