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g - GaAs/Alx Ga1-x As , .

511600 -



: - .. .

­ 2012



1 1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 g - GaAs/Alx Ga1-x As . . . . . . . 1.3 g - . . . . . . . . . . . . . 1.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 2 4 8 9 10

2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3 4 17 24

1


1
, , . - : [1], [2], - [3]. , , , . , [4]. , ( , "" , ) . g - ґ. g -, , (). 1944 [5].

1.1

.

(2 ),, GaAs/Alx Ga1-x As . , . 2


1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

0

1

2

3

4

5

. 1.2: = 1, = 0, [2]. E - g µB B e2 /lB . , - . , .

, , . , . , , - k r : . 1.1: GaAs/Alx Ga1-x As 2. , - .

3


k=

r 2 lB

(1.1)

lB - . , , . (. 1.2) Kallin, Halperin 1984 [2]. . , , , , . , , g -.

1.2

g - GaAs/Alx Ga .

1-x

As -

(GaAs, Alx Ga1-x As) Td , g - , . , ґ g - . , - -

- . 1.3: (S-) (. 1.3), - . . g - Alx Ga1-x As x Weisbuch 1977 ([6]). Al, , , 4


0.8 0.6 0.4 0.2 0 -0.2 -0.4 0 5 10 20 25

. 1.4: g - GaAs/Alx Ga1-x As . - [8], - [12]( x = 0.33). - . , , g - g0 . Roth, Lax, Zwerdling 1959 ([7]): g = g0 - 2 P2 0 +C 3 m0 E0 (E0 + 0 )
l

(1.2)

g0 - g - ; E0 ,0 - (. 1.3); P - p, ^ ; Cl - . , , . GaAs/Alx Ga1-x As , 5


[001] D2d . g - (g


= g ).

([9, 8]), [13, 15, 16, 17, 14, 12]. g - (. . 1.4) ( pump-probe, [13, 14], [15], [16, 17])., . g - ( ) GaAs. , GaAs, , .. - g -. , , ґ , , ( GaAs g = -0.44, Al0.3 Ga0.7 As g = +0.4), g -. [001] C2v , g ґ ( gx = gy = gz ), ^ . g - . , , ([19]) Al ([20]). g . g [18]. , O z ( [001]). O O [100], [010] . , H O . H "" , ; - p O . - 6


, - - D R: p -- 2 R ( p ) = /h -p Ї 0


- - p Ї , D () = /h2



-p p 0



(1.3)

- R - , - - [10]. R , - , p O , H , .. - ^ g . - D - , - - [11], D , , O H , .. - g . ^ [18]: g


=g



=

2 e (p h 3 µB Ї

2 z

z - p2 z ) z

(1.4)

- . . ( g = g , g


= g ), g ^

[001], [110], [110]. , ( [001], [110], [110] - O x, O y O z ) g . B ^ 2 , 2 , O x . g - h : Ї g=
2 2 2 gz z cos2 + gxx sin2 cos2 + gyy sin2 sin2

(1.5) (1.6)

h = µB B Ї

2 2 2 gz z cos2 + gxx sin2 cos2 + gyy sin2 sin2

, g -

7


1.3

g - .

2 , GaAs/Alx Ga1-x As , , g - . [24] , g - - :

g = g0 + aB

(1.7)

g0 - g - , a -, ( , ). , a N (a (N + 1/2)). g (B ) [25, 26]. a = g / B . , a g . ^ ^ ( ) 1.5, B: g (B ) = g (B = 0) + a B a = 1 g (B = 0 ) gij aij k ni nj nk
i, j , k

(1.8) (1.9)

- - - , B : n nx = sincos, ny = sinsin, nz = cos (1.10)

, a - az z z . , a . ^

8


1.4

.


, g

-

. , g . , GaAs/Alx Ga1-x As . g- GaAs/Alx Ga1-x As : , a, ^ g


a .

9


2
2.1 .

2.1: ( ). hetero junction(#1) width, nm n, 1011 cm- µ, 10
6 cm2 Vs 2

AQW (#2) 25 4.0 1.0

AQW(#3) AQW(#4) 25 3.6 0.7 20 4.4 0.6

SQW(#5) 20 4.8 0.5

1.4 3.0

. MBE [001]. Al 30% 33%. - GaAs/Alx Ga1-x As n 1.3 в 1011 cm-2 µ 3 в 106 cm2 /V s . GaAs/Alx Ga1-x As . 2,3 - - 25nm, n 4 в 1011 cm-2 µ 106 cm2 /V s. 4 5 - (n 4.5 в 1011 cm-2 , µ 0.6 в 106 cm2 /V s). , , , 10


. , [110] [110] .

2.2

.

[28], , (2), . , 1983 Stein, von Klitzing, Weinman [26]: , , - . Rxx .

(. . 2.2). (f 2k H z ,I
r ms

= 5µA). -

, 40H z 100%. , Rxx . -, Rxx , . Rxx (B ) Rxx (B ) 2 . 2.3. 11 . 2.1: , . .


- -. . . . 2.5. f , , g - . ., , ( [21]). . 1.5 4 10. 1,3,5,7. ( , ) . , . (. . 2.4). , , . (. 2.4 )), , , 45 . . , 3D- . , . , - . (.. )[29, 21], [27]: . , , , ( [30]), . , [27]. 12


. 2.2: . , , , Princeton Applied Research 5301A, Rxx . -, AnritsuMG3696 . Stanford Research Systems SR830 , Rxx , . ( ), .

13


. 2.3: Rxx (B ) Rxx (B ). 2. = 30, = 0 . .

14






)







3D

) . 2.4: 3D , , ( )), = 45 . . , ( )) ( )). , , 45 . 3D . . 15


. 2.5: , - . 1() 2() 1.5.

16


3

)

)

. 3.1: f (B ) g (B ), 1 ( )) 3 ( )). g - , .. g -, g (B ) . , g (B ) -. , . ( = 1, 3, 5, 7) f (B ) g (B ). (. . 17


3.1), , f (B ) = f0 + (g0 - aB )B , f0 , a (N + 1/2), N - , , g (B ) . , f (B ) g (B ). , , g [001], [110] ^ [110]. , f (B ) , (. 3.2)), hf g gz . , g (B ) = µB B (. 3.2)).

)

)

. 3.2: f (B )( )) g (B ) ( )), 2 = 90 . ) g -, . 1.5 , ( [110](O x) [110](O y )):
2 2 g 2 = gz z cos2 + gxx sin2 , B

Ox

(3.1)

18


2 2 g 2 = gz z cos2 + gyy sin2 , B

Oy

(3.2)

, g - cos2 (. . 3.3) cos2 g (. . 3.3). ^ , g
zz



. 3.1. , g- . 3.1: g ^ (O x [110], O y [110] O z [001]) AQW (#2) g
xx yy zz

AQW (#4) SQW(#2) -0.292 -0.347 -0.403 -0.340 -0.340 -0.414

-0.289 -0.359 -0.410

g

g

, g 20 25 nm ^ . , g ( "" -0.44 ). , g - . 3 (. . 3.4), - [110] ( A) [110] ( B) . g - (. . 3.4): , ( = 58 ), [110] [110] . g (B ) , , g. 19


0.18 y 0.16 x

0.18

0.16

0.12

0.12

y

x A QW SQW

0.10

0.10

0.08 0.0

0.2

0.4
c o s 2 ( t h e

0.6
t a )

0.8

1.0

0.08 0.0

0.2

0.4

0.6

0.8

1.0

)

)

. 3.3: g cos2 , 2( )) 4,5( )). - , - . gxx , g
yy

3.1, 3.2. , -

g , - . g -, . = 45 , . gz z , = 0 , 1.5 g -: g () =
2 2g 2 ( = 45 , ) - gz z , . 3.5 ). 1.5

g ( ):
2 2 g 2 () = gxx cos2 + gyy sin2

(3.3)

( ) 3.3 , g [001], [110] [110] . ^ , 20


. 3.4: g - , ( 3). A B . - B O z , = 58 (

B x y .) g -, , -, . g 3.2. , ^ 3.1 3.2 , , - . a ^ g , : a = dg 1 = dB g (B = 0 ) gij aij k ni nj nk
i, j , k

(3.4)

. a ^ 21


3.2: g a (O x ^^ Oy [110] O z [001]) SQW (#5) axxz (T ayyz (T az z z (T
-1 -1 -1

[110],

AQW (#4) g
xx yy zz

AQW (#4) ) ) ) 0.002± 0.001 0.012± 0.001 0.017± 0.0001

SQW (#5) 0.0075 ± 0.0005 0.0090 ± 0.0005 0.016 ± 0.0001

-0.292 ± 0.05 -0.343 ± 0.04 -0.347 ± 0.05 -0.350 ± 0.04 -0.403 ± 0.01 -0.414 ± 0.01

g

g

= 0 , az z z . , a ^ , 3.4 : a = gz z az z z cos3 gz z az z z n3 z = g (B = 0 ) g (B = 0 ) (3.5)

a . . 3.5), a -
g
z z az z z

cos3 g (B =0)

. ,

( g ()). , g (), g ^ . , a ^ az z z . gij , i = j , gii aiik n2 nk i a . , 3.5, ,
2 gxx axxz nx nz gyy ayyz n2 nz , . y

, a 3.5 : ^ a = 1 (gz z az z z cos3 + [gxx axxz cos2 + gyy ayyz sin2 ]sin2 cos) g (B = 0 )

(3.6)

g ^ . , ai
ik

-

, g -, . a 3.2. ^

22


0 .3 6
0 .0 0 4

AQW SQW

0 .3 4
AQW SQW
0 .0 0 3

0 .0 0 2

0 .3 0

0 .0 0 1

0 .2 8

0 .0 0 0

-9 0

-6 0

-3 0

30

60

90

-9 0

-6 0

-3 0

30

60

90

)

)

. 3.5: g ( )) a g - ( )) , 4( ) 5( ). a . - 3.3 3.5 .

23


4
: 1. , . 2. . 3. - g - , , . 4. g c ^ 25 20 nm 4 в 1011 cm-2 4.4 в 1011 cm-2 20 nm 4.8 в 1011 cm-2 . g : AQW (#2) AQW (#4) g
xx yy zz

SQW (#5) -0.343 -0.350 -0.414

-0.289 -0.359 -0.410

-0.292 -0.347 -0.403

g

g

5. , g - . 6. , g - 24


, . 7. , g ^ [001], [110], [110]. 8. g ^ 20nm 4 в 1011 cm-2 . , a . ^ a : AQW (#4) axxz (T ayyz (T az z z (T
-1 -1 -1

SQW (#5) 0.0075 ± 0.0005 0.0090 ± 0.0005 0.016 ± 0.0001

) )

0.002± 0.001 0.012± 0.001 0.017± 0.0001

)

[21], [22], [23] : X , 54 . , . . , . . , , .

25



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[17] A. Malinowski and R. T. Harley, Phys. Rev. B 62, 2051 (2000). [18] V.K. Kalevich and V.L. Korenev, Pis'ma v ZhETF 57, 557 (1993) [JETP Lett. 57, 571 (1993)]. [19] S. Hallstein, M. Oestreich, W.W. Ruhle, K. Kohler, Pro ceedings of 12th International Conference High Magnetic Fields in the Physics of Semiconductors, p. 593 (1996) [20] P. S. Eldridge et al.,Phys. Rev. B 83, 041301(R) (2011) [21] Yu.A. Nefyo dov, A.A. Fortunatov, A.V. Shchepetilnikov, and I.V. Kukushkin, Pis'ma v ZhETF 91, 385 (2010) [JETP Lett. 91, 357 (2010)]. [22] Yu.A. Nefyo dov, A.V. Shchepetilnikov, I.V. Kukushkin et al., Phys. Rev. B 83, 041307(R) (2 0 1 1 ). [23] Yu.A. Nefyo dov, A.V. Shchepetilnikov, I.V. Kukushkin et al., Phys. Rev. B 84, 233302 (2 0 1 1 ). [24] G.Lommer, F.Malcher, and U.Rossler, Phys. Rev. B 32, 6965 (1985). Ё [25] M. Dobers, K.v. Klitzing and G. Weimann, Phys. Rev. B 38, 5453 (1988). [26] D. Stein, K.v. Klitzing and G. Weimann, Phys. Rev. Lett. 51, 130 (1983). [27] A. Berg, M. Dobers, P. R. Gerhardts, and K. von Klitzing, Phys. Rev. Lett. 64, 2563 (1 9 9 0 ). [28] N. Nestle, G. Denninger, M. Vidal, C. Weinzierl, K. Brunner, K. Eberl, and K.v. Klitzing, Phys. Rev. B 56, R4359 (1997). [29] S.Dickmann and S.L.Artyukhin, 89, 153 (2008) [30] Albert W. Overhauser, Phys. Rev. 92, 411 (1953)

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