Anomalous Cross Section Induced by Topological Quantum Interference

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

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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 in partial wave theory and anomalous cross section in two dimensions • Quantum interference in partial wave theory and anomalous cross section in three dimensions • Composite bonsons and fermions

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

19. D. Bohm and Y. Aharonov in 1959 found AB effect Interference pattern Charged particle 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 topologicalin the sense that the phase shift is unaffected when is deformed within the field free region. 3. It is geometricalin the sense that the above phase factor represents parallel transport (holonomy transformation) around with respect to the electromagnetic connection gauge.

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

27. The system is very important in understanding thequantum Hall effect, superconductivity, and thetransport 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 solution in exterior region The general solution of a scattering particle reads

36. The scattering amplitude The total cross section

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. Magnetic flux y e e x

50. where