Hall effects B IOHE 1980 K. V Klitzing FOHE 1982
11 Hall effects B + + + + + + + + + + - - - - - - - - - - - - - - - - 1980 1982 J
Spin hall effect ns(a u. J E. Hirsch, PRL 83, 1834(1999) S Murakami, N Nagaosa, and S C Zhang Science -so 301,1348(2003) J Inova et al, PrL92, 126603 (2004) 100 YK. Kato et al science 2004 15O 4-2002040 Position < un》 YK. Kato et al Science 12
12 Spin Hall effect J J. E. Hirsch, PRL 83, 1834 (1999); S. Murakami, N. Nagaosa, and S. C. Zhang, Science 301, 1348 (2003); J. Sinova et al, PRL92, 126603 (2004); Y. K. Kato et al Science 2004; Y. K. Kato et al Science
Effective magnetic fields l)-3)b 3 Q G. Juzeliunas PRL(2004) G. Juzeliunas et al PRA(2006) 13
13 Effective magnetic fields G. Juzeliunas et al PRA (2006) G. Juzeliunas PRL (2004)
Introduction: geometric phase The aharonov-Bohm effect The adiabatic approximation The berry phase The Aharonov-Anandan phase
14 Introduction: geometric phase • The Aharonov-Bohm effect • The adiabatic approximation • The Berry phase • The Aharonov-Anandan phase
The Aharonov-Bohm effect aharonov and Bohm 1959 q q 1÷9 已 solenoi The charge never" field The fringe shift is gauge invariant The phase shift depends only on the path integral 15
15 The Aharonov-Bohm effect solenoid = A dl q e AB 0 / • The charge never “touches” field • The fringe shift is gauge invariant • The phase shift depends only on the path integral Aharonov and Bohm 1959 q q