The quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems and may have ...Read More. The alternative of measuring the electron’s anomalous magnetic moment does give the fine-structure constant with somewhat greater precision. If you continue browsing the site, you agree to the use of cookies on this website. Recently, the quantum Hall e ect (QHE) has been observed in graphene [1, 2] and studied extensively [3]. Systems of interest are quantum wires, quantum wells, and quantum Hall effect. 30 T). Quantum transport: Transport regimes and mesoscopic quantum transport, Scattering theory of conductance and Landauer-Buttiker formalism, Quantum point contacts, Quantum electronics and selected examples of mesoscopic devices (quantum interference devices). 1. Quantum Spin Hall Effect • The QSH state can be thought of as B eff two copies of QH states, one for each spin component, each seeing the opposite magnetic field. quantities of interest: ... Slide 1 Last modified by: The quantum Hall effect: experimental data¶. Experiments on a nearly spin degenerate two-dimensional electron system reveals unusual hysteretic and relaxational transport in the fractional quantum Hall effect regime. The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without an external magnetic field. The original, classical Hall e ect was discovered in 1879 by Edwin Hall. The “free-electron quantum gas” model still predicts a hall coefficient of 1/nq and zero magnetoresistance [5]. The quantum Hall effect (QHE), which was previously known for two-dimensional (2-D) systems, was predicted to be possible for three-dimensional (3-D) … Charge transport and nanoelectronics. Quantum spin hall effect and topological phase transition in hgte quantum wells. In large B field. CNR NANOTEC - Institute of Nanotechnology The quantum Hall effect is usually observed in 2D systems. σ = ne2/h. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. Slide 2 For the FQHE the experimental conditions in Slide 2 have been very successful. Description: The objective of this educational module is to measure the Hall effect germanium and determine the carrier concentration (and type) as a function of temperature. In real space, the CDW splits the 3D Fermi energy Energy x B B k Charge density wave 2D 3D Energy x y FIG. quantum Hall effect René Meyer Kavli IPMU, Tokyo University August 2, 2013 with Elias Kiritsis, Matthew Lippert and Anastasios Taliotis, 1308.xxxx. Here’s the set-up. Eventually the time dependence will cease. The benefit of using a quantum approach becomes apparent when it is coupled with a more realistic model of solid matter, specifically, crystalline. in equilibrium . (2000) Buhmann (2011) 7. Full Text HTML; Download PDF The full lecture notes are around 230 pages. This will provide a useful background for our discussion of the quantum Hall e ect. Hall Effect Measurement in Germanium (Electrical Transport Option) Prof. Richard Averitt, UC San Diego . Find many great new & used options and get the best deals for Quantum Hall Effects : Field Theoretical Approach and Related Topics by Zyun F. Ezawa (2008, Hardcover) at the best online prices at eBay! Clipping is a handy way to collect important slides you want to go back to later. Suddards, A. Baumgartner, M. Henini and C. J. Mellor, New J. Phys. E k n=1 n=2 n=3 n=4 n=5 n=0 Figure 12: Integer quantum Hall e↵ect Figure 13: Landau levels Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system 1. the fractional quantum Hall effect Roger Mong (California Institute of Technology) University of Virginia Feb 24, 2014. Charge transport and nanoelectronics. !# 0". The feature of a quantum system whereby it exists in several separate quantum states at the same time. Complex effects in condensed-matter systems can often find analogs in cleaner optical systems. Observations of the effect clearly substantiate the theory of quantum mechanics as a whole. Molecular electronics: Donor-Acceptor systems, Nanoscale charge transfer, Electronic properties and transport in molecules and biomolecules; single molecule transistors. Looks like you’ve clipped this slide to already. B • QHE (especially integer) is robust-Hall resistance Rxy is quantized even in very messy samples with dirty edges, not so high mobility. The fine-structure constant α is of dimension 1 (i.e., it is simply a number) and very nearly equal to 1/137. The quantum Hall effect (QHE) and its relation to fundamental physical constants was discovered in 1980 by Klaus von Klitzing for which he received a Nobel prize in 1985. Quantum spin Hall effect in semiconductor quantum wells [Bernevig, Hughes, Zhang, Science 314, 1757 (2006)] Quantum spin Hall effect in 2D topological insulator HgTe quantum well [Koenig et al., Science 318, 766 (2007)] Observation of QSHE in quantum wells [Du et al.,PRL 114 (2015) 096802] Quantum Hall effect of 2D Bloch electrons in a periodic potential Conductivity for finite time Conductivities oscillate in short time. II. This means you're free to copy and share these comics (but not to sell them). Outline Introduction: Modular invariance in FQHE Review: Dyonic Black Holes and Modular Invariance SL(2,Z) and the Real-Analytic Eisenstein Series Via per Arnesano, 73100, Lecce (Italy) If you continue browsing the site, you agree to the use of cookies on this website. around -272°C) and very powerful magnetic fields (max approx. (& FISICA DELLE NANOSTRUTTURE) QUANTUM HALL University of Basel Magnonic Quantum Hall Effect & the Wiedemann-Franz Law Kouki Nakata KN, J. Klinovaja & D. Loss, arXiv:1611.09752 (2016) All the responsibilities of this slide rest with Kouki Nakata (Jan. 2017) See also [KN, P. Simon, and D. Loss: Phys. The quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems and may have potential applications in future electronic devices. Quantum Hall Effect II V xy V xx • Low temperature, observe plateaus: 2DEG’s in GaAs, Si, graphene (!) The first four chapters require only basic quantum mechanics; the final two chapters need techniques from quantum field theory. About this Attention Score In the top 5% of all research outputs scored by Altmetric. Two groups have now observed quantum anomalous Hall effect in intrinsically magnetic … These conditions are favorable for the Integer Quantum Hall Effect (IQHE). Germanium is an indirect bandgap semiconductor with a room temperature Quantum Hall effect integer Laughlins argument L B x y V I r m r m-1 shift by one ''trajectory'' net shift of 1 el from outer to inner edge potential energy fixed current electromagnetic energy per filled Landau level energy argument moving electron against electric potential (V) inductive energy David Tong: Lectures on the Quantum Hall Effect. Altmetric Badge. The results are so precise that the standard for the measurement of electrical resistance uses the quantum Hall effect, which also underpins the … 2-D system, perpendicular magnetic field. See our User Agreement and Privacy Policy. The doping, however, introduces inhomogeneity, reducing the temperature at which the effect occurs. 6) Statistics calculation . It is the "coupling constant" or measure of the strength of the electromagnetic force that governs how electrically charged elementary particles (e.g., electron, muon) and light (photons) interact. At the end of the 1970’s researchers used extremely low temperatures (only a few degrees from absolute zero, i.e. Customer Code: Creating a Company Customers Love, Be A Great Product Leader (Amplify, Oct 2019), Trillion Dollar Coach Book (Bill Campbell), No public clipboards found for this slide. Quantized values of Hall Conductivity. The extracted quantum mobility is about five times smaller than the Hall and field effect mobilities and characterizes the effective broadening of the Landau levels due to disorder. In 2005, Kane and Mele discovered in graphene a topological phase known as the quantum spin Hall effect . We’ll start these lectures by reviewing the underlying physics of the Hall e ect. 1.3 Quantum Hall E↵ects 10 1.3.1 Integer Quantum Hall E↵ect 11 1.3.2 Fractional Quantum Hall E↵ect 13 1.4 Landau Levels 14 1.4.1 Landau Gauge 18 1.4.2 Turning on an Electric Field 21 1.4.3 Symmetric Gauge 22 1.5 Berry Phase 27 1.5.1 Abelian Berry Phase and Berry Connection 28 1.5.2 An Example: A Spin in a Magnetic Field 32 Collaborators Michael Zaletel UC Berkeley (Stanford/Station Q) Frank Pollmann Max Planck (Dresden) Michael Zaletel, RM, PRB 86, 245305 [arXiv:1208.4862] If you continue browsing the site, you agree to the use of cookies on this website. balances the Lorentz force. In the presence of a magnetic field, the electron may exist in two possible spin states, usually referred to as spin up and spin down. 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. Does not depend on material or impurities or geometry. For a short introduction, see also N. Read, Physics Today, July 2012, p. 38 More details. EFFECT You can change your ad preferences anytime. Dip. Now customize the name of a clipboard to store your clips. Edwin Herbert Hall (1879): discovery of the Hall effect. Fractal Quantum Hall Effect (-3, 1) R xx (kW) 0 15 Temperature Dependence Fractal Gap Size 83 K . The fundamental quantum of Hall resistance is h/e2 =25,813Ω. Quantum anomalous Hall effect—the appearance of quantized Hall conductance at zero magnetic field—has been observed in thin films of the topological insulator Bi2Se3 doped with magnetic atoms. See our Privacy Policy and User Agreement for details. In the original experiment, silver atoms were sent through a spatially varying magnetic field, which deflected them before they struck a detector screen, such as a glass slide. Introductory idea of integral & fractional quantum hall effect and by imposing the idea of composite fermions showing the existence of fractional charge. Question: Try To Explain Briefly But Clearly From Both An Experimental And Quantum Mechanics Point Of View The "Quantum Hall Effect" This question hasn't been answered yet Ask an expert. Behavior depends on the Fermi energy. The 3D quantum Hall effect may be realized in other systems with novel surface states. The Stern–Gerlach experiment demonstrated that the spatial orientation of angular momentum is quantized.Thus an atomic-scale system was shown to have intrinsically quantum properties. Quantum Hall effect, quantum transport Y. Ji et al., Nature 422 (2003) 415. In this lab we will only be concerned with the Hall coefficient. Quantum Hall Effect. JNVU (Department of Physics). Jesse Noffsinger ; Group Meeting Talk (As required by the Governor of the State of California) April 17, 2007; 2 Classical Hall Effect Experimental Values B Metal RH (-1/nec) Li 0.8 Na 1.2 Rb 1.0 Ag 1.3 Be -0.2 Ex, jx VH Ey - - - - - - - - - - - - - - - - - - … 4) Fractional quantum Hall effect . j. y = 0 → the transverse field (the Hall field) E. y. due to the accumulated charges . and electromechanical properties in a resonator geometry. The conventional quantum Hall effect is a particular example of the general relation if one views the electric field as a rate of change of the vector potential. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. Even in the absence of an external magnetic field, electronic bands with topological properties are possible when the spin-orbit coupling of electrons is sufficiently strong . The transition between the spin-polarized (with fill fraction ν = 1/3) and spin-unpolarized (ν = 2/5) states is accompanied by a complicated series of hysteresis loops reminiscent of a classical ferromagnet. x x • Insulating gap in the bulk. Introduzione Nanoscienze e Nanotecnologie. It is a simple consequence of the motion of charged particles in a magnetic eld. The quantum Hall effect can also be regarded as an appealingly straightforward precision measurement of the fine-structure constant, e 2 /ħc, yielding a value of 1/137.0360 0300(270). SUBMITTED BY: VISHAL KUMAR JANGID,M.Sc(Final) 2016-17 B 92, 134425 (2015)] Figure 1: (Left) The quantum Hall effect (QHE) occurs in a two-dimensional electron system under a large applied magnetic field. See our User Agreement and Privacy Policy. Looks like you’ve clipped this slide to already. Aharonov-Bohm effect in graphene Fabry Pérot quantum Hall Interferometers Yuval Ronen 1† , Thomas Werkmeister 2† , Danial Najafabadi 1 , Andrew T. 1Pierce 1 , Laurel E. Anderson , Young J. Shin 3 , Si Young Lee 4 , 4Young Hee Lee , Bobae Johnson 1 , Kenji Watanabe 5 , Takashi Taniguchi 6 , The spin Hall effect in a quantum gas M. C. Beeler*, R. A. Williams, K. Jimenez-Garcia, L. J. LeBlanc, A. R. Perry, I. This is a course on the quantum Hall effect, given in TIFR, Mumbai. It represents good example of physical systems where quantization effect could be observed microscopically as a result of the interplay of the topology, interactions of electron with magnetic field, electron-electron interactions, and disorder. Each Landau level can accommodate a large, but finite number of electrons. di Matematica e Fisica, Università del Salento, Tunneling: Scanning tunneling microscopy and spectroscopy (and wavefunction mapping in nanostructures and molecules), Nanoelectronic devices based on tunneling, Coulomb blockade, Single electron transistors, Kondo effect. This work is licensed under a Creative Commons Attribution-NonCommercial 2.5 License. giuseppe.maruccio@unisalento.it Instead, a completely unexpected result was measured for the first time by Klaus von Klitzing. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details. famous Quantum Hall Effect4. The quantum Hall effect continues to reveal its secrets to mathematicians and physicists. Overview of attention for news story in Nature. 0" from states with electron character ! The quantum Hall effect is a well-accepted theory in physics describing the behavior of electrons within a magnetic field at extremely low temperatures. 1. The quantum numbers to be manipulated are the spin index, valley index, and layer index in multilayer systems, measured at low temperatures and high magnetic fields where Luttinger liquids, quantum Hall ferromagnets, and multi-valley systems can be probed. Quantum Hall Effect. The quantum anomalous Hall (QAH) effect, considered as a quantized version of anomalous Hall effect discovered in 1881 , has been theoretically proposed for magnetic topological insulators (TIs) [8–13], where the ferromagnetic ordering and spin–orbit coupling (SOC) are sufficiently strong that they can give rise to a topologically non-trivial phase with a finite Chern number. Acknowledgement Funding: Christoph Brüne, Andreas Roth, Hartmut Buhmann, Ewelina M Hankiewicz, Laurens W Molenkamp, Joseph Maciejko, Xiao-Liang Qi, and Shou-Cheng Zhang. The transverse resistance (ρ x y) takes on quantized values while the longitudinal resistance (ρ x x) vanishes. 7) Topological Quantum Computation . The carrier Hall mobility of hexagonal boron nitride (hBN) encapsulated InSe flakes can be up to 5000 cm 2 V −1 s −1 at 1.5 K, enabling to observe the quantum Hall effect in a synthesized van der Waals semiconductor. 8) Conclusion . group 3 Quantum Hall Effects: 2D electron gas (2DEG) in magnetic field, Landau levels, de Haas- van Alphen and Shubnikov-de Haas Effects, integer and fractional quantum Hall effects, Spin Hall Effect, Anomalous Hall effect and Topological Insulators. Introduction. The fractional quantum Hall effect has been one of the most active areas of research in quantum condensed matter physics for nearly four decades, serving as a paradigm for unexpected and exotic emergent behavior arising from interactions. Quantum Hall Effect: 2D electron gas (2DEG) in magnetic field, Landau levels, de Haas-van Alphen and Shubnikov-de Haas Effects, integer and fractional quantum Hall effects, Spin Hall Effect. Free shipping for many products! Quantized Landau Levels We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. NANOELETTRONICA The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without an external magnetic field. Title: Quantum Hall Effect 1 Quantum Hall Effect. Typical experimental data looks like this (taken from M.E. Electronic properties of nanomaterials, Customer Code: Creating a Company Customers Love, Be A Great Product Leader (Amplify, Oct 2019), Trillion Dollar Coach Book (Bill Campbell), No public clipboards found for this slide, II_Quantum Hall Effects&Quantum Transport. Spin polarization of the quantum spin hall edge states. We illustrate our findings by analyzing the response of interacting spin chains to a rotating magnetic field. For example, electrons possess a quantum feature called spin, a type of intrinsic angular momentum. Quantum Hall Effect in Vanishing Magnetic Fields Wei Pan Sandia National Labs Sandia is a multi-mission laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. Science, 314(5806):1757–1761, 2006. Clipping is a handy way to collect important slides you want to go back to later. We studied the breakdown of the quantum Hall state in graphene with two-fold motivation. Each electron, until it is measured, will Quantum Hall state • simplest example: noninteracting electrons filling n Landau levels (interger QH effect) • Fractional QH effect: much more complicated theory (Laughlin) • gapped, no low-energy degree of freedom • The effective action can be expanded in polynomials of external fields • To lowest order: Chern-Simons action S = 4 d3 xµ A µ A encodes Hall conductivity B. Spielman Joint Quantum Institute, National Institute of Standards and Technology and Department of Physics, University of Maryland, Gaithersburg, MD 20899, USA Introduction to spin Hall effect w Because of the topological constraint, the Fermi arc at a single surface has an open Fermi surface, which cannot host the quantum Hall effect. In this 3D quantum Hall effect, the edge states are located at only one edge on the top surface and at the opposite edge on the bottom surface (green and orange arrowed lines in Fig. Hall effect and magnetoresistance. world of 2d electrons is exciting modulation doping – high purity enables ‘ballistic transport’ – easy electrostatic control gates close to surface – unique excitations (e.g., fractional statistics) Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. The transverse resistance is precisely quantized at h / … 1d and e), which can be probed by scanning tunneling microscopy. SUBMITTED TO: Prof. R.S SINGH The essence of the quantum spin Hall effect in real materials can be captured in explicit models that are particularly simple to solve. the Lorentz force. The main conditions for this phenomenon to be observed are extremely low temperatures and the presence of a s… Current advances: The fine-structure constant and quantum Hall effect . Note that there will be a Landau level at zero energy that separates states with hole character !!" Hall performed his experiments at room temperature and with moderate magnetic fields of less than one tesla (T). 1. Giuseppe Maruccio The Quantum Hall effect (QHE) is the observation of the Hall effect in a two-dimensional electron gas system (2DEG) such as graphene and MOSFETs. The anomalous integer quantum Hall effect In the presence of disorder, Landau levels get broad-ened and mobility edges appear !Laughlin, 1981". Scanning Probe Microscopy M. A. Topinka et al., Science 289 (2000) 2323. Giuseppe Maruccio In the SI system the Hall coefficient unit is (volt m)/(amp tesla) or Ωm/T , We show that the Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological semimetals. Manabu Machida, Naomichi Hatano, and Jun … (Right) The quantum anomalous Hall effect has quantum Hall features without an applied field. Today: Device Characterization by low-temperature magneto-transport Hall effect measurements in organic semiconductors Edward Burt Driscoll Paralleling the use of Hall effect measurements used in inorganic conductors … Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. Enormous Precision, Used as a standard of resistance. Rev. (Bernevig and Zhang, PRL, 2006) • The QSH state does not break the time reversal symmetry, and can exist without any external magnetic field. Firstly, in graphene the cyclotron gaps are unequally spaced and are much Fig. 3D quantum Hall effect relies on the charge density wave (CDW), which may gap the 1D Landau band so that the bulk is insulating. 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. High Attention Score compared to … 4 There is also a fractional quantum Hall effect. Hall Effect E. Hall H R H 1881 Anomalous HE H R H H R H h/e2 h/2e2 1980 Integer QHE (Si) 1982 Fractional QHE (GaAs) K. von Klitzing B. Laughlin H. Stormer D. Tsui 1985 1998 IQHE FQHE 2010 Half-integer QHE (graphene) A. Geim K. Novoselov From Hall Effect to Quantum Hall Effects (QHE) Quantum Anomalous Hall Effect? Try to explain briefly but clearly from both an experimental and quantum mechanics point of view the "Quantum Hall Effect" Quantum Hall effect • quantized states of Hall resistance appear • attributed to spin density transitions • Landau levels Schön et al. Magnonic Quantum Hall Effect & the Wiedemann-Franz Law 1. Via a ``wormhole'' tunneling assisted by the Weyl nodes, the Fermi arcs at … I. Interpreting recent experimental results of light interactions with matter shows that the classical Maxwell theory of light has intrinsic quantum spin Hall effect properties even in free space. Magnetism, when combined with an unconventional electronic band structure, can give rise to forefront electronic properties such as the quantum anomalous Hall effect, axion electrodynamics, and Majorana fermions. Now customize the name of a clipboard to store your clips. QUANTUM HALL EFFECT SUBMITTED TO: Prof. R.S SINGH SUBMITTED BY: VISHAL KUMAR JANGID,M.Sc(Final) 2016-17 JNVU (Department of Physics) Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. 5) Conformal field theory constructions . A quantum twist on classical optics. Single Layer Graphene Hofstadter’s Butterfly R xx (Ohm) R xy (Ohm) B 1/2-6 -4 -2 +2 +4 Similar physics is observed in single layer graphene on hBN R xx R xy. Our observed magnetotransport features are comparable to those observed for typical exfoliated graphene samples [ 36 ] and high-quality CVD-graphene samples [ 40 , 41 ]. The experimental data for the Hall resistivity shows a number of plateaux labelled by an integer ⌫.Meanwhile,theenergyspectrumforms Landau levels, also labelled by an integer. You can change your ad preferences anytime. • mostly used in inorganic semiconductors • at low temperatures, graphene is shown to behave according to the 2-D quantum Hall effect in its ground state Kane and Mele (2005) 2005: Quantum Spin Hall Effect/Z 2 topological insulator Bernevig and Zhang, 2006 helical)edge)states Energy)spectrum) (for)one)edge)) Experimental observation of HgTe TI Topological phases of matter: from the quantum Hall effect to spin liquids The understanding of collective quantum phenomena in condensed-matter systems has been a central topic in physics, since the beginning of the 20th century and the discovery of superconductivity and superfluidity. J. Weis, in Encyclopedia of Condensed Matter Physics, 2005. We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. Will be a Landau level can accommodate a large, but finite number of.! We use your LinkedIn profile and activity data to personalize ads and to show you more relevant.. Can accommodate a large, but finite number of electrons within a field... These conditions are favorable for the Integer quantum Hall effect reducing the at!... Read more New J. Phys • Landau levels Schön et al the effect occurs Giuseppe Dip! Slides you want to go back to later Fermi arcs can give to! Of interest are quantum wires, quantum transport y. Ji et al., Nature 422 ( 2003 415. Improve functionality and performance, and quantum Hall effect is a course on the anomalous! ; Download PDF Title: quantum Hall effect ( IQHE ) 2.5 License four chapters require only basic quantum ;. Final two chapters need techniques from quantum field theory i.e., it simply..., A. Baumgartner, M. Henini and C. J. Mellor, New J. Phys often find analogs in optical! Only a few degrees from absolute zero, i.e in slide 2 have been very successful is of dimension (... Scored by Altmetric need techniques from quantum field theory effect realized in other systems with surface! Integer quantum Hall effect ( IQHE ) electrons possess a quantum feature called spin, a of. Nearly equal to 1/137 of Virginia Feb 24, 2014 quantum hall effect slideshare all research outputs scored by Altmetric Richard,. Transverse field ( the Hall e ect and performance, and to show you more relevant ads Germanium is indirect... Topinka et al., Nature 422 ( 2003 ) 415 electrons within a magnetic eld chains to a distinctive quantum! This means you 're free to copy and share these comics ( but to. ; Download PDF Title: quantum Hall features without an external magnetic field LinkedIn profile and activity data to ads! Science 289 ( 2000 ) 2323 that the Fermi arcs can give rise to a rotating magnetic.... Name of a clipboard to store your clips agree to the accumulated.. Tunneling microscopy you 're free to copy and share these comics ( but not to sell them ) somewhat Precision! Functionality and performance, and quantum Hall effect is defined as a standard resistance! • Landau levels Schön et al have been very successful constant and quantum Hall effect realized in other systems novel... Maruccio Dip -272°C ) and very powerful magnetic fields ( max approx of quantum hall effect slideshare 1 i.e.! Fermions showing the existence of fractional charge this lab we will only be concerned with Hall... Commons Attribution-NonCommercial 2.5 License and transport in molecules and biomolecules ; single molecule transistors,. Is h/e2 =25,813Ω 1879 ): discovery of the motion of charged particles in a eld... Systems of interest are quantum wires, quantum transport y. Ji et al., Science 289 2000... Under a Creative Commons Attribution-NonCommercial 2.5 License data looks like this ( taken from M.E spin Hall effect, in! Biomolecules ; single molecule transistors observation of the quantum anomalous Hall effect has quantum Hall state graphene! Electrons within a magnetic eld ρ x x ) vanishes experimental data looks like (... Of integral & fractional quantum Hall effect may be realized in a system without an external magnetic.! By Klaus von Klitzing these lectures by reviewing the underlying physics of the quantum Hall effect Mong...