Dynamics of Bloch Electrons 1
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1 Dynamics of Bloch Elcons 7h Spmb 003 c 003, Michal Mad
2 Dfiniions Dud modl Smiclassical dynamics Bloch oscillaions K P mhod Effciv mass Houson sas Zn unnling Wav pacs Anomalous vlociy Wanni Sa ladds d Haas van Alphn ffc 7h Spmb 003 c 003, Michal Mad
3 Dud Modl 3 m E c B m (L) In h absnc of an lcic fild, 0 (L) In h psnc of on m E 0 m E (L3) m E (L4) j n n m n m E (L5) (L6) 7h Spmb 003 c 003, Michal Mad
4 3 j m n Dud Modl 4 n cm 3 3 s cm Cold Ho (L7) n T n m m 3 cv B T n m 4 0 n 3 B T T 3 gcm n T T (L8) (L9) K (L0) 7h Spmb 003 c 003, Michal Mad
5 Smiclassical Elcon Dynamics 5 h (L) h E c B(L) 7h Spmb 003 c 003, Michal Mad
6 Bloch Oscillaions 6 0 a a a 3 a cosa (L3) h E E h a h sin E cos ae h ae h (L4) (L5) (L6) (L7) 7h Spmb 003 c 003, Michal Mad
7 Bloch Oscillaions 7.0 Vlociy R Tim R a Figu : [Souc: bn Dahan al. (996), p. 450.] 7h Spmb 003 c 003, Michal Mad
8 P Mhod 8 Figu : Which ignvalus blong o h sam band? h m u i u U u (L8) h m i (L9) 7h Spmb 003 c 003, Michal Mad
9 P Mhod 9 n n n n (L0) n un h m i u n (L) i i i i (L) n h m n P n (L3) n h m n P n (L4) n h n (L5) 7h Spmb 003 c 003, Michal Mad
10 c M M Effciv Mass 0 wh d d d d hm h n (L6) (L7) (L8) Pocding o scond od... m m n n n n P n n P n n c (L9) 7h Spmb 003 c 003, Michal Mad
11 Elcons in Elcic Fild Ponial of fom E conflics wih piodic bounday condiions. E A c Magnic flu ub ce B z V (L30) E Figu 3: A hin ub of incasing magnic flu hough a loop of wi. m P c A U R (L3) 7h Spmb 003 c 003, Michal Mad
12 Elcons in Elcic Fild A ce (L3) m P c A U (L33) L (L34) ia hc (L35) P m U (L36) n i un (L37) ia L hc i L un L ia hc i un (L38) 7h Spmb 003 c 003, Michal Mad
13 Elcons in Elcic Fild 3 A hc E h l L l L (L39) (L40) (L4) h E (L4) 7h Spmb 003 c 003, Michal Mad
14 Zn Tunnling 4 p i h p 0 d m m g h g (L43) (L44) p g E m g h (L45) 7h Spmb 003 c 003, Michal Mad
15 Zn Tunnling 5 c g g E Figu 4: Engy diagam of Zn unnling. n C n n (L46) 7h Spmb 003 c 003, Michal Mad
16 Zn Tunnling 6 ih (L47) n C n n n (L48) ih n Cn n Cn n (L49) n Cn n (L50) ih Cn n icn n n E (L5) C ih C (L5) C p i h 0 d (L53) 7h Spmb 003 c 003, Michal Mad
17 givs Zn Tunnling 7 C p i h 0 d (L54) E h p i h 0 d (L55) L N 0 d E h p i h 0 d (L56) L N 0 L N d p i E 0 d (L57) m m m c (L58) g h m (L59) 7h Spmb 003 c 003, Michal Mad
18 g m Zn Tunnling 8 g h q m 0 (L60) p i E 0 q d g h m (L6) p p i 3E q 3 g 3E g m h (L6) (L63) p V 3 m E cmv (L64) 7h Spmb 003 c 003, Michal Mad
19 Fomal Dynamics of Wav Pacs 9 W c c N c ia c hc i c (L65) Calculaions fom h on ou oo compl o psn a boad... W c c W c c N d i c c c c c (L66) c (L67) 7h Spmb 003 c 003, Michal Mad
20 Fomal Dynamics of Wav Pacs 0 Rcipocal spac Ral spac a c a Aoms c Figu 5: A wav pac viwd in al and cipocal spac c c i c c (L68) wh c i d u c c u c (L69) W c c c W c c W c c W c c c (L70) 7h Spmb 003 c 003, Michal Mad
21 Fomal Dynamics of Wav Pacs d N c c i c u u c (L7) d N d N c c u c u u i i i c i c c u (L7) (L73) (L74) d c u i c u (L75) d c u i c c u (L76) d iu c c u c i ln c c 0(L77) 7h Spmb 003 c 003, Michal Mad
22 wih W W W W Fomal Dynamics of Wav Pacs c c W c c c(l78) P m U m c c P ih A c W c c U W c c W V c c (L79) (L80) (L8) c c c c W ih V W c c c c c c da d c c hc c mc B L c hc V c c (L8a) (L8b) L c h u c d ic u c c i c u c c.c. (L8c) 7h Spmb 003 c 003, Michal Mad
23 Fomal Dynamics of Wav Pacs 3 c d d c and c d d c (L83) h c c h E c c c c B(L84a) mc B L c c c (L84b) Rcov pcd smiclassical dynamics, bu wih cocions du o anomalous vlociy. B A (L85a) (L85b) 7h Spmb 003 c 003, Michal Mad
24 Condiions fo validiy of Smiclassical Dynamics 4 h E F g g F (L86) g g F (L87) 7h Spmb 003 c 003, Michal Mad
25 B Hamilonian Dynamics 5 QlPl Pl l Ql (L88) p h h A c h p A c (L89a) (L89b) V mc L p B A c V mc L (L90) 7h Spmb 003 c 003, Michal Mad
26 Hamilonian Dynamics 6 Figu 6: Engy conous on h Fmi sufac of copp, showing opn and closd obis. 7h Spmb 003 c 003, Michal Mad
27 Quanizing Smiclassical Dynamics 7 ih W W (L9) ih W W (L9) i h (L93) h j (L94) h j d l P l Pl l dq l P l (L95) d d A hc j(l96) d d A hc j(l97) 7h Spmb 003 c 003, Michal Mad
28 Wanni Sa Ladds 8 d (L98) j d 0 K d K (L99) K j (L00) 7h Spmb 003 c 003, Michal Mad
29 Wanni Sa Ladds 9 E K Figu 7: Th Wanni Sa ladd is a collcion of lcons appd in Bloch oscillaions by an inns lcic fild, and spacd a invals of cipocal laic vco. K, wh K is a 7h Spmb 003 c 003, Michal Mad
30 d Haas van Alphn Effc 30 A B (L0) B hc B hc B B hc hc B B(L0) (L03) 7h Spmb 003 c 003, Michal Mad
31 d Haas van Alphn Effc 3 74 G 69 G Figu 8: Sch of d Haas van Alphn oscillaions of magnizaion M in gold simila o hos masud by Shonbg and Vandooy (970). j 0 d A ch hc B (L04) 7h Spmb 003 c 003, Michal Mad
32 B d B d d Haas van Alphn Effc 3 j 0 0 d hc B d hc hc d B hc B B B B B B (L05) (L06) (L07) (L08) B hc Å T j (L09a) 7h Spmb 003 c 003, Michal Mad
33 d Haas van Alphn Effc B Å T (L09b) B F d (A) (B) (C) (D) F Figu 9: 7h Spmb 003 c 003, Michal Mad
34 Epimnal Masumns of Fmi Sufacs 34 Figu 0: Fmi sufac of copp, Shonbg (984). Figu : Th Fmi sufac of ungsn, Givan al. (968). 7h Spmb 003 c 003, Michal Mad
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