Scattering theory for quantum Hall anyons in a saddle point potential

Physical Review B - Condensed Matter and Materials Physics

Volumn 80, Issue 16, 2009, Pages

  Matthews, A ^a   Cooper, N R ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

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EID: 72649098266     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.80.165309     Document Type: Article

References (21)

1. The Quantum Hall Effect, 2nd ed., edited by, R. E. Prange, and, S. M. Girvin, (Springer-Verlag, Berlin, 1990).
2. Perspectives in Quantum Hall Effects: Novel Quantum Liquids in Low-Dimensional Semiconductor Structures, edited by, S. Das Sarma, and, A. Pinczuk, (Wiley, New York, 1997).
3. R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983). 10.1103/PhysRevLett.50. 1395
4. B. I. Halperin, Phys. Rev. Lett. 52, 1583 (1984). 10.1103/PhysRevLett.52. 1583
5. D. Arovas, J. R. Schrieffer, and F. Wilczek, Phys. Rev. Lett. 53, 722 (1984). 10.1103/PhysRevLett.53.722
6. V. J. Goldman and B. Su, Science 267, 1010 (1995). 10.1126/science.267. 5200.1010
7. R. de Picciotto, M. Reznikov, M. Heiblum, V. Umansky, G. Bunin, and D. Mahalu, Nature (London) 389, 162 (1997). 10.1038/38241
8. L. Saminadayar, D. C. Glattli, Y. Jin, and B. Etienne, Phys. Rev. Lett. 79, 2526 (1997). 10.1103/PhysRevLett.79.2526
9. J. Martin, Shahal Ilani, Basile Verdene, Jurgen Smet, Vladimir Umansky, Diana Mahalu, Dieter Schuh, Gerhard Abstreiter, and Amir Yacoby, Science 305, 980 (2004). 10.1126/science.1099950
10. S. B. Isakov, T. Martin, and S. Ouvry, Phys. Rev. Lett. 83, 580 (1999). 10.1103/PhysRevLett.83.580
11. S. Vishveshwara, Phys. Rev. Lett. 91, 196803 (2003). 10.1103/PhysRevLett. 91.196803
12. E.-A. Kim, M. Lawler, S. Vishveshwara, and E. H. Fradkin, Phys. Rev. Lett. 95, 176402 (2005). 10.1103/PhysRevLett.95.176402
13. K. T. Law, D. E. Feldman, and Y. Gefen, Phys. Rev. B 74, 045319 (2006). 10.1103/PhysRevB.74.045319
14. D. E. Feldman, Y. Gefen, A. Kitaev, K. T. Law, and A. Stern, Phys. Rev. B 76, 085333 (2007). 10.1103/PhysRevB.76.085333
15. C. Korff, G. Lang, and R. Schrader, J. Math. Phys. 40, 1831 (1999). 10.1063/1.532837
16. F. Wilczek, Phys. Rev. Lett. 49, 957 (1982). 10.1103/PhysRevLett.49.957
17. We note that two distinguishable particles which exhibit mutual anyon statistics-e.g. quasiparticles of two different quantum Hall fluids-cannot be viewed as noninteracting, except for the cases Δ=0,1 for which the boundary condition becomes trivial.
18. H. A. Fertig and B. I. Halperin, Phys. Rev. B 36, 7969 (1987). 10.1103/PhysRevB.36.7969
19. Applying the next correction, as in the Wentzel-Kramers-Brillouin (WKB) approximation, leads to ψj ∼ 1 j exp [i θ0 j+ e-2i θ0 (ε/4) lnj] for the waves with θ0 =±π/4,±3π/4.
20. S. Datta, Electronic Transport in Mesoscopic Systems, 2nd ed. (Cambridge University Press, Cambridge, 1995).
21. E. Comforti, Y. C. Chung, M. Heiblum, V. Umansky, and D. Mahalu, Nature (London) 416, 515 (2002). 10.1038/416515a