Расчет энергетических зон, спиновой поляризации и транспорта в наноструктурах со спин-орбитальным взаимодействием: Методические указания к лабораторной работе




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(3)

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InAs/AlGaSb [6].

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"%() *%+) (2) , -.!!"/0%#1% (3) & 23  4 !"#$% &' &1%, 4( !5&, (6&. 664 7.,!#5!5U & 9% ,"/56,%6 (": $%!5,;) & (%66 7"#7.&(6,'& !5.#'5#.. #6';,8 (5) & !5%;,6%.6 #.%&66,4 @.A(,69..% ! 9% ,"/56,%6 (4), ) 7"#$% !,!5 # (� ",6 6)0 (6 (6)0 #.%&66,4 6% ' 7665) !7,6.% c : 1, 2    k2  − E  c1 + zc2 = 0   2m  2   k * − E  c2 = 0,
z c1 +  2m

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9( z = α (k y + ik x ) + β (k x + ik y ). !"&, .%&6!5&% 6#"8 7.(",5": !,!5 ) (6) 71&":5 6%45, =6.95,$!',4 !7'5.: k2 2 2 Eλ (k ) = + λ (αk y + β k x ) + (αk x + βk y ) , 2m

λ = ±1.

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B!" =59 C6 6%45, ' 7665) !7,6.% c1, 2 , 5. . &"6 >#6';,8, '5.%: , 5 &,(: Ψλk =

e

ikr

  

1

2 λe

iθ (k )

,

θ (k ) = Arg[αk y + βk x − i (αk x + βk y )],

9( λ = ±1. (8) % ', .%1 , =6.95,$!',4 !7'5. (7) , &"6&) >#6';,, (8) 9% ,"/546,%6% (4) 0%.%'5.,1#85!: 6%. '&%65&)0 $,!" (λ , k ). %' , & "6& &'5., ,.", , 7#"/!, 1(!/ 7,!4 )&%5 7"!'#8 &"6# 5%' C, '.56 5!#5!5&, !7,6- ,5%"/69 &1%, ( !5&,:. &) :&":5!: (,!'  '&%65 & $,!" λ = ±.%1, !5&5!5 ( &5&: 4 ,!0(69 7%.%",$!'9 !7'5.%, !7"A66)0 23 &1%, 4( !5&, . - !5&,5"/6, ,1 (7) "9' &,(5/, $5 & 5!#5!5&, 23 &1%, ( !5&,:, 5. . 7., α = β = 0 , ) 7"#$, 7.!54 7%.%",$!',4 1%'6 (,!7.!,,. 3(6, ,1 6%," &%C6)0 &7.!&, &16,'%8,0 7., .%!! 5.6,, : 1%(%$%  .%!7.("6,, !7,6& & 7. !5.%6!5& !,!5 ! #$A5 !7,6%, :&":5 ! '&%65 &)0 $,!". %', 7.!5.%6!5& & 6%+ !"#$% :&":5!: 7"!'!5/ (k x , k y ) , 7#"/!& (&# .69 ="'5.669 9%1%, 6% '5.4 C6 7!5.,5/ .%!7.("6,: !7,6& (": '%C(4 &5&, !7'5.% (7) ! λ = ±1. -5-

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.

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B(!5%&":: & &).%C6, (9) &"6 >#6';,8 (8), ) 7"#$% , $5 σ z = 0 5C(!5&66 (": "8 )0 16%$6,4 (λ , k ), 5. . !7,6) 7":.,1&%6) & 7"!'!5, (&# .69 ="'5. 669 9%1%.  7665) C 7.';,4 !7,6& & 7"!'!5, (k x , k y ) .%1#85 &'5.6 7" ! !"(#84 !5.#'5#.4:
σ λk = (σ x ,σ y ) = λ (cosθ , sin θ ),

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9( >%1% θ (k ) 7.(":5!: & (8).   

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k2 E R (λ , k ) = + λk , (11) λ = ±1. 2m          !( (!  ," 0'! "" " " "  &  + ' ! - * /*$ #*      (11) # / #  # $ # ) 0!" ',' " ,&1 5'"; ' ' 0' ! & " k = (kx , k y ) # $ $  .1  # #  *  λ = ±1. ) 3)) *25= &/(4'7) ' :48(,9+.3, %4:43)7:43, E41/. α ≠ α , β = 0 , %:, G7&3 1 2 :)*)() :) :4 *)7 ( 9)+ (0747 7. % H α 1 → 0 /5 %& 5 85 /& [9]. 74+&2;4 84*49, '=)347,9)';, %&;484+4 +4 E,'.5. E4''347:,24)7'6 &' :4'')6+,, *25=;&3%&+)+7+.= '%,+&:&2 2,*4 (8), 62(6@F,='6 84*494 & 72)++.3, '&'7&6+,63, *253):+&-& G();7: &++&-& -484. E4'')6+,) '&/' +4 -:4+,>) x = 0 *25= &/(4'7)A ' %4:43)7:43, '%,+-&: /,74(0+&-& %:4,3 &,'=*) &*,7 A'72,6 α 2 ()2&3 %&(5%:&'7:4+'72) , α 2 %:42&3 %&(5%: &'7:4+'72). 28 & H:, 8+49)+,, β =10 +4/)-4@F46 2&(+4 ,3))7 2,* 2 N K ikr L 1 I e (12) x < 0 : Ψin = M J , θ (k ) = Arg[k y − ik x ], λ = ±1, 2 λe iθ (k ) , =4:4;7):,85)7'6 ;&3%&+)+743, ,3%5(0'4 (k , k ) , 9,'(&3 λ = ±1, x y A :,+4*()