lecture 12: quantum point contact · 1/4/2016 eecs 277b adv. semiconductor devices © 2013 p. burke...
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1/4/2016 EECS 277B Adv. Semiconductor Devices © 2013 P. Burke Lecture 11, p. 1
Lecture 12: Quantum point contact
Resistance is independent of length.
d ~ lFermi
212.5
2quantum
hR k
e
1/4/2016 EECS 277B Adv. Semiconductor Devices © 2013 P. Burke Lecture 11, p. 2
Readings this lecture covers
Ferry pp. 124-139
Van Wees PRL (reading packet)
Marcus APL (reading packet)
Zhou APL (reading packet)
1/4/2016 EECS 277B Adv. Semiconductor Devices © 2013 P. Burke Lecture 11, p. 3
Ballistic vs. diffusive transport
W
W
l
l
L
Ballistic
Diffusive
?R
2
LR
W
1/4/2016 EECS 277B Adv. Semiconductor Devices © 2013 P. Burke Lecture 11, p. 4
1d system:22 22 2 2 2 2
2 2 2( )
2 2
x y zn n n
x y z
x y z
k k kE n n n
m m L L L
xL 0yL 0zL
E
kx=nx/Lx
22 22
2
2x
x y z
E nm L L L
22 22
2 222
x
x y z
E nm L L L
22 22
2 232
x
x y z
E nm L L L
Fermi energy
1/4/2016 EECS 277B Adv. Semiconductor Devices © 2013 P. Burke Lecture 11, p. 5
Resistance quantumBallistic conductor
Right
contact
Left
contact
E
kx=2nx/Lx
eV
Fermi energy
225 quantum
hR k
e
212.5
2quantum
hR k
e
With spin:
22quantum
eG
h
22eG T
h
If injection from leads is not perfect:
T is the transmission probability.
1/4/2016 EECS 277B Adv. Semiconductor Devices © 2013 P. Burke Lecture 11, p. 6
Variable width wire:
E
kx=nx/Lx
Fermi energy
1/4/2016 EECS 277B Adv. Semiconductor Devices © 2013 P. Burke Lecture 11, p. 7
Landauer formula:
22eG n
h
If the leads are not perfect injectors into each “channel” then:
22n
eG T
h
1/4/2016 EECS 277B Adv. Semiconductor Devices © 2013 P. Burke Lecture 11, p. 8
Experimental realizations:
Pinch-off gate in semiconductor 2DEG (QPC)
Break junction
Electrochemical addition of atoms
Scanning tunneling microscope
1/4/2016 EECS 277B Adv. Semiconductor Devices © 2013 P. Burke Lecture 11, p. 9
Quantum point contact
1/4/2016 EECS 277B Adv. Semiconductor Devices © 2013 P. Burke Lecture 11, p. 10
Quantum point contact
B.J. van Wees et al. (1988), Phys. Rev. Lett., 60, 848.
1/4/2016 EECS 277B Adv. Semiconductor Devices © 2013 P. Burke Lecture 11, p. 11
0.7 anomaly
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Break junction
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Zhou, et al, Applied Physics Letters 67, 8 (1995) p. 1160.
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Electroplating
A.F.Morpurgo, C.M.Marcus and D. B. Robinson,
Controlled Fabrication of Metallic Electrodes with Atomic Separation, Appl. Phys. Lett. 74, 2084 (1999).