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. In this Letter, we develop a theory for the CDW mechanismof 3D quantumHall effect. The quantum Hall effect is usually observed in 2D systems. `8������0�A� � X�)3�׆ i�׼��.��@p�0X�:{�< �T�� � %�e� 0000006042 00000 n The quantum Hall effect as an electrical resistance standard 1605 1. It is invariant under smooth distortions of the Hamiltonian, as long as the energy gap does not collapse. The unique band structure of graphene allows reconfigurable electric-field control of carrier type and density, making graphene an ideal candidate for bipolar nanoelectronics. Topological aspects of the quantum Hall effect, including both the integral and fractional cases, are discussed. kg �a�x�����z The “free-electron quantum gas” model still predicts a hall coefficient of 1/nq and zero magnetoresistance [5]. This is not the way things are supposed to be. 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. Via a ``wormhole'' tunneling assisted by the Weyl nodes, the Fermi arcs at … The quantization of electron orbits in a magnetic field results in equally-spaced energy levels — Landau levels. FRACTIONAL QUANTUM HALL EFFECT: DIRAC COMPOSITE FERMIONS The fractional quantum Hall e ect occurs when Landau levels are fractionally lled. xref of only is Q=e/3 assumed ∆(I2) 64 •No uniform flow of charge carriers ! ISBN : 978-0-387-97177-3,978-1-4612-3350-3. 0000002790 00000 n 4 There is also a fractional quantum Hall effect. 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. trailer The fundamental quantum of Hall resistance is h/e2 =25,813Ω. 0000009867 00000 n After the discovery of this … Series : Graduate Texts in Contemporary Physics. 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 full lecture notes are around 230 pages. The quantum Hall effect as an electrical resistance standard 1605 1. 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. 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. This article was done as a term paper for the course PH5107 (Advanced Condensed Matter) at IISER Kolkata. This value is independent of the material, geometry and microscopic details of the semiconductor. <> 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 3D quantum Hall effect may be realized in other systems with novel surface states. Du,1,4 C.M. ?l�w�j��������09��*�TRp���RU�G%Yr��|���o�/��嚳�����Z���~Z_0� 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. But in high-quality two-dimensional systems such as gallium arsenide quantum wells or … 554 0 obj<> endobj The quantum Hall effect is a phenomenon occurring in a 2-dimensional electron gas. The nonlinear Hall coefficient is a rank-two pseudotensor, … The fractional quantum Hall effect is a variation of the classical Hall effect that occurs when a metal is exposed to a magnetic field. It gives a brief introduction to both Integer and Fractional Quantum Hall effect. I … 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) Description. 1 The Integer Quantum Hall Effect Johar M. Ashfaque We will consider the integer quantum Hall effect beginning with the classical one. 0000007329 00000 n The Quantum Hall Effect by Prange 2nd edition pdf : Pages 473. 1, A and B), similar to those of the quantum spin Hall (QSH) effect … 0000000934 00000 n Band, Yshai Avishai, in Quantum Mechanics with Applications to Nanotechnology and Information Science, 2013. 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. x�bbRg`b``Ń3� ���ţ�1���� 0 �� 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. Yehuda B. 0000004024 00000 n :��$7o{�U��k�AyglFl�h-���!Uz��(fm�H�2�" ~yV,#���R��� � �^�gl��p�c/��&������hѱ�dp�F3,qzD��8ŽLF{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�. This nonlinear Hall effect has a quantum origin arising from the dipole moment of the Berry curvature in momentum space, which generates a net anomalous velocity when the system is in a current-carrying state. 0000007865 00000 n … %%EOF The quantum Hall effect A century later, the Hall effect was revived as a source of astonishing new physics. x�b```b``-d`��� cc`a�8� ����h���}2����D,,[ ��x�P����ޠ�c������2.��e�9�>��'d\o�sKQb��>7���H�N���瑉��%����8|��8��`�b���a����-[D����[e�xt��e=��Vq��``��h Z(&�4:��@�hZX��% ,�"�:�Ҍ��=2��~@Z���"J���`�gi`�������� Electrons in the lattice feel the effect of a periodic potential on their motion. endstream endobj 584 0 obj<>/W[1 1 1]/Type/XRef/Index[52 502]>>stream 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. In the SI system the Hall coefficient unit is (volt m)/(amp tesla) or Ωm/T , The integer quantum Hall effect is peculiar due to the zero energy Landau level. 0000010576 00000 n The Quantum Hall Effect References: H. Stormer, The Fractional Quantum Hall Effect, Nobel Lecture, December 8, 1998 R.B. famous Quantum Hall Effect4. <>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> For example, the unit of time, the second, is now defined as the duration of a fixed … The resistance in longitudinal direction in limits of every plateau, as it was mentioned, falls almost to zero (fig. %���� 0000002018 00000 n 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 endobj The integer Quantum Hall Effect (QHE) was discovered by K. von Klitzing, G. Dorda, and M. Pepper in 1980 [1]. Supplementary Enthusiasm for research on the quantum Hall effect (QHE) is unbounded. 2 0 obj (Right) The quantum anomalous Hall effect has quantum Hall features without an applied field. 0000025192 00000 n ��K}\���l�� 0���;� �y�>��k?P@��eh����P�S�K�ꏫ�߄f�,�1�,�D(�S^8������?�� Theory for the Charge-Density-Wave Mechanism of 3D Quantum Hall Effect Fang Qin (覃昉) ,1,2,3 Shuai Li,1 Z.Z. We find that electron-phonon inter-actions … x x • Insulating gap in the bulk. 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. 0000009140 00000 n The quantum Hall eect (QHE) is one of the most remark- able condensed-matter phenomena discovered in the second half of the 20th century, and our talk is mainly about the integer quantum hall eect. The measurement of the Hall resistance showed that electronic resistance could be defined precisely in terms of fundamental constants, even in a disordered and irregular sample. 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. 0000004731 00000 n 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 In a MOSFET, the electrons are trapped at the interface between silicon, which is a semiconductor, and silicon oxide, an insulator. Ԉ:�_ xlV�"�v�3$�aEQ��ӌ���. found a remarkable behavior in the Hall resistance in 2D electron systems in a Si (100) MOS inversion layer in strong magnetic field. Because of the topological constraint, the Fermi arc at a single surface has an open Fermi surface, which cannot host the quantum Hall effect. The integer quantum Hall effect. 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 … The quantum Hall effect (QHE) refers to a set of phenomena and associated phases of matter found in two-dimensional electron gases subjected to a large perpendicular magnetic field 1 . 0000006681 00000 n 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 The quantization of the conductance is in terms of the number of completely filled Landau levels. They are also available to download at the arXiv. Laughlin, Fractional Quantization, December 8th, 1998 The integral quantum Hall effect was discovered in 1980 by Klaus von The QHE is one of the most fascinating and beautiful phenomena in all branches of physics. Wang,5,1,4 Wenqing Zhang,1,3 Dapeng Yu,1,4 Hai-Zhou Lu,1,4,* and X.C. I. 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. 0000001922 00000 n 0000001878 00000 n Figure 1: (Left) The quantum Hall effect (QHE) occurs in a two-dimensional electron system under a large applied magnetic field. 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 4 0 obj It implies that many electrons, acting in concert, can create new particles having a charge smaller than the charge of any indi-vidual electron. As in the ordinary IQHE, states on the Landau level energy are extended, and at these energies, ρ x x and σ x x are peaked, and σ x y is not quantized. 0000024882 00000 n 0000013246 00000 n Het effect is genoemd naar de onderzoeker Edwin Hall.. De polariteit van de spanning hangt af van de aard van de ladingsdragers. 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. The basic results are ˙ xx= 0 and ˙ 554 31 Landau level substructure and mixing in the relativistic quantum Hall effect. 1). 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. 556 0 obj<>stream 0000005376 00000 n The observation of Quantum Hall effect (QHE) in ultra-thin 3D TIs opens the possibility of TI based dissipa … 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. 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 … Lecture 3 - Electromagnetic wave propagation in a metal, plasma frequency, thermal conductivity and thermoelectric effect. CLASSICAL HALL EFFECT Consider a quasi-2-dimensional sample of conducting material (metal) with length L in the x-direction and width W in the y-direction and negligible extensions in the third direction. The quantum Hall effect was discovered on about the hundredth anniversary of Hall's original work, and the finding was announced in 1980 by von Klitzing, Dorda and Pepper. 0000008544 00000 n x��=�r�r�[�����T�(�B�L�������v,�Tj�#j$1���]+��t7@ �*���h4}�|���5���K����e�m���M���ա�^^=}�^���k���9��>y��u������w,a,�dru��K2�?Kr%SƓB�B�_�?˒;������+��3�������|�1ΪR%�YWI`l��ͳ��|c��?�N��_qC?�~�&�. �)ܱ�p��MP�s>�9�/F��|� Xie6,7,8 1Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China The spacing of these levels is proportional to the classical cyclotron frequency != eB m. 5.4.5 E ective Theories of Non-Abelian Quantum Hall States 200 6. endstream endobj 555 0 obj<>>>/LastModified(D:20041028140746)/MarkInfo<>>> endobj 557 0 obj[558 0 R 559 0 R] endobj 558 0 obj<>>> endobj 559 0 obj<>>> endobj 560 0 obj<>/Font<>/XObject<>/ProcSet[/PDF/Text/ImageC]/ExtGState<>>>/StructParents 0>> endobj 561 0 obj<> endobj 562 0 obj<> endobj 563 0 obj<> endobj 564 0 obj<> endobj 565 0 obj<> endobj 566 0 obj<>stream 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. (Bernevig and Zhang, PRL, 2006) • The QSH state does not break the time reversal symmetry, and can exist without any external magnetic field. 0000024651 00000 n 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. 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. By Richard E. Prange, Richard E. Prange and Steven M. Girvin. 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