%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. 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