33 years ago(25 January)

Already in 1963 I started in the PTB as a student trainee in the field of

“..precision measurements

of resistances, voltages and currents”.

33 years ago:

Max Planck Society

Practical unit of electrical resistance (international Ohm until

1948):Since 1884: column of mercury with diameter 1 mm²

and length 106.0 cmSince 1893: column of mercury with diameter 1 mm²

and length 106.3 cm

1960: Introduction of SI System

1 Ωint 1 Ωabs

up to 1990: resistance standard represented by wire resistor

since 1990:conventional value for thequantized Hall resistance

≡

25812,807 Ohm(fundamental constant)

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Max Planck: Ann.Physik 1, 69-122 (1900)

“....with the help of

fundamental constants

we have the possibility of establishing

units

of

length, time, mass, and temperature, which necessarily retain their significance for all cultures, even unearthly and nonhuman ones.“

Metrology and Fundamental Constants

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My First “Metrology”

Manuscript(submitted 30.5.1980 to PRL)

Starting Point of Quantum Hall S

cience

publication in Philosophical Transaction of Royal Society Aby Jürgen

Weis

and K.v.K. with the focus on the““Microscopic Picture of the QHEMicroscopic Picture of the QHE””

News from BIPM:The relevant Consultative Committees continue to monitor and review the situationin relation to potential redefinitions of the SI base units and

there is now a firm consensus in favour

of:

a kilogram definition based on the Planck constant, h;

a definition of the ampere based on a fixed value of the elementary charge, e;

a definition of the kelvin

based on the value of the Boltzmann constant, kB

a definition of the mole based on a fixed value of the Avogadro

constant, NA

c : fixed valueh : fixed valuee : fixed valuekB

:

fixed value NA

:fixed

value

NONO

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http://physics.nist.gov/cuu/Constants/index.html

The The ““fundamental constant Rfundamental constant RKK--9090

””will disappear in the new systemwill disappear in the new system

Max Planck SocietyRecommendationsComité International des Poids et Mesures

(October 4-6, 1988)

THE FUTURE IS NOW!

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http://physics.nist.gov/cuu/Constants/index.html

fixed value

NEW SI:NEW SI:

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von Klitzing constant

………….

…………

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Max Planck Society

KILOGRAM

AMPERE

VOLT

OHM

h: fixed value

e: fixed value

KJ = 2e/h: fixed value

RK = h/e²: fixed value

h

= 6,62606·10-34 Js

e

= 1,60217·10-19 C

2e/h = 4,8359658681026130158797233952001642001430714481909 ·1014Hz/V

h/e²

= 25812,98168142762768702549980273195633231220734657508139 Ω

A New SI System with fixed values for h

and e

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von Klitzing constant

25812,98168142762768702549980273195633231220734657508139

UNREALISTIC

25812,98168142762768702549980273195633231220734657508139

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fixed values for h/e2

and e

h/e

and

h obtained just by multiplications

Two of the four constants e, h, h/e, h/e2

will be fixed

SAVE THE VON KLITZING CONSTANT !SAVE THE VON KLITZING CONSTANT !

Max Planck Society

Two of the four constants e, h, h/e, h/e2

will be fixed

SAVE THE VON KLITZING CONSTANT !SAVE THE VON KLITZING CONSTANT !

Since h/e2 and 2e/h are the only “fundamental constants”

which can be measured with such a high precision, that conventional values were introduced for metrological applications, one may think to fix these numbers instead of fixing e and h which are not directly accessible by experiment with high accuracy.

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Alternative solution for the two fixed quantities containing h and e:

e determined from G0

· Φ0

h determined from G0

· (Φ0

)2

CONDUCTANCE QUANTUM

: G0

= 2e2/hFLUX QUANTUM: Φ0 = h/2e

Fixed Values for Fundamental Constants

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http://physics.nist.gov/cuu/Constants/index.html

finestructureconstant

quantized Hall resistance not quantized Hall resistance not useful for the determination useful for the determination

of of finestructurefinestructure

constantconstant

fixed value

NEW SI:NEW SI:

Max Planck SocietyFirst publication about theQUANTUM HALL EFFECT

wrong title within the new SI system

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What happens with the finestructure

constant αif

e, h and c are

fixed?

137/12

02

c

heSI SI ––

units:units:

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What happens with the finestructure

constant αif

e, h and c are

fixed?

137/12

02

c

heSI SI ––

units:units:

“OLD”

SI system: µ0

, ε0 and c are

fixed

numbers

“NEW”

SI system: µ0

and ε0 are

unknown

numbers

metrologia

36, 9-14 (1999)

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µ0

in “New SI”

System

µ0 has to be determined experimentally (QHE + Thomson-Lampert

Capacitor)

DEVIATIONS FROM THE PRESENT VALUE

µ0

= 4π·10-7

Vs/Awill highlight the incompetence of the

committee which fixes the values of h and e

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Are “Fundamental Constants”

Stable?

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How Stable are Fundamental Constants?

10 billion years ago: 510)116.0543.0(

corresponds to: 11610)35.140.6( yr

t

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11710)3.26.1( yr

(t) Not Confirmed by High Precision Spectroscopy

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Keck

European

Southern

Observatory

0

t

0

t

Were Fundamental Constants Different in the Past?

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Newest Speculation

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Different -values for Different Quasars?

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Most Recent Review about δα/δt

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Fundamental constants may change with time and space

but nobody has convinced the scientific community that such a change has been observed.

ANYWAY-FUNDAMENTAL CONSTANTS

ARE THE MOST STABLE QUANTITIES IN THE UNIVERSE

Conclusion

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Quantum Hall Effect and Metrology

Resistance h/e2

Voltage 2e/h

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Quantum Hall Effect and Metrology

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J. Phys.Chem. Ref. Data 37,1187 (2008)CODATA recommended values: 2006

Max Planck SocietyComparison between four differentQHE devices

Wheatstone bridge

input voltage

outputvoltage

RK1

RK4RK

3

RK2

.

RK = 25812,807xxx

Ω

x-digits unknown within our International System of Units (SI)International System of Units (SI)

Result:Result:RK

1,2,3,4 identical within an accuracy of some parts in 1011

(acquisition time t = 46 000 s)

RK1

RK3 RK

4

RK2

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QHE against wire resistor

TEGAM SR102 A2041297SR102

1.000

1.200

1.400

1.600

1.800

2.000

2.200

01/09/2002 09/11/2004 18/01/2007Date

(R-1

00)/1

00 (

)

10-7

wire resistors show time-dependent variations

Comparison of the 100 Ω

standard

resistor

at LNE with

a QHE device

(RK-90

≡

25812.807 Ω)

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QHEGalliumarsenide

QHEGalliumarsenide

10-11

QHESilicon

3.5 parts in 1010identical results between GaAs

and C with an accuracyof +0.4 ±

3 parts in 109

QHEGraphenenaturenanotechnology17 January 2010

Quantized Hall Resistance for Different Materials

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Conclusion from Experiment:

The value of the quantized Hall resistance is universal (GaAs, Si, C) with an uncertainty smaller than 1 part in 109.

Reproducibility of better than 1 part in 1011

is

observed (different devices from same wafer).

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Josephson Voltage Universal within 2 Parts in 1016

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THEORY: Corrections for RK

=h/e2 ?

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..we

obtain

the

final expression

for

the

von Klitzing constant:

2

22

21

180231

2 mceBeRK

correction

≈

10-20

QEDQED--CorrectionCorrection

to QHE?to QHE?

2

22 180231

cmE

ehR

e

CyclK

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PREREQUISITE FOR ACCURATE QHE MEASUREMENTS

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QHE Device

current flow?

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F.Dahlem, E.Ahlswede, J.Weis, and K.v.K.PRB 82, 121305 (2010)

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QHARS 129: 100 Hall bars in parallelQHARS 100:

16 Hall bars in series

+129 Hall bars in parallelRH = 16RK

/4130

100 (within

10-5)

W. Poirier et al., Metrologia 41, 285 (2004)

0

25

50

75

100

125

150

0 1 2 3 4 5 6 7 8 9 10 11B (T)

RH

C3 (B

+) (

)

05101520253035404550

Rxx

a ( )

T=1,3KI=100 µA

QHARS 129

QHARS 100

Hall bar width= 400 m

ns =4.3.1011

cm-2

= 310 000 cm2V-1s-1

Arrays of QHE Devices(Contact Resistances are Important)

B

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quantumfluxoneofareaelectrononebyoccupiedarea

BehF

2DEG in strong magnetic fields: 2DEG in strong magnetic fields: DISCRETE ENERGY SPECTRUMDISCRETE ENERGY SPECTRUM

Degeneracy for each Landau level:

ns

=eB/h

Energy

E Filling Factor 1

fully occupied energy level= incompressible electron system

Halleffect

UH

=(B/ns

e)·I

= h/e2·I

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COMPRESSIBLESTRIPE

(transition regionfrom occupied to

unoccupied states)

Fundamental QHE (=1)

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COMPRESSIBLESTRIPE

(transition regionfrom occupied to

unoccupied states)

Fundamental QHE (=1)

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SOURCE

DRAIN

ν=1

ν

= 0 1

compressible stripe

Ideal QHE Device at Filling Factor 1

2DEG

the compressible stripesadopt the electrochemical potential of source/drain

Hall-field drives a bulk current in theincompressible region of filling factor 1

SOURCESOURCE

DRAIN

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SOURCE

DRAIN

SOURCE

Contact without any influence on carrier

density in 2DEG

Contact withreduced carrierdensity in 2DEG

QHE at Bulk Filling Factor 2

=2

DRAIN

RSD

=h/2e2

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SOURCE

DRAIN

SOURCE

Contact without any influence on carrier

density in 2DEG

Contact withreduced carrierdensity in 2DEG

QHE at Bulk Filling Factor 2

=2

DRAIN

RSD

=h/2e2 RSD

=h/1e2

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10

0

20

Bulk Filling Factor,

0 4 8

23456

10

0

20

Magnetic Field (Tesla)

RSD

[01-

1]R

SD[0

11]

filling factor 3

filling factor 2

[011]

[01-1]

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Transmission line measurements:

Orientation Dependent “Contact Resistance”

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E. Ahlswede

et al., Physica

A 298 (2001)

Hall Potential drops associated to incompressible stripes (no screening)

00

Res ω.k2

dFΔω

Electron

mobility: 50 m²

/ Vs

dF

Force

Gradient Resonance

frequency

shift

2DES Hall potential profiles in the quantum Hall regime

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Properties of Different Contacts

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Contact Geometry Influences the Contact Resistance

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Music and Fundamental Constants“Synfonia

de Motu”

Wojciech

Kilar

Sinfonia

de motu, dedicated To Polish Physicists, was written in 2005 -

that is, the World Year of Physics. At the beginning of the score, the composer gives the works musical motto. It is a motif comprised of five notes: g-e-c-h-a. In this motif, the composer enciphered the fundamental concepts and values of physics: the gravitational constant, the electron charge, the speed of light, the Planck constant, and the atom.