1d and e), which can be probed by scanning tunneling microscopy. We consider the unperturbed operator $H_0: = (-i \nabla - {\bf A})^2 + W$, self-adjoint in $L^2({\mathbb R}^2)$. The measurement of the Hall resistance showed that electronic resistance could be defined precisely in terms of fundamental constants, even in a disordered and irregular sample. To date however, rare clear-cut examples concern-ing topologically ordered phases of Bose-Fermi mixtures which possess diverse quantum particle statistics, have been conclusively sought for. Du,1,4 C.M. Sohn, A. Pinczuk, B.S. Two prominent ones are • Prange and Girvin, “The Quantum Hall Eﬀect” This is a collection The integer quantum Hall effect is peculiar due to the zero energy Landau level. E k n=1 n=2 n=3 n=4 n=5 n=0 Figure 12: Integer quantum Hall e↵ect Figure 13: Landau levels Introduction: materials, transport, Hall effects ?integer quantum Hall effect: resolved Landau levels with localization between centers of Landau levels?low disorder 2D electron systems show fractional quantum Hall effect – correlations of electrons as described by the Laughlin wave function?what about many fractional quantum Hall states? I. The Half-Filled Landau level. We’ll start these lectures by reviewing the underlying physics of the Hall e↵ect. Residing between the conventional stripe phases (lower N) … 1.3 The Classical Hall E ect Let us rst look at the classical Hall e ect and then see how it di ers from the quantum Hall e ect. Although its extension to three dimensions has been long-sought and inspired theoretical proposals, material candidates have been lacking. tional quantum Hall eﬀects and of superconducting high Tc cuprates [9]. Quantum Hall e ect is a relativity new discovered phenom-ena and one of the most interesting phenomena within condensed matter physics. 0031-9007= The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. 4. Quasi-Holes and Quasi-Particles. The basic experimen- H is the external magnetic field, and M is the magnetization. Si tenemos un campo magnético constante B en la dirección z y electrones restringidos a moverse en el plano (x,y), aparece una corriente I en la dirección x. El Efecto Hall nos dice que esto produce un voltaje V H en la dirección y. 0038%1098/95 $9.50 + .OO 0038-1098(94)00828-O DISPERSIVE COLLECTIVE EXCITATION MODES IN THE QUANTUM HALL REGIME L.L. The original, classical Hall e↵ect was discovered in 1879 by Edwin Hall. We consider an infinite graphene sheet with weak disorder that leads to broadening of Landau levels. The 3D quantum Hall effect may be realized in other systems with novel surface states. 3. Band, Yshai Avishai, in Quantum Mechanics with Applications to Nanotechnology and Information Science, 2013. 1 The Integer Quantum Hall Effect Johar M. Ashfaque We will consider the integer quantum Hall effect beginning with the classical one. Most prior theoretical and Yehuda B. L. Wang3,b) 1National Lab of Solid State Microstructures, Department of Physics, Nanjing University, Nanjing 210093, People’s Republic of China Xie6,7,8 1Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China In previous work on the quantum Hall effect on an annulus, we used O(d, d; Z) duality transformations on the action describing edge excitations to generate the Haldane hierarchy of Hall conductivities. 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