the integral & fractional quantum hall effect
TRANSCRIPT
![Page 1: The integral & fractional quantum hall effect](https://reader036.vdocuments.mx/reader036/viewer/2022062821/589b8a251a28abc0098b50d1/html5/thumbnails/1.jpg)
THE INTEGRAL &FRACTIONAL QUANTUM
HALL EFFECT
SUDIPTO DAS
15PH40041
Presented by
IIT Kharagpur
![Page 2: The integral & fractional quantum hall effect](https://reader036.vdocuments.mx/reader036/viewer/2022062821/589b8a251a28abc0098b50d1/html5/thumbnails/2.jpg)
Outline
Classical to quantum hall effect
2 Dimensional Electron gas (2DEG) in B-field
Integral Quantum Hall Effect
Fractional Quantum Hall Effect
Composite Fermion
Application
![Page 3: The integral & fractional quantum hall effect](https://reader036.vdocuments.mx/reader036/viewer/2022062821/589b8a251a28abc0098b50d1/html5/thumbnails/3.jpg)
From Classical to Quantum hall effect
xx
LWRne
xyBRne
Electrical resistance
Hall Resistance
xy
xx
![Page 4: The integral & fractional quantum hall effect](https://reader036.vdocuments.mx/reader036/viewer/2022062821/589b8a251a28abc0098b50d1/html5/thumbnails/4.jpg)
Low temperature T<4KHigh Magnetic FieldHigh mobility > 2 x 104 cm2/Vs
From Classical to Quantum hall effect
xy
xx
xx
LWRne
xyBRne
Electrical resistance
Hall Resistance
![Page 5: The integral & fractional quantum hall effect](https://reader036.vdocuments.mx/reader036/viewer/2022062821/589b8a251a28abc0098b50d1/html5/thumbnails/5.jpg)
2DEG in quantizing B-field
2
*
12
H p eAm
Landau Gauge,
(0, )A xB
2
* *
( );
2 2yx
y y
eBx kpH p km m
2* 2 2
* *1 ( )
2 2;k c
xc
pH m x Bx
mem yk
k eBx
,
( 1/ 2)
( , ) ( ) y
n
ik yn k n k
E n
x y xx e
xk centre coordinate
![Page 6: The integral & fractional quantum hall effect](https://reader036.vdocuments.mx/reader036/viewer/2022062821/589b8a251a28abc0098b50d1/html5/thumbnails/6.jpg)
xq= xk + (h/eBL)
Thus flux between neighbouring states, ɸ0 = B.{ (xq-xk)L } = h/e Dirac flux
quanta
Degeneracy of States
![Page 7: The integral & fractional quantum hall effect](https://reader036.vdocuments.mx/reader036/viewer/2022062821/589b8a251a28abc0098b50d1/html5/thumbnails/7.jpg)
Integral Quantum Hall Effect
The Nobel Prize in Physics 1985 was awarded to Klaus von Klitzing "for the discovery of the quantized Hall effect”
![Page 8: The integral & fractional quantum hall effect](https://reader036.vdocuments.mx/reader036/viewer/2022062821/589b8a251a28abc0098b50d1/html5/thumbnails/8.jpg)
Integral Quantum Hall Effect
RH =
RH = hall Resistance i = filling factor (having values1,2,…. for Integer QHE)
xy
xx
![Page 9: The integral & fractional quantum hall effect](https://reader036.vdocuments.mx/reader036/viewer/2022062821/589b8a251a28abc0098b50d1/html5/thumbnails/9.jpg)
Fractional Quantum Hall Effect
From where this fractional terms came !!
![Page 10: The integral & fractional quantum hall effect](https://reader036.vdocuments.mx/reader036/viewer/2022062821/589b8a251a28abc0098b50d1/html5/thumbnails/10.jpg)
Electrons in B-field
Flux quantum:
ɸ0 = BA = Bπr2 = h/e
Degeneracy:
nɸ = B/ɸ0 = eB/h
Filling factor:
v = ne/ nɸ
![Page 11: The integral & fractional quantum hall effect](https://reader036.vdocuments.mx/reader036/viewer/2022062821/589b8a251a28abc0098b50d1/html5/thumbnails/11.jpg)
Fractional QHE
H. Stormer, Physics B 177 (1992)
![Page 12: The integral & fractional quantum hall effect](https://reader036.vdocuments.mx/reader036/viewer/2022062821/589b8a251a28abc0098b50d1/html5/thumbnails/12.jpg)
Flux Attachment Transformation
Fermionic:
1, Z2) = - (Z2, Z1) Fermionic Antisymmetry
Bosonic:
1, Z2) = - (Z2, Z1)eiπ Fermionic Antisymmetry1, Z2) = + (Z2, Z1) +2π phase shift
![Page 13: The integral & fractional quantum hall effect](https://reader036.vdocuments.mx/reader036/viewer/2022062821/589b8a251a28abc0098b50d1/html5/thumbnails/13.jpg)
Composite FermionsA new kind of quasi-
particlsJ. Jain
PRL. (1989)
V = 1/2B* CF = 0
B = magnetic fieldv = ne/nɸ = filling factor
B* = B - 2ɸ0ne = effective field v*CF = nCF/nɸ = effective v
![Page 14: The integral & fractional quantum hall effect](https://reader036.vdocuments.mx/reader036/viewer/2022062821/589b8a251a28abc0098b50d1/html5/thumbnails/14.jpg)
Composite Fermions
v = 1
v*CF = 1
v*CF = 2
v = 1/3 v*CF = p v =
v = 2/3 v*CF = p v =
q* CF= 2(e/3) + (-e) = - e/3 q*CF =
q* CF= 2(2e/3) + (-e) = + e/3 q*CF =
Charge of flux quantumΡbkgnd = +ene q+ = A Ρbkgnd = +ene/nɸ = +ev
![Page 15: The integral & fractional quantum hall effect](https://reader036.vdocuments.mx/reader036/viewer/2022062821/589b8a251a28abc0098b50d1/html5/thumbnails/15.jpg)
Fractional QHE
![Page 16: The integral & fractional quantum hall effect](https://reader036.vdocuments.mx/reader036/viewer/2022062821/589b8a251a28abc0098b50d1/html5/thumbnails/16.jpg)
Applications Used as Magnetometers, i.e. to measure magnetic field.
Hall effect sensor is also used as Current Sensor.
Magnetic Position Sensing in Brushless DC Electric Motors
Automotive fuel level indicator.
Spacecraft propulsion.
Quantum hall effect can be used for a determination of h/e2 or as a resistance standard.
Since the inverse fine structure constant α-1 is more or less identical h/e2 , high-precision measurements of the quantized hall resistance are important for all areas in physics that are connected with the fine structure constant.
![Page 17: The integral & fractional quantum hall effect](https://reader036.vdocuments.mx/reader036/viewer/2022062821/589b8a251a28abc0098b50d1/html5/thumbnails/17.jpg)
THANK YOU