Alexandre R. Rocha200.145.112.249/webcast/files/Journeys17-Class03.pptx.pdf · 2017-07-12 · T=8...
Transcript of Alexandre R. Rocha200.145.112.249/webcast/files/Journeys17-Class03.pptx.pdf · 2017-07-12 · T=8...
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AlexandreReilyRocha 2
IL=IR
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ΓL
ΓR εV µR
µL
V ≠ 0 2|EF-ε|
V = 0
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AlexandreReilyRocha 5
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AlexandreReilyRocha 6
( ) ( ) - 0 0 f N U - + = µ ε ε ε
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( ) ( ) - 0 0 f N U - + = µ ε ε ε
Canyoudoabitofcoding?
Mathema4ca/Matlab/Fortran/C/C++/Python/Punchcards/byhand?
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( ) ( ) - 0 0 f N U - + = µ ε ε ε
L L R
R
ΓL
ΓR εV µR
µL
V ≠ 0 V = 0
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@⇢ (~r, t)
@t= �r ~J
⇢ (~r, t) �! ⇢ = | lih l|
@⇢
@t=
1
i~
hH, ⇢
i=
1
i~
⇣H | lih l|� | lih l| H
⌘
Con4nuityequa4on
Classical DensityMatrix
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I = j ∂ρ∂t
j
Ψ =e−iEkt
Neilka
l∑ l = cl
k t( )l∑ l
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j ∂ρ∂t
j =Yj+1→ j +Yj−1→ j
Yj+1,j = � i
~
hhj
���H��� j + 1ickj+1 (t) c
k⇤j (t)� hj + 1
���H��� jickj+1 (t) c
k⇤j (t)
i
Yj�1,j = � i
~
hhj
���H��� j � 1ickj�1 (t) c
k⇤j (t)� hj � 1
���H��� jickj�1 (t) c
k⇤j (t)
i
Yj�1,j = � 2�
~N sin (k) Yj+1,j =2�
~N sin (k)
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€
Ψ =1N
eilkal∑ ψl
€
Ψ =1N
e−ilkal∑ ψl
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Yj�1,j = � 2�
~N sin (k) Yj+1,j =2�
~N sin (k)
v E( ) = 1∂E∂k
= −2βasin ak( )
Yj�1,j =vkNa
=vkL
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€
E = ε0 + 2β cos ka( ) v E( ) = 1!∂E∂k
= −2βasin ak( )
!
∂n(E)∂E
= DOS E( ) = 22π
La
12β sinka
DOS = 2h
Lv E( )
I = n(E)ev(E)E=µR
µL
∑ = eµR
µR
∫ ∂n(E)∂E
v E( )dE = 2ehe µ1 −µ2( ) = 2e
2
hΔV
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€
I =2ehe µ1 −µ2( ) =
2e2
hΔV
dIdV
=G =2e2
h
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Daniel Ugarte e Varlei Rodrigues (Unicamp)
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AlexandreReilyRocha 26€
ψ0
€
ψ1
€
ψ2
€
ψ−1
€
β
€
ε0
€
ε0
€
Γ
€
ε0
€
ε0
€
ε0
€
ε0
€
Ψ =1N
eilkal∑ ψl
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€
β
€
ε0
€
ε0
€
ε0
€
ε0
€
ε0
€
ε0
€
β
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AlexandreReilyRocha 28
€
β
€
ε0
€
ε0
€
Γ
€
ε0
€
ε0
€
ε0
€
ε0
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AlexandreReilyRocha 29
E k( ) = ε0 + 2β cos ka( )
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T = 4β 2Γ2 sin2 kaβ 2e−ika −Γ2eika
2 ≈ 4Γβ
$
%&
'
()
2
sin2 ka
€
Γ << β
€
β
€
ε0
€
ε0
€
Γ
€
ε0
€
ε0
€
ε0
€
ε0
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T = 4β 2Γ2 sin2 kaβ 2e−ika − Γ2eika
2€
β
€
ε0
€
ε0
€
Γ
€
ε0
€
ε0
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ε0
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AlexandreReilyRocha 32
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€
β
€
ε0
€
ε0
€
Γ
€
ε0
€
ε0
€
ε0
€
ε0
ε1
β1
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| i =
8>><
>>:
| k, 1i + r | �k, 1i if j �1 andchain 1c |0, 0i if j = �1 andchain 0
t1 | �k, 0i if j �1 andchain 0t2 | k, 0i if j � 1 andchain 0
T =
����v1kv0k
���� |t1|2 +
����v1kv0k
���� |t1|2
|vk| =2a�
~ sin ka
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T = 8 βΓ2
β1sink1asink2a
1Γ2eik1a + i2β sink2a
2
T ≈ 2 Γ2
β1βsink1asink2a
DOSsurf E( ) = 2 12π
12β sinka
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DOSsurf E( ) = 2 12π
12β sink2a
DOStip E( ) = 2 12πsink1aβ1
T ≈16π 2Γ2DOSsurf (E)DOStip(E)
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T ≈16π 2Γ2DOSsurf (E)DOStip(E)
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ε0ε1
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ε0
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ε0
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