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Unformatted text preview: Solid State Theory Exercise 9 FS 11 Prof. M. Sigrist Corbino disk and the integer quantum Hall effect Exercise 9.1 The lowest Landau level in the Corbino geometry The Hamilton operator for an electron ( e < 0) restricted to the plane z = 0 and exposed to a magnetic field is given by H = 1 2 m * p- e c A 2 + U ( r ) (1) where r 2 = x 2 + y 2 . The annular potential U ( r ) = C 1 r 2 + C 2 r 2 + C 3 (2) with C 1 ,C 2 > 0 yields a Corbino 1 geometry confining the electron on a two-dimensional ring. The constant term C 3 only leads to a shift of the energy which is why we neglect it in the following. Let the magnetic field B be homogeneous and directed along the z-axis for r > 0. In addition, a magnetic flux Φ = ν Φ through the origin ( r = 0) that does not physically touch the electron is assumed: B = [ B + ν Φ δ ( r )] e z , (3) with B,ν > 0. Φ = hc/ | e | = 2 π ~ c/ | e | is the magnetic flux quantum....
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This note was uploaded on 10/04/2011 for the course PHYS fs11 taught by Professor Sigrist during the Spring '11 term at Swiss Federal Institute of Technology Zurich.
- Spring '11