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. Via a ``wormhole'' tunneling assisted by the Weyl nodes, the Fermi arcs at … He discovered, in essence, that the Hall conductance, as a function of the strength of the magnetic field … trailer 0000013246 00000 n It gives a brief introduction to both Integer and Fractional Quantum Hall effect. 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. 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. After the discovery of this … FRACTIONAL QUANTUM HALL EFFECT: DIRAC COMPOSITE FERMIONS The fractional quantum Hall e ect occurs when Landau levels are fractionally lled. 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 invariant under smooth distortions of the Hamiltonian, as long as the energy gap does not collapse. (3) The quantum Hall Effect, as well as ordinary Hall Effect, is characterized by Hall resistance rising (but stepwise) at magnetic field increasing. 0000006042 00000 n Topological aspects of the quantum Hall effect, including both the integral and fractional cases, are discussed. Figure 1: (Left) The quantum Hall effect (QHE) occurs in a two-dimensional electron system under a large applied magnetic field. Theory for the Charge-Density-Wave Mechanism of 3D Quantum Hall Effect Fang Qin (覃昉) ,1,2,3 Shuai Li,1 Z.Z. x x • Insulating gap in the bulk. 0000001844 00000 n Quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems, and may have potential applications in future electronic devices. 2 0 obj 0000002790 00000 n The “free-electron quantum gas” model still predicts a hall coefficient of 1/nq and zero magnetoresistance [5]. <>>> 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. The fundamental quantum of Hall resistance is h/e2 =25,813Ω. Du,1,4 C.M. Abstract. We consider an infinite graphene sheet with weak disorder that leads to broadening of Landau levels. ISBN : 978-0-387-97177-3,978-1-4612-3350-3. Ԉ:�_ xlV�"�v�3$�aEQ��ӌ���. 0000009867 00000 n The quantum Hall effect is usually observed in 2D systems. 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. Yehuda B. 0000007329 00000 n Quantum Hall effect Masatsugu Sei Suzuki Department of Physics, SUNY at Binghamton (Date: May 09, 2013) In 1980, Klitzing et al. Klaus von KIitzing was awarded the 1985 Nobel prize in physics for this discovery. The 3D quantum Hall effect may be realized in other systems with novel surface states. 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. 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. 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 integer quantum Hall effect can be explained by the quantization of the magnetic flux in terms of the unit ~/e with the flux quantum number being the number of states in a single Landau level. 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