quantum hall effect pdf

This is not the way things are supposed to be. quantum Hall effect has been observed in 3D crystals of ZrTe5 [41], providing a platform to study this rare phase of matter where both order parameter and topological number coexist. 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. ��K}\��l�� 0��;� �y�>��k?P@��eh��P�S�K�ꏫ�߄f�,�1�,�D(�S^8��?�� Edge Modes 201 6.1 Laughlin States 201 6.1.1 The View from the Wavefunction 201 6.1.2 The View from Chern-Simons Theory 203 6.1.3 The Chiral Boson 208 6.1.4 Electrons and Quasi-Holes 210 6.1.5 Tunnelling 215 6.2 The Bulk-Boundary Correspondence 217 6.2.1 Recovering the Laughlin Wavefunction 217 6.2.2 Wavefunction for Chern … It gives a brief introduction to both Integer and Fractional Quantum Hall effect. TOBIAS KRAMER1,2, CHRISTOPH KREISBECK1, AND VIKTOR KRUCKL¨ 1 1Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany 2Department of Physics, Harvard University, Cambridge, MA 02138, USA January 21, 2020 Abstract We calculate the local density of states for a relativistic … endobj We show that the Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological semimetals. The quantum Hall effect as an electrical resistance standard 1605 1. Het effect is genoemd naar de onderzoeker Edwin Hall.. De polariteit van de spanning hangt af van de aard van de ladingsdragers. Fractional Quantum Hall Effects in Graphene (C Dean, P Kim, J I A Li and A Young) Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions (S H Simon) Engineering Non-Abelian Quasi-Particles in Fractional Quantum Hall States — A Pedagogical Introduction (A Stern) trailer Search in Amazon.com. 4 0 obj In the SI system the Hall coefficient unit is (volt m)/(amp tesla) or Ωm/T , The Quantum Hall Effects: Discovery, basic theory and open problems K. Das Gupta IIT Bombay Nanoscale Transport 2016, HRI (Feb 24 & 25, 2016) Topics The classical Hall voltage Current flow pattern in a Hall bar (How to solve) Discovery of the Quantum Hall The role of mobility For example, the unit of time, the second, is now deﬁned as the duration of a ﬁxed … The quantum spin Hall state of matter is the cousin of the integer quantum Hall state, and that does not require the application of a large magnetic field. It implies that many electrons, acting in concert, can create new particles having a charge smaller than the charge of any indi-vidual electron. The transverse resistance (ρ x y) takes on quantized values while the longitudinal resistance (ρ x x) vanishes. 1). 0000004024 00000 n startxref 0000002018 00000 n (3) The quantum Hall Effect, as well as ordinary Hall Effect, is characterized by Hall resistance rising (but stepwise) at magnetic field increasing. ��-�i(��%O�'�"i�F��L2�ك�"v��0HBr��j�� v�+b�~�� ?r��uAN ȏ��m}Q�~ �� Ch�$�T�G�Bn�� r3J%��ҝ':�C��D6dE!H4�;�QQ,�BW9ɩ=v�m�`c��;cQN1(�j� 0000002380 00000 n Het kwantum-hall-effect (QHE) is de kwantummechanische versie van het klassieke hall-effect, waargenomen in tweedimensionale elektronsystemen wanneer deze onderworpen worden aan extreem lage temperaturen en sterk magnetische velden.Hierbij ondergaat de hall-geleiding (σ H) bepaalde (kwantum) hall-overgangen en neemt deze gekwantiseerde waarden aan. The … 0000000934 00000 n 554 0 obj<> endobj 0000024651 00000 n Classically, the Hall conductivity 휎 x y —defined as the ratio of the electrical current to the induced transverse voltage—changes smoothly as the field strength increases. Introduction Parallel to the progress made in the physical sciences and in technology, the International System of Units SI has evolved from an artefact-based system to a system mainly based on From the … The first four chapters require only basic quantum mechanics; the final two chapters need techniques from quantum field theory. Quantum Hall effect requires • Two-dimensional electron gas • strong magnetic field • low temperature Note: Room Temp QHE in graphene (Novoselov et al, Science 2007) Plateau and the importance of disorder Broadened LL due to disorder We find that electron-phonon inter-actions … 1D confinemrnt of 2D electron gas (QP contact) e/3 Strong pinch-off weak pinch-off Shot noise weak pinch off,, p=1/3 fitted to eq. One tesla [T — equal to one (newton sec)/(coulomb m) ] is equivalent to ten kilogauss (kG). <> 0000013246 00000 n He discovered, in essence, that the Hall conductance, as a function of the strength of the magnetic field … f��E�9��9+~%��Q�o�'�f��IU��t��Z�e�\�zуC#�k��M�n�[��-�`�E�Ik�P�%�R��5h��Q�ٻL�#L��H��?I�u`�H��]?n�j�GɌV(d!J��r�2s�0&c#�،"�/p��!G�yf�}�۬��KR��=�R Series : Graduate Texts in Contemporary Physics. Originally, it was observed using a metal-oxide-semiconductor transistor (MOSFET). 556 0 obj<>stream �)ܱ�p��MP�s>�9�/F��|� kg �a�x��z xref The basic results are ˙ xx= 0 and ˙ endobj Electrons in the lattice feel the eﬀect of a periodic potential on their motion. The quantum spin Hall state is a state of matter proposed to exist in special, two-dimensional, semiconductors that have a quantized spin-Hall conductance and a vanishing charge-Hall conductance. 5.4.5 E ective Theories of Non-Abelian Quantum Hall States 200 6. The QHE is one of the most fascinating and beautiful phenomena in all branches of physics. The first proposal for the existence of a quantum spin Hall state was developed by Charles Kane and Gene Mele who adapted an earlier model for graphene by F. Duncan M. Haldane which exhibits an integer quantum Hall effect. %PDF-1.5 0000024882 00000 n The quantization of the conductance is in terms of the number of completely filled Landau levels. Topological aspects of the quantum Hall effect, including both the integral and fractional cases, are discussed. L. Wang3,b) 1National Lab of Solid State Microstructures, Department of Physics, Nanjing University, Nanjing 210093, People’s Republic of China This article was done as a term paper for the course PH5107 (Advanced Condensed Matter) at IISER Kolkata. Publisher : Springer-Verlag New York, Year : 1990. Although its extension to three dimensions has been long-sought and inspired theoretical proposals, material candidates have been lacking. %PDF-1.4 %�� The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without external magnetic field. Integer Quantum Hall Effect in Graphene. Het hall-effect is het verschijnsel dat een elektrische spanning optreedt in de dwarsrichting van een stroomdrager als loodrecht op de stroom- en dwarsrichting een magnetisch veld aangelegd wordt. Quantum Hall Effect Emergence in the Fractional Quantum Hall Effect Abstract Student Luis Ramirez The experimental discovery of the fractional quantum hall effect (FQHE) in 1980 was followed by attempts to explain it in terms of the emergence of a novel type of quantum liquid. (Right) The quantum anomalous Hall effect has quantum Hall features without an applied field. 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. :��$7o{�U��k�AyglFl�h-��!Uz��(fm�H�2�" ~yV,#��R�� ^�gl��p�c/��&��hѱ�dp�F3,qzD��8LF{ӳ��Bg��M�5�;�BTi�}��Q��w��s��*gzN c.�݁�Yl�1ĽΔ��*�� R �'�l[�vԃ;�4`��Ӣ��6�&��ԑ;�� \�A/��i�{O(q;SP+2Y��@��#?9cIk��~k�4m��^�#�Uv�芎��=%�z0�4��6����"��Ί'.�,-r�[��g��Q��H%�S��]1��I.��.�^V��LkHQ��8��@[�Mϝ!��gD�e\��lQ�р1k��AfMx\��S�y(��;"`EJ�. Yehuda B. The essence of the quantum spin Hall effect in real materials can be captured in explicit models that are particularly simple to solve. Introduction Parallel to the progress made in the physical sciences and in technology, the International System of Units SI has evolved from an artefact-based system to a system mainly based on fundamental constants and atomic processes during the last century. Abstract. 0000004731 00000 n 0000004101 00000 n Plotting the Hall resistance (essentially the reciprocal of the Hall conductance) of a low-temperature two-dimensional 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 plateau. The phenomena are typically divided into two classes, the integer quantum Hall effect (IQHE) It is one of the most significant phenomena in condensed matter physics because it depends exclusively on fundamental constants and is not affected by irregularities in the semiconductor like impurities or interface effects [2]. %�� The observation of extensive fractional quantum Hall states in graphene brings out the possibility of more accurate quantitative comparisons between theory and experiment than previously possible, because of the negligibility of finite width corrections. 1 The Integer Quantum Hall Effect Johar M. Ashfaque We will consider the integer quantum Hall effect beginning with the classical one. These include the quantized Hall conductance (for both IQHE and FQHE) as a topological invariant, the role of fractional statistics in the FQHE and the ground state degeneracy of the FQH states on a compactified space. Band, Yshai Avishai, in Quantum Mechanics with Applications to Nanotechnology and Information Science, 2013. The integer quantum Hall effect is peculiar due to the zero energy Landau level. The two-dimensional topological insulator mercury telluride can be described by an effective Hamiltonian that is essentially a Taylor expansion in the wave vector k of the interactions between the lowest conduction band and the highest valence band: 2 2. The quantum Hall effect (QHE) is a quantisation of resistance, exhibited by two-dimensional electronic systems, that is defined by the electron charge e and Planck’s constant h. Klaus von KIitzing was awarded the 1985 Nobel prize in physics for this discovery. Quantum Hall effect K. von Klitzing, G. Dorda, M. Pepper (1980) L 2π eBL √1 eB Wave function: Ψ(x,y) = ei2πmx L ψ(y−ym) ψ(y−ym) harmonic oscillator centered at ym = 2πm eBL Density of quantum states with n Landau levels ﬁlled: ρ= neB 2π Quantum Hall conductivity: R−1 = 2nα= n/RK von Klitzing constant: RK = h e2 A. Penin, U of A DESY 2012 – p. 27/34. Transport measurements in the quantum Hall … Tremendous theoretical and experimental developments are still being made in this sphere. ?l�w�j��09��*�TRp��RU�G%Yr��|��o�/��嚳��Z��~Z_0� Landau level substructure and mixing in the relativistic quantum Hall effect. Observation of Quantum Hall effect in an ultra-thin (Bi 0.53Sb 0.47) 2Te 3 film Wenqin Zou,1,a) Wei Wang,2,a) Xufeng Kou,3 Murong Lang,3 Yabin Fan,3 Eun Sang Choi,4 Alexei V. Fedorov,5 Kejie Wang,2 Liang He,2,3,b) Yongbing Xu,2,b) and Kang. We report the realization of a single-layer graphene p-n junction in which carrier type and density in two adjacent regions are locally controlled by electrostatic gating. The Quantum Hall Effect - Landau Levels FIG. The Quantum Hall Effect References: H. Stormer, The Fractional Quantum Hall Effect, Nobel Lecture, December 8, 1998 R.B. The “free-electron quantum gas” model still predicts a hall coeﬃcient of 1/nq and zero magnetoresistance [5]. The beneﬁt of using a quantum approach becomes apparent when it is coupled with a more realistic model of solid matter, speciﬁcally, crystalline. After the discovery of this … found a remarkable behavior in the Hall resistance in 2D electron systems in a Si (100) MOS inversion layer in strong magnetic field. The quantum Hall effect A century later, the Hall effect was revived as a source of astonishing new physics. This book, featuring a collection of articles written by experts and a Foreword by Klaus von Klitzing, the discoverer of quantum Hall effect and winner of … FRACTIONAL QUANTUM HALL EFFECT: DIRAC COMPOSITE FERMIONS The fractional quantum Hall e ect occurs when Landau levels are fractionally lled. … They are also available to download at the arXiv. We consider an infinite graphene sheet with weak disorder that leads to broadening of Landau levels. The electron density could be controlled in a range of 0.7 × 1012 to 3.7 × 1012 per square centimeter by tuning the magnesium content in the barriers and the growth polarity. In this Letter, we develop a theory for the CDW mechanismof 3D quantumHall effect. It rivals superconductivity in its fundamental signi cance as a manifestation of quantum mechanics on macroscopic scales. The fractional quantum Hall effect is a very counter-intuitive physical phenomenon. Xie6,7,8 1Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China <<8ab83acfb9e49a4a82edb8f20a8413d2>]>> 0000007329 00000 n In a MOSFET, the electrons are trapped at the interface between silicon, which is a semiconductor, and silicon oxide, an insulator. endstream endobj 584 0 obj<>/W[1 1 1]/Type/XRef/Index[52 502]>>stream The “free-electron quantum gas” model still predicts a hall coeﬃcient of 1/nq and zero magnetoresistance [5]. 554 31 Lecture 3 - Electromagnetic wave propagation in a metal, plasma frequency, thermal conductivity and thermoelectric effect. Plotting the Hall resistance (essentially the reciprocal of the Hall conductance) of a low-temperature two-dimensional 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 plateau. fluctuations in number of carriers (shot noise) ∆(I2) = 2QI 0∆f! 0000009867 00000 n The quantum Hall e ect (QHE) is one of the most remarkable condensed-matter phenomena dis-covered in the second half of the 20th century. Quantum Hall effect Masatsugu Sei Suzuki Department of Physics, SUNY at Binghamton (Date: May 09, 2013) In 1980, Klitzing et al. <>>> 0000001844 00000 n In 1980 at the Grenoble High Magnetic Field Laboratory in France, Klaus von Klitzing was studying the Hall conductance of a two-dimensional electron gas at very low temperatures. Lecture 4 - The Sommerfeld model for electrons in a metal, the ideal quantum gas of fermions, ground state of the electron gas, the Fermi energy The quantized Hall effect (QHE) was discovered early in February 1980, when Klaus von Klitzing performed a series of experiments at the high-field magnetlaboratories in Grenoble, France, in order to investigate the transport properties of silicon based metal-oxide-semiconductor field-effect-transistors (MOSFET’s), which up to now form the basic building blocks of highest-integrated electrical circuits. of only is Q=e/3 assumed ∆(I2) 64 •No uniform flow of charge carriers ! The integer quantum Hall effect. The quantum Hall effect as an electrical resistance standard 1605 1. 1d and e), which can be probed by scanning tunneling microscopy. 1 0 obj We observed Shubnikov–de Haas oscillation and the quantum Hall effect in a high-mobility two-dimensional electron gas in polar ZnO/Mg x Zn1– x O heterostructures grown by laser molecular beam epitaxy. The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance Rxy exhibits steps that take on the quantized values at certain level The observation of Quantum Hall effect (QHE) in ultra-thin 3D TIs opens the possibility of TI based dissipa … Quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems, and may have potential applications in future electronic devices. Laughlin (1981) B E I … Description. We consider an infinite graphene sheet with weak disorder that leads to broadening of Landau levels. The unique band structure of graphene allows reconfigurable electric-field control of carrier type and density, making graphene an ideal candidate for bipolar nanoelectronics. The nonlinear Hall coefficient is a rank-two pseudotensor, … For example, the integer quantum Hall effect is characterized by a topological integer n(15), which determines the quantized value of the Hall conductance and the number of chiral edge states. The basic experimen- 0000001878 00000 n The spacing of these levels is proportional to the classical cyclotron frequency != eB m. 0000006681 00000 n The full lecture notes are around 230 pages. x x • Insulating gap in the bulk. 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. 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 counter-propagating, spin-filtered helical edge channels (Fig. Lecture 2 - Hall effect, a.c. conductivity. The fractional quantum Hall effect is a variation of the classical Hall effect that occurs when a metal is exposed to a magnetic field. • Quantum Hall effect •Split-gate electrode ! Download PDF Abstract: Unconventional features of relativistic Dirac/Weyl quasi-particles in topological materials are most evidently manifested in the 2D quantum Hall effect (QHE), whose variety is further enriched by their spin and/or valley polarization. The most famous and simplest example is the Laughlin state at = 1=3, for which Laughlin proposed a trial wavefunction with all the correct properties. 3 0 obj <> \"�� I … %%EOF 0000001922 00000 n The beneﬁt of using a quantum approach becomes apparent when it is coupled with a more realistic model of solid matter, speciﬁcally, crystalline. The quantum Hall effect is a phenomenon occurring in a 2-dimensional electron gas. The discovery of the quantum Hall effect (QHE) marked a turning point in condensed-matter physics. 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