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Lesson 6 Magnetic field induced transport in nanostructures

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Lesson 6

Magnetic field induced transport in

nanostructures

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- Short review of the effects of a magnetic field on an electron in bulk system

- Effects of a magnetic field on an electron in 0D, 1D, 2D nanostructures (modification of the density of states!!)

- Quantization of the magnetic flux

- Quantum Hall effect

(3)

A) Effect of a uniform magnetic field on a crystal

(4)
(5)

Free electrons in y and z. Confined electrons in x (by harmonic potential)

Landau Levels

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Landau Levels

Key consequence: Changing the electrons density of states

n

3D

n

1D

Landau Levels

(8)

n

3D

n

1D

General effect of a magnetic field on the

electrons density of states: restriction by 2

dimensions

n

2D

n

0D

B) Low dimensional systems in magnetic fields

2D

0D

(9)

C) Density of states of a 2D system in a magnetic field (Towards the quantum Hall effect)

(10)

D) The Aharonov-Bohm effect: evidence for the magnetic flux quantization

L

>>L, B0Electrons interference effects

(11)

Webb experiment to prove the Aharonov-Bohm effect

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(15)
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E) 2D system in a magnetic field: Landau levels and filling factor

(17)

4 2 2

(18)
(19)

F) The quantum Hall effect

- Classical Hall effect

(20)
(21)
(22)

Quantum Hall effect

- Experimental facts and elementary theory of integer quantum Hall effect

Low-Dimensional

semiconductor (ex. 2DEG)

(23)

Rxx Rxy=RH

(24)

RK=h/e2 von Klitzing constant (quantum of resistance)

(25)

=

= ���

��� �2=

��2

�= �=h�2

��

= h

2 1

(26)

n=

(27)

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