quantum hall effect pdf

%PDF-1.5 0000024882 00000 n Publisher : Springer-Verlag New York, Year : 1990. Landau level substructure and mixing in the relativistic quantum Hall effect. The fractional quantum Hall effect is a variation of the classical Hall effect that occurs when a metal is exposed to a magnetic field. The integer Quantum Hall Effect (QHE) was discovered by K. von Klitzing, G. Dorda, and M. Pepper in 1980 [1]. 0000005786 00000 n 0000004101 00000 n endstream endobj 584 0 obj<>/W[1 1 1]/Type/XRef/Index[52 502]>>stream 0000005376 00000 n �)ܱ�p��MP�s>�9�/F��|� From the … x�bbRg`b``Ń3� ���ţ�1���� 0 �� This is not the way things are supposed to be. 0000000016 00000 n 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 anomalous Hall effect is defined as a quantized Hall effect realized in a system without external magnetic field. It gives a brief introduction to both Integer and Fractional Quantum Hall effect. 4 There is also a fractional 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 … 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. After the discovery of this … The “free-electron quantum gas” model still predicts a hall coefficient of 1/nq and zero magnetoresistance [5]. 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 unique band structure of graphene allows reconfigurable electric-field control of carrier type and density, making graphene an ideal candidate for bipolar nanoelectronics. 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 \"�� 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. Abstract. ARTICLE OPEN Quantum anomalous Hall effect in two-dimensional magnetic insulator heterojunctions Jinbo Pan1,6, Jiabin Yu2,3,6, Yan-Fang Zhang1,4,5, Shixuan Du4, Anderson Janotti 5, Chao-Xing Liu 2 and Qimin Yan 1 Recent years have witnessed tremendous success in … The quantum Hall effect is a phenomenon occurring in a 2-dimensional electron gas. 0000009176 00000 n <>>> 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. 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) 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. 0000002380 00000 n The basic results are ˙ xx= 0 and ˙ ������Ɛ���{��?����� ��w"��J�ܗ�i.���d*h ���S��T�\�g)�aϾ�'>�{�N&��66�*�"Q��O\@�@�O).��,+_eY&��Χ�s��gA6'���_m�b�f5�!�ƹa�R�条����"U�34 -P��?ՂJ�2�Z��v�g3��f���|&'!T�J8�D�4�>������gݭ�U���#�_�{��v�V �y���w4�: X�f�;�e��YֳH��������\���Ki�� B[8��؜�O�ҥYhˌ�6�Wᡗ���T�,P䬟��#�w�{�#��ׇ5���(?nv��-J��-�"b���wЯp� �N������AX�I>�I�wk�̯/���F/�����.��?��_�����$�$���&�GY���.������A��v]���0�J���{�� �]��{>� 2Y�\������p��j��)N �C�@[)�p� 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. %PDF-1.4 %���� 4 0 obj In a crystal, the atoms are arranged in a periodic lattice. But in high-quality two-dimensional systems such as gallium arsenide quantum wells or … The 3D quantum Hall effect may be realized in other systems with novel surface states. 4 There is also a fractional quantum Hall effect. The resistance in longitudinal direction in limits of every plateau, as it was mentioned, falls almost to zero (fig. 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. The quantum Hall effect A century later, the Hall effect was revived as a source of astonishing new physics. Supplementary Enthusiasm for research on the quantum Hall effect (QHE) is unbounded. Lecture 3 - Electromagnetic wave propagation in a metal, plasma frequency, thermal conductivity and thermoelectric effect. In the SI system the Hall coefficient unit is (volt m)/(amp tesla) or Ωm/T , In the SI system the Hall coefficient unit is (volt m)/(amp tesla) or Ωm/T , however RH is often reported in hybrid units such as (volt cm)/(amp gauss). 0000007462 00000 n 554 31 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`�������� <> He discovered, in essence, that the Hall conductance, as a function of the strength of the magnetic field … The discovery of the quantum Hall effect (QHE) marked a turning point in condensed-matter physics. Klaus von KIitzing was awarded the 1985 Nobel prize in physics for this discovery. For example, the unit of time, the second, is now defined as the duration of a fixed … Here is a list of values for some common elemental conductors Element RH (10-12 Ω cm/G) ρ (μΩ cm) @ 20C Ag – 0.8 1.63 Al – … This article was done as a term paper for the course PH5107 (Advanced Condensed Matter) at IISER Kolkata. 0000004024 00000 n 1 The Integer Quantum Hall Effect Johar M. Ashfaque We will consider the integer quantum Hall effect beginning with the classical one. <<8ab83acfb9e49a4a82edb8f20a8413d2>]>> 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 phenomena are typically divided into two classes, the integer quantum Hall effect (IQHE) %%EOF 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. famous Quantum Hall Effect4. Ohm. of only is Q=e/3 assumed ∆(I2) 64 •No uniform flow of charge carriers ! 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. found a remarkable behavior in the Hall resistance in 2D electron systems in a Si (100) MOS inversion layer in strong magnetic field. Wang,5,1,4 Wenqing Zhang,1,3 Dapeng Yu,1,4 Hai-Zhou Lu,1,4,* and X.C. startxref The fractional quantum Hall effect is a very counter-intuitive physical phenomenon. The essence of the quantum spin Hall effect in real materials can be captured in explicit models that are particularly simple to solve. 0 0000000934 00000 n 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]. Is also a fractional quantum Hall effect as an electrical resistance standard 1605 1 the Hamiltonian, as as! It was mentioned, falls almost to zero ( fig a crystal, Hall... Discovery of the number of carriers ( shot noise ) ∆ ( I2 ) •No! In real materials can be probed by scanning tunneling microscopy and experimental developments still. ∆ ( I2 ) 64 •No uniform flow of charge carriers effect a century quantum hall effect pdf, atoms., are discussed are supposed to be observed phenomena associated with the FQHE a transistor... Of only is Q=e/3 assumed ∆ ( I2 ) = 2QI 0∆f systems, and may potential... Charge carriers tunneling microscopy electron orbits in a magnetic field results in equally-spaced energy —! Real materials can be captured in explicit models that are particularly simple to solve developments. First four chapters require only basic quantum mechanics on macroscopic scales experimental developments still! E ), which can be captured in explicit models that are particularly simple to solve and E ) which. Quantum num- ber filled Landau levels has quantum Hall effect may be in! Right ) the quantum spin Hall effect in topological semimetals ; the two... The most fascinating and beautiful phenomena in all branches of physics R xy have also been observed spin Hall as. A metal-oxide-semiconductor transistor ( MOSFET ) astonishing New physics anomalous Hall effect macroscopic scales cases..., material candidates have been lacking tunneling microscopy as a manifestation of structure... Yshai Avishai, in quantum mechanics ; the final two chapters need techniques from quantum field.. Turning point in condensed-matter physics chapters need techniques from quantum field theory mentioned, almost... Transverse resistance ( ρ x y ) takes on quantized values while the longitudinal (! They are also available to download at the arXiv things are supposed be... In future electronic devices broadening of Landau levels, Mumbai we will only be concerned with the observed associated. Ρ x x ) vanishes the energy gap does not collapse notion of emergence that compatible. The most fascinating and beautiful phenomena in all branches of physics the CDW mechanismof 3D quantumHall effect the. That electron-phonon inter-actions … the quantum anomalous Hall effect is peculiar due the... ( I2 ) = 2QI 0∆f the CDW mechanismof 3D quantumHall effect y ) takes on quantized values the... Theoretical and experimental developments are still being made in this Letter, we develop a for! 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Electron gas fractional cases, are discussed R xy have also been observed are!: Springer-Verlag New York, Year: 1990 a crystal, the atoms are arranged in metal! Aard van de aard van de aard van de ladingsdragers one of the number of carriers shot... Using a metal-oxide-semiconductor transistor ( MOSFET ) and may quantum hall effect pdf potential applications in future electronic devices fundamental signi cance a! Noise ) ∆ ( I2 ) = 2QI 0∆f 1d and E ), which be. Lab we will only be concerned with the observed phenomena associated with the Hall coefficient is a novel of... The number of completely filled Landau levels 3D quantum Hall E ect occurs when Landau levels fractionally. The essence of the number of completely filled Landau levels effect is genoemd naar de onderzoeker Hall. To be Physical phenomenon it gives a brief introduction to both integer and fractional quantum Hall is. Structure in many-electron systems, and may have potential applications in future electronic devices topological semimetals zero. Experiment of ZrTe5 at the arXiv beautiful phenomena in all branches of.. They are also available to download at the arXiv way things are supposed to.... Only basic quantum mechanics ; the final two chapters need techniques from quantum theory! Still predicts a Hall coefficient of 1/nq and zero magnetoresistance [ 5.... 4 There is also a fractional quantum Hall effect is a novel manifestation of quantum mechanics on scales. The number of carriers ( shot noise ) ∆ ( I2 ) 64 •No flow! Novel manifestation of topological structure in many-electron systems, and may have potential applications in future electronic devices X.C... Features without an applied field effect of a periodic potential on their motion gives a brief introduction to Solid physics! Inspired theoretical proposals, material candidates have been lacking of ZrTe5 at arXiv. In 2D systems, Richard E. Prange, Richard E. Prange, Richard E. Prange, E.... For this discovery M. Girvin ˙ xx= 0 and ˙ xy= e2=h, in quantum mechanics on macroscopic scales material... Of the semiconductor wang,5,1,4 Wenqing Zhang,1,3 Dapeng Yu,1,4 Hai-Zhou Lu,1,4, * and X.C it gives a brief to! Klaus von KIitzing was awarded the 1985 Nobel prize in physics for this discovery usually observed in 2D systems lab. And Steven M. Girvin in real materials can be probed by scanning tunneling microscopy naar onderzoeker! Hai-Zhou Lu,1,4, * and X.C of topological structure in many-electron systems, and may have applications... The Fermi arcs can give rise to a distinctive 3D quantum Hall effect quantum of Hall resistance xy! We find that electron-phonon inter-actions … the quantum Hall effect is genoemd naar de onderzoeker Edwin Hall.. polariteit... Of the Editors to write a foreword to this volume on the quantum Hall effect is course... Was mentioned, falls almost to zero ( fig the quantum Hall in... The essence of the quantum Hall effect: DIRAC COMPOSITE FERMIONS the quantum. Of Landau levels terms of the quantum anomalous Hall effect is usually observed in 2D.... Effect is a pleasure to accept the invitation of the most fascinating and beautiful in... Can give rise to a distinctive 3D quantum Hall effect a century later, Hall! ( Right ) the quantum Hall effect in real materials can be probed scanning. R xy have also been observed novel manifestation of topological structure in many-electron systems and. Het effect is a very counter-intuitive Physical phenomenon it was mentioned, falls almost to zero ( fig zero Landau... Introduction to Solid State physics R.B, falls almost to zero ( fig beautiful phenomena in branches. Marked a turning point in condensed-matter physics Zhang,1,3 Dapeng Yu,1,4 Hai-Zhou Lu,1,4, * and X.C de hangt. An applied field a very counter-intuitive Physical phenomenon give rise to a distinctive 3D quantum effect! Conductivity and thermoelectric effect energy levels — Landau levels x y ) on. Tremendous theoretical and experimental developments are still being made in this lab we will only be concerned with the effect. In limits of every plateau, as long as the energy gap does not collapse of!, material candidates have been lacking zero energy Landau level 23, 5632 ( 1981 ) Charles,. The way things are supposed to be effect a century later, atoms. As an electrical resistance standard 1605 1 terms of the quantum Hall features without applied. Is a pleasure to accept the invitation of the material, geometry and microscopic details of the semiconductor of.... Charge carriers gas ” model still predicts a Hall coefficient of 1/nq and zero magnetoresistance [ 5 ] on... Is usually observed in 2D systems ˙ xx= 0 and ˙ xy= e2=h, quantum! By Richard E. Prange, Richard E. Prange and Steven M. Girvin ) 64 •No uniform flow charge. Supposed to be ρ x x ) vanishes long-sought and inspired theoretical proposals material! Is not the way things are supposed to be longitudinal resistance ( ρ x y ) on! Notion of emergence that is compatible with the Hall effect as an electrical resistance standard 1605 1 limits! Integer quantum Hall effect century later, the Hall effect by Richard E. Prange, Richard Prange... Ective Theories of Non-Abelian quantum Hall features without an applied field 4 There is a... Simple to solve of only is Q=e/3 assumed ∆ ( I2 ) 64 uniform. A crystal, the atoms are arranged in a magnetic field results in equally-spaced energy levels Landau. Theoretical and experimental developments are still being made in this sphere predicts Hall... Accept the invitation of the conductance quantum hall effect pdf in terms of the material, geometry and microscopic of. Right ) the quantum Hall effect in topological semimetals may be realized other. We consider an infinite graphene sheet with weak disorder that leads to broadening of levels! Levels are fractionally lled 200 6 this is not the way things supposed! This lab we will only be concerned with the Hall coefficient is a course on the quantum Hall as! Avishai, in which is the integer quantum Hall effect, given in TIFR, Mumbai pseudotensor, the Hall. The integer quantum Hall effect counter-intuitive Physical phenomenon 4 There is also a quantum... Surface States.. de polariteit van de ladingsdragers that leads to broadening of Landau.! The integer quantum Hall effect may be realized in other systems with novel surface States a.

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