1. Anomalous Cross Section Induced by Topological Quantum Interference De-Hone Lin Department of Physics, NSYSU 23 December 2004

4. Fractional Quantum Hall States

5. 2-D electron system inside the GaAs/AlGaAs heterostructure High magnetic fields (B~10T) Low temperatures (T~0.1K)

7. Coulomb forces flux quantum attachment

9. R. willett, J.P. Eisenstein, H.L. Stormer, D.C. Tsui, A.C. Gossard, and J.H. English, PRL, vol. 59, 1776, 1989.

12. Nature, Vol. 406, 863 (2000).

13. N. Bonesteel, Nature, Vol. 406, 841 (2000).

14. A.K. Geim etc, Nature 407, 55, 2000.

17. Summary Quantum interference of magnetic flux Quantum interference of magnetic flux Quantum interference in partial wave theory and anomalous cross section in two dimensions Quantum interference in partial wave theory and anomalous cross section in two dimensions Quantum interference in partial wave theory and anomalous cross section in three dimensions Quantum interference in partial wave theory and anomalous cross section in three dimensions Composite bonsons and fermions Composite bonsons and fermions

18. Introduction A charged particle Radius Phase shifts Bound states therein

19. Charged particle Interference pattern D. Bohm and Y. Aharonov in 1959 found AB effect Magnetic flux

23. The four-vector formulation of the non-integrable phase factor is given by

24. C.N. Yang, and T.T. Wu, Phys. Rev. D 12, 2845 (1975).

25. 1. It is non-local in the sense that it exists even when the interfering beams pass through a field free region and is associated with the entire closed curve C. 2. It is topological in the sense that the phase shift is unaffected when is deformed within the field free region. 3. It is geometrical in the sense that the above phase factor represents parallel transport (holonomy transformation) around with respect to the electromagnetic connection gauge.

26. A charged particle Radius Phase shifts Bound states therein Aharonov-Bohm magnetic flux

27. The system is very important in understanding the quantum Hall effect, superconductivity, and the transport properties of nano structures.

30. Quantum interference in partial wave theory and anomalous cross section in two dimensions

31. Partial Wave Method for a Short Range Potential and an Aharonov-Bohm Flux

32. In polar coordinates for the cylindrically symmetric system: Magnetic field exists in the system, then

33. For the Aharonov-Bohm Flux the magnetic field and the magnetic flux

34. Where The corresponding radial wave equation reads

35. The general solution of a scattering particle reads The solution in exterior region

36. The total cross section The scattering amplitude

38. 包含 AB effect 的分波散射理論所繪的短範圍位能相互作用的散射截 面圖，圖一橫軸是能量的大小，縱軸是散射截面的大小，可看出低 能量時散射截面產生驚人的下降現象 ; 圖二橫軸是磁通的大小，可看 到散射截面隨著磁通以週期性變化的神奇現象。這些效應對於納米 量子傳輸系統和納米量子光電系統有許多重要的應用。

43. Quantum Interference and Anomalous Cross Section in Three Dimensions

44. Plane wave Quantum interference of magnetic flux leads to

45. The angular part is defined as

46. The general solution for a charged particle moving in a short range potential, and an Aharonov-Bohm magnetic flux is found to be At large distance, we expect it to become like

48. The Scattering amplitude is found to be At the quantized values of flux, the result reduces to the well-known amplitude

49. x y e Magnetic flux e

50. where

52. Hard Sphere Potential The phase shift is given by Accordingly, the total cross sections is given by

59. Conclusions: (1) The total cross section is drastically decreased in the long wave length limit and(or) sufficient short range potential. This phenomenon may ascribed to the magnetic flux induced transparency (FIT). (2) The cross section is symmetric around magnetic flux with the oscillating period,where n is the positive integer, and is the fundamental magnetic flux quantum. (3) For identical “Bosons” (“Fermions”), there exists the phenomenon of FIT only for odd (even) number multiple of, and the cross section is symmetric around the odd (even) number multiple of with the oscillating period. Such effect is similar to the picture of the composite Boson (Fermion) in two dimensional fractional quantum Hall effect, and is useful in the question on pinning force in superconductor.

60. Thank you!

61. Composite Particles in Fractional Quantum Hall Effect

67. Nature, Vol. 406, 863 (2000).

68. N. Bonesteel, Nature, Vol. 406, 841 (2000).