quantum hall effect pdf

1d and e), which can be probed by scanning tunneling microscopy. <>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> Het effect is genoemd naar de onderzoeker Edwin Hall.. De polariteit van de spanning hangt af van de aard van de ladingsdragers. 0000004101 00000 n 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. Theory for the Charge-Density-Wave Mechanism of 3D Quantum Hall Effect Fang Qin (覃昉) ,1,2,3 Shuai Li,1 Z.Z. Similarly, the number of helical edge states, deﬁned modulo two, of the QSH state is also invariant … 1). The discovery of the quantum Hall effect (QHE) marked a turning point in condensed-matter physics. (Bernevig and Zhang, PRL, 2006) • The QSH state does not break the time reversal symmetry, and can exist without any external magnetic field. Laughlin, Physical Review B 23, 5632 (1981) Charles Kittel, Introduction to Solid State Physics R.B. 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. startxref 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. 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. <> 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. This is a course on the quantum Hall effect, given in TIFR, Mumbai. L. Wang3,b) 1National Lab of Solid State Microstructures, Department of Physics, Nanjing University, Nanjing 210093, People’s Republic of China endobj 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. The resistance in longitudinal direction in limits of every plateau, as it was mentioned, falls almost to zero (fig. 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. ISBN : 978-0-387-97177-3,978-1-4612-3350-3. 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. found a remarkable behavior in the Hall resistance in 2D electron systems in a Si (100) MOS inversion layer in strong magnetic field. The full lecture notes are around 230 pages. Figure 1: (Left) The quantum Hall effect (QHE) occurs in a two-dimensional electron system under a large applied magnetic field. 0000003778 00000 n From the … In this Letter, we develop a theory for the CDW mechanismof 3D quantumHall effect. But in high-quality two-dimensional systems such as gallium arsenide quantum wells or … 0000000016 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. 0000004024 00000 n 4 There is also a fractional quantum Hall effect. 0000010576 00000 n The basic experimen- The fractional quantum Hall effect is a very counter-intuitive physical phenomenon. The quantum Hall (QH) effect is one of the most remarkable phenomena discovered in the last century. The Quantum Hall Effect - Landau Levels FIG. 0000001878 00000 n 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. 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. By Richard E. Prange, Richard E. Prange and Steven M. Girvin. The basic results are ˙ xx= 0 and ˙ 0000007462 00000 n Description. 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. \"�� 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 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. The spacing of these levels is proportional to the classical cyclotron frequency != eB m. endobj 2 0 obj endstream endobj 584 0 obj<>/W[1 1 1]/Type/XRef/Index[52 502]>>stream 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 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. 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]. %PDF-1.5 It implies that many electrons, acting in concert, can create new particles having a charge smaller than the charge of any indi-vidual electron. It is invariant under smooth distortions of the Hamiltonian, as long as the energy gap does not collapse. This project seeks to articulate a notion of emergence that is compatible with the observed phenomena associated with the FQHE. 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. The beneﬁt of using a quantum approach becomes apparent when it is coupled with a more realistic model of solid matter, speciﬁcally, crystalline. �)ܱ�p��MP�s>�9�/F��|� 0000002790 00000 n %PDF-1.4 %�� Integer Quantum Hall Effect in Graphene. Although its extension to three dimensions has been long-sought and inspired theoretical proposals, material candidates have been lacking. endobj 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. 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 Electrons in the lattice feel the eﬀect of a periodic potential on their motion. The integer Quantum Hall Effect (QHE) was discovered by K. von Klitzing, G. Dorda, and M. Pepper in 1980 [1]. 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. One tesla [T — equal to one (newton sec)/(coulomb m) ] is equivalent to ten kilogauss (kG). Thetheorycaptures the main features in the experiment of ZrTe5 at the quantitative level. 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. I. The quantum Hall effect A century later, the Hall effect was revived as a source of astonishing new physics. 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