Transport measurements in the quantum Hall … The spacing of these levels is proportional to the classical cyclotron frequency != eB m. FRACTIONAL QUANTUM HALL EFFECT: DIRAC COMPOSITE FERMIONS The fractional quantum Hall e ect occurs when Landau levels are fractionally lled. The integer quantum Hall effect is peculiar due to the zero energy Landau level. 0000009140 00000 n I. Supplementary Enthusiasm for research on the quantum Hall effect (QHE) is unbounded. 0000004731 00000 n ������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� 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. Gauge invariance argument R.B. Integer Quantum Hall Effect in Graphene. 0000024651 00000 n 0000002380 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. Quantum Hall effect Masatsugu Sei Suzuki Department of Physics, SUNY at Binghamton (Date: May 09, 2013) In 1980, Klitzing et al. The quantization of the conductance is in terms of the number of completely filled Landau levels. 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. 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 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 essence of the quantum spin Hall effect in real materials can be captured in explicit models that are particularly simple to solve. • Quantum Hall effect •Split-gate electrode ! Theory for the Charge-Density-Wave Mechanism of 3D Quantum Hall Effect Fang Qin (覃昉) ,1,2,3 Shuai Li,1 Z.Z. The benefit of using a quantum approach becomes apparent when it is coupled with a more realistic model of solid matter, specifically, crystalline. It is invariant under smooth distortions of the Hamiltonian, as long as the energy gap does not collapse. 4 There is also a fractional quantum Hall effect. The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without external magnetic field. This is a course on the quantum Hall effect, given in TIFR, Mumbai. Search in Amazon.com. 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. x�bbRg`b``Ń3� ���ţ�1���� 0 �� (Bernevig and Zhang, PRL, 2006) • The QSH state does not break the time reversal symmetry, and can exist without any external magnetic field. The full lecture notes are around 230 pages. 554 0 obj<> endobj fluctuations in number of carriers (shot noise) ∆(I2) = 2QI 0∆f! The QHE is one of the most fascinating and beautiful phenomena in all branches of physics. 3 0 obj 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. \"�� Description. <>>> 0000001844 00000 n 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`�������� Landau level substructure and mixing in the relativistic quantum Hall effect. (3) The quantum Hall Effect, as well as ordinary Hall Effect, is characterized by Hall resistance rising (but stepwise) at magnetic field increasing. endstream endobj 584 0 obj<>/W[1 1 1]/Type/XRef/Index[52 502]>>stream I … 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. 0000006681 00000 n We find that electron-phonon inter-actions … of only is Q=e/3 assumed ∆(I2) 64 •No uniform flow of charge carriers ! The benefit of using a quantum approach becomes apparent when it is coupled with a more realistic model of solid matter, specifically, crystalline. endobj The Quantum Hall Effect by Prange 2nd edition pdf : Pages 473. 0000009867 00000 n 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 1d and e), which can be probed by scanning tunneling microscopy. The Quantum Hall Effect - Landau Levels FIG. determine Q average current frequency interval (Approximate for T=0 and weak transmission) •More … `8������0�A� � X�)3�׆ i�׼��.��@p�0X�:{�< �T�� � %�e� 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?�~�&�. The 3D quantum Hall effect may be realized in other systems with novel surface states. Du,1,4 C.M. Quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems, and may have potential applications in future electronic devices. This is not the way things are supposed to be. • Quantum Hall effect 55 Skipping cyclotron orbits Four-terminal sample configuration to measure the Hall and longitudinal resistivities • Quantum Hall effect 56 •For a given plateau not a perfect conductor, ρ xx = 0, ρ xy!= 0 ⇒ electrons move with zero longitudinal resistance. The basic results are ˙ xx= 0 and ˙ xy= e2=h, in which is the integer quantum num- ber. The “free-electron quantum gas” model still predicts a hall coefficient of 1/nq and zero magnetoresistance [5]. 5.4.5 E ective Theories of Non-Abelian Quantum Hall States 200 6. The integer Quantum Hall Effect (QHE) was discovered by K. von Klitzing, G. Dorda, and M. Pepper in 1980 [1]. ISBN : 978-0-387-97177-3,978-1-4612-3350-3. famous Quantum Hall Effect4. The integer quantum Hall effect. Xie6,7,8 1Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China 0000007865 00000 n 0000009176 00000 n The observation of Quantum Hall effect (QHE) in ultra-thin 3D TIs opens the possibility of TI based dissipa … The integer quantum Hall effect is peculiar due to the zero energy Landau level. 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. The integer QH effect was discovered in 1980 by Klaus von Klitzing, while the fractional QH effect was discovered in 1982 by Daniel Tsui, Horst Strömer and Arthur Gossard. Publisher : Springer-Verlag New York, Year : 1990. �)ܱ�p��MP�s>�9�/F��|� 1, A and B), similar to those of the quantum spin Hall (QSH) effect … 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. One tesla [T — equal to one (newton sec)/(coulomb m) ] is equivalent to ten kilogauss (kG). We show that the Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological semimetals. We consider an infinite graphene sheet with weak disorder that leads to broadening of Landau levels. The integer 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. 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. Klaus von KIitzing was awarded the 1985 Nobel prize in physics for this discovery. The quantization of electron orbits in a magnetic field results in equally-spaced energy levels — Landau levels. 0000007462 00000 n ?l�w�j��������09��*�TRp���RU�G%Yr��|���o�/��嚳�����Z���~Z_0� stream The phenomena are typically divided into two classes, the integer quantum Hall effect (IQHE) 0000005376 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. 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. 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 0000025192 00000 n By Richard E. Prange, Richard E. Prange and Steven M. Girvin. trailer <> 0000024882 00000 n He discovered, in essence, that the Hall conductance, as a function of the strength of the magnetic field … 0000000016 00000 n This value is independent of the material, geometry and microscopic details of the semiconductor. 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