3. Lectures of Superconductivity given at Palai - Physics - Indian ...

Superconductivity
A nine-hour journey
Vijay B. Shenoy
(shenoy@physics.iisc.ernet.in)
Indian Institute of Science, Bangalore
St. Thomas College, Palai, March 11, 2011
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Acknowledgement
2 / 41

Acknowledgement
Collaborators: Sandeep Pathak, Somnath Bhowmick, Jayanth
Vyasanakere, Yogeshwar Saraswat, Sudeep Ghosh, Amal Medhi,
Shizhong Zhang
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Acknowledgement
Collaborators: Sandeep Pathak, Somnath Bhowmick, Jayanth
Vyasanakere, Yogeshwar Saraswat, Sudeep Ghosh, Amal Medhi,
Shizhong Zhang
Thanks to: H. R. Krishnamurthy (IISc), T. V. Ramakrishnan
(BHU/IISc), M. Randeria (OSU), N. Trivedi (OSU), G. Baskaran
(IMSc), R. Shankar (IMSc), T.-L. Ho (OSU)
2 / 41

Acknowledgement
Collaborators: Sandeep Pathak, Somnath Bhowmick, Jayanth
Vyasanakere, Yogeshwar Saraswat, Sudeep Ghosh, Amal Medhi,
Shizhong Zhang
Thanks to: H. R. Krishnamurthy (IISc), T. V. Ramakrishnan
(BHU/IISc), M. Randeria (OSU), N. Trivedi (OSU), G. Baskaran
(IMSc), R. Shankar (IMSc), T.-L. Ho (OSU)
Funding: Department of Science and Technology, Department of
Atomic Energy
2 / 41

Motivation: Why Bother?
3 / 41

Motivation: Why Bother?
Superconducting state has zero resistance...can distribute power
without losses
3 / 41

Motivation: Why Bother?
Superconducting state has zero resistance...can distribute power
without losses
“Unfortunately” superconductivity is a low-temperature
phenomenon...need room-temperature superconductors
3 / 41

Motivation: Why Bother?
Superconducting state has zero resistance...can distribute power
without losses
“Unfortunately” superconductivity is a low-temperature
phenomenon...need room-temperature superconductors
...
3 / 41

Motivation: Why Bother?
Superconducting state has zero resistance...can distribute power
without losses
“Unfortunately” superconductivity is a low-temperature
phenomenon...need room-temperature superconductors
...
Superconductivity – taught us lots of “new physics”
3 / 41

Motivation: Why Bother?
Superconducting state has zero resistance...can distribute power
without losses
“Unfortunately” superconductivity is a low-temperature
phenomenon...need room-temperature superconductors
...
Superconductivity – taught us lots of “new physics”
Ideas applicable from condensed matter physics, astrophysics, high
energy physics etc.
3 / 41

Motivation: Why Bother?
Superconducting state has zero resistance...can distribute power
without losses
“Unfortunately” superconductivity is a low-temperature
phenomenon...need room-temperature superconductors
...
Superconductivity – taught us lots of “new physics”
Ideas applicable from condensed matter physics, astrophysics, high
energy physics etc.
...
3 / 41

Motivation: Why Bother?
Superconducting state has zero resistance...can distribute power
without losses
“Unfortunately” superconductivity is a low-temperature
phenomenon...need room-temperature superconductors
...
Superconductivity – taught us lots of “new physics”
Ideas applicable from condensed matter physics, astrophysics, high
energy physics etc.
...
Above all...
3 / 41

Motivation: Why Bother?
Superconducting state has zero resistance...can distribute power
without losses
“Unfortunately” superconductivity is a low-temperature
phenomenon...need room-temperature superconductors
...
Superconductivity – taught us lots of “new physics”
Ideas applicable from condensed matter physics, astrophysics, high
energy physics etc.
...
Above all...it is superinteresting!
3 / 41

Overall Plan of the Lectures
4 / 41

Overall Plan of the Lectures
Goal: To prepare ourselves to know when to be surprised
4 / 41

Overall Plan of the Lectures
Goal: To prepare ourselves to know when to be surprised
Six lectures will be organized as:
4 / 41

Overall Plan of the Lectures
Goal: To prepare ourselves to know when to be surprised
Six lectures will be organized as:
◮ Review of metal physics
4 / 41

Overall Plan of the Lectures
Goal: To prepare ourselves to know when to be surprised
Six lectures will be organized as:
◮ Review of metal physics
◮ Superconducting phenomenon
4 / 41

Overall Plan of the Lectures
Goal: To prepare ourselves to know when to be surprised
Six lectures will be organized as:
◮ Review of metal physics
◮ Superconducting phenomenon
◮ Phenomenological approaches
4 / 41

Overall Plan of the Lectures
Goal: To prepare ourselves to know when to be surprised
Six lectures will be organized as:
◮ Review of metal physics
◮ Superconducting phenomenon
◮ Phenomenological approaches
◮ Microscopic theory
4 / 41

Overall Plan of the Lectures
Goal: To prepare ourselves to know when to be surprised
Six lectures will be organized as:
◮ Review of metal physics
◮ Superconducting phenomenon
◮ Phenomenological approaches
◮ Microscopic theory
◮ Superconducting effects
4 / 41

Overall Plan of the Lectures
Goal: To prepare ourselves to know when to be surprised
Six lectures will be organized as:
◮ Review of metal physics
◮ Superconducting phenomenon
◮ Phenomenological approaches
◮ Microscopic theory
◮ Superconducting effects
◮ Current problems – from Curpates to Cold Atoms
4 / 41

Prerequisites
5 / 41

Prerequisites
Must:
5 / 41

Prerequisites
Must:
◮ Understanding of classical mechanics and electrodynamics
5 / 41

Prerequisites
Must:
◮ Understanding of classical mechanics and electrodynamics
◮ Working knowledge of quantum mechanics (at the level of Griffiths)
5 / 41

Prerequisites
Must:
◮ Understanding of classical mechanics and electrodynamics
◮ Working knowledge of quantum mechanics (at the level of Griffiths)
◮ Statistical mechanics and thermodynamics (at the level of Kittel and
Kromer)
5 / 41

Prerequisites
Must:
◮ Understanding of classical mechanics and electrodynamics
◮ Working knowledge of quantum mechanics (at the level of Griffiths)
◮ Statistical mechanics and thermodynamics (at the level of Kittel and
Kromer)
Desirable:
5 / 41

Prerequisites
Must:
◮ Understanding of classical mechanics and electrodynamics
◮ Working knowledge of quantum mechanics (at the level of Griffiths)
◮ Statistical mechanics and thermodynamics (at the level of Kittel and
Kromer)
Desirable:
◮ Solid state physics (at the level of Kittel)
5 / 41

Prerequisites
Must:
◮ Understanding of classical mechanics and electrodynamics
◮ Working knowledge of quantum mechanics (at the level of Griffiths)
◮ Statistical mechanics and thermodynamics (at the level of Kittel and
Kromer)
Desirable:
◮ Solid state physics (at the level of Kittel)
◮ Ideas of Phase Tansitions (at the level of Yeomans)
5 / 41

Prerequisites
Must:
◮ Understanding of classical mechanics and electrodynamics
◮ Working knowledge of quantum mechanics (at the level of Griffiths)
◮ Statistical mechanics and thermodynamics (at the level of Kittel and
Kromer)
Desirable:
◮ Solid state physics (at the level of Kittel)
◮ Ideas of Phase Tansitions (at the level of Yeomans)
◮ Ideas of “Second quantization” (at the level of Ziman)
5 / 41

References
6 / 41

References
Ramakrishnan, T. V. and Rao, C. N. R., Superconductivity Today –
an excellent elementary introduction to superconductivity
6 / 41

References
Ramakrishnan, T. V. and Rao, C. N. R., Superconductivity Today –
an excellent elementary introduction to superconductivity
Ibach, H. and Lüth, H., Solid State Physics – contains a very nice
discussion of superconductivity (and many other solid state physics
topics)
6 / 41

References
Ramakrishnan, T. V. and Rao, C. N. R., Superconductivity Today –
an excellent elementary introduction to superconductivity
Ibach, H. and Lüth, H., Solid State Physics – contains a very nice
discussion of superconductivity (and many other solid state physics
topics)
Tilley and Tilley, Superconductivity and Superfluidity – a very nice
approach with a unified view of superfluidity of 4 He and
superconductivity of metals
6 / 41

References
Ramakrishnan, T. V. and Rao, C. N. R., Superconductivity Today –
an excellent elementary introduction to superconductivity
Ibach, H. and Lüth, H., Solid State Physics – contains a very nice
discussion of superconductivity (and many other solid state physics
topics)
Tilley and Tilley, Superconductivity and Superfluidity – a very nice
approach with a unified view of superfluidity of 4 He and
superconductivity of metals
Tinkham, M., Superconductivity – Standard text book, very nice in
parts
6 / 41

References
Ramakrishnan, T. V. and Rao, C. N. R., Superconductivity Today –
an excellent elementary introduction to superconductivity
Ibach, H. and Lüth, H., Solid State Physics – contains a very nice
discussion of superconductivity (and many other solid state physics
topics)
Tilley and Tilley, Superconductivity and Superfluidity – a very nice
approach with a unified view of superfluidity of 4 He and
superconductivity of metals
Tinkham, M., Superconductivity – Standard text book, very nice in
parts
de Gennes, P., Superconductivity of Metals and Alloys – My favourite
6 / 41

References
Ramakrishnan, T. V. and Rao, C. N. R., Superconductivity Today –
an excellent elementary introduction to superconductivity
Ibach, H. and Lüth, H., Solid State Physics – contains a very nice
discussion of superconductivity (and many other solid state physics
topics)
Tilley and Tilley, Superconductivity and Superfluidity – a very nice
approach with a unified view of superfluidity of 4 He and
superconductivity of metals
Tinkham, M., Superconductivity – Standard text book, very nice in
parts
de Gennes, P., Superconductivity of Metals and Alloys – My favourite
Leggett, A. J., Quantum Liquids – A very original and wonderfully
clear exposition from a Nobel laureate –a must read!
6 / 41

References
Ramakrishnan, T. V. and Rao, C. N. R., Superconductivity Today –
an excellent elementary introduction to superconductivity
Ibach, H. and Lüth, H., Solid State Physics – contains a very nice
discussion of superconductivity (and many other solid state physics
topics)
Tilley and Tilley, Superconductivity and Superfluidity – a very nice
approach with a unified view of superfluidity of 4 He and
superconductivity of metals
Tinkham, M., Superconductivity – Standard text book, very nice in
parts
de Gennes, P., Superconductivity of Metals and Alloys – My favourite
Leggett, A. J., Quantum Liquids – A very original and wonderfully
clear exposition from a Nobel laureate –a must read!
Parks, R. D. (Editor), Superconductivity – Wonderful collection of
chapters by the well known authors
6 / 41

References
Ramakrishnan, T. V. and Rao, C. N. R., Superconductivity Today –
an excellent elementary introduction to superconductivity
Ibach, H. and Lüth, H., Solid State Physics – contains a very nice
discussion of superconductivity (and many other solid state physics
topics)
Tilley and Tilley, Superconductivity and Superfluidity – a very nice
approach with a unified view of superfluidity of 4 He and
superconductivity of metals
Tinkham, M., Superconductivity – Standard text book, very nice in
parts
de Gennes, P., Superconductivity of Metals and Alloys – My favourite
Leggett, A. J., Quantum Liquids – A very original and wonderfully
clear exposition from a Nobel laureate –a must read!
Parks, R. D. (Editor), Superconductivity – Wonderful collection of
chapters by the well known authors
Bennemann, K. H. and Ketterson, J. B. (Editors), Superconductivity
– Modern version of Parks
6 / 41

What Participants Should Expect to Gain
7 / 41

What Participants Should Expect to Gain
A review of the theory of metals
7 / 41

What Participants Should Expect to Gain
A review of the theory of metals
An understanding of the phenomenology of superconductivity in
metals...and why is it surprising
7 / 41

What Participants Should Expect to Gain
A review of the theory of metals
An understanding of the phenomenology of superconductivity in
metals...and why is it surprising
Construction of phenomenological theories based on phenomena
7 / 41

What Participants Should Expect to Gain
A review of the theory of metals
An understanding of the phenomenology of superconductivity in
metals...and why is it surprising
Construction of phenomenological theories based on phenomena
Ideas of broken symmetry and phase transition
7 / 41

What Participants Should Expect to Gain
A review of the theory of metals
An understanding of the phenomenology of superconductivity in
metals...and why is it surprising
Construction of phenomenological theories based on phenomena
Ideas of broken symmetry and phase transition
Ideas of mean field theory (both “quantum” and “statistical”)
7 / 41

What Participants Should Expect to Gain
A review of the theory of metals
An understanding of the phenomenology of superconductivity in
metals...and why is it surprising
Construction of phenomenological theories based on phenomena
Ideas of broken symmetry and phase transition
Ideas of mean field theory (both “quantum” and “statistical”)
Ideas of macroscopic quantum phenomenon
7 / 41

What Participants Should Expect to Gain
A review of the theory of metals
An understanding of the phenomenology of superconductivity in
metals...and why is it surprising
Construction of phenomenological theories based on phenomena
Ideas of broken symmetry and phase transition
Ideas of mean field theory (both “quantum” and “statistical”)
Ideas of macroscopic quantum phenomenon
A glimpse of some open problems...in particular why the cuprates are
fascinating
7 / 41

How it all Started!
Kamerlingh Onnes @ Leiden was obsessed with low temperatures...he
liquified helium!
8 / 41

How it all Started!
Kamerlingh Onnes @ Leiden was obsessed with low temperatures...he
liquified helium!
8 / 41

How it all Started!
Kamerlingh Onnes @ Leiden was obsessed with low temperatures...he
liquified helium!
(Wikipedia)
8 / 41

How it all Started!
Kamerlingh Onnes @ Leiden was obsessed with low temperatures...he
liquified helium!
(Wikipedia)
Discovered (1911) that the resistance of mercury drops to “zero”
below 4.2K!
8 / 41

How it all Started!
Kamerlingh Onnes @ Leiden was obsessed with low temperatures...he
liquified helium!
(Wikipedia)
Discovered (1911) that the resistance of mercury drops to “zero”
below 4.2K!
Aptly called superconductivity Not sure: By whom?
8 / 41

Superconductivity “everywhere”
Most elemental metals yield to the charms of superconductivity...
9 / 41

Superconductivity “everywhere”
Most elemental metals yield to the charms of superconductivity...
(From somewhere on the web!)
9 / 41

Superconductivity “everywhere”
Most elemental metals yield to the charms of superconductivity...
(From somewhere on the web!)
...perhaps under duress!
9 / 41

Superconductivity Period Table
Periodic Table of Superconductivity
Some elements have to be pressurised!
(dedicated to the memory of Bernd Matthias)
30 elements superconduct at ambient pressure, 23 more superconduct at high pressure.
(From somewhere on the web!)
10 / 41

Superconductivity Period Table
Periodic Table of Superconductivity
Some elements have to be pressurised!
(dedicated to the memory of Bernd Matthias)
30 elements superconduct at ambient pressure, 23 more superconduct at high pressure.
(From somewhere on the web!)
10 / 41

Superconductivity in Metals and Alloys
Some of the “best” conventional superconductors are
alloys/intermetallics
11 / 41

Fig. 1.3. Histor
first 70 years f
tivity in 1911.
interest in the
Superconductivity in Metals and Alloys
Some of the “best” conventional superconductors are
alloys/intermetallics
Fig. 1.2
(blue)
superc
tion m
Other
marke
tempe
(Benemmann and Ketterson)
11 / 41

Fig. 1.3. Histor
first 70 years f
tivity in 1911.
interest in the
Superconductivity in Metals and Alloys
Some of the “best” conventional superconductors are
alloys/intermetallics
Fig. 1.2
(blue)
superc
tion m
Other
marke
tempe
(Benemmann and Ketterson)
Key observation: Almost all metallic elements and alloys become
superconducting Question: Can an insulator become a superconductor?
11 / 41

Fig. 1.3. Histor
first 70 years f
tivity in 1911.
interest in the
Superconductivity in Metals and Alloys
Some of the “best” conventional superconductors are
alloys/intermetallics
Fig. 1.2
(blue)
superc
tion m
Other
marke
tempe
(Benemmann and Ketterson)
Key observation: Almost all metallic elements and alloys become
superconducting Question: Can an insulator become a superconductor?
Need to understand what a metal is!
11 / 41

What is a Metal? – Survey of Metallic Properties
12 / 41

What is a Metal? – Survey of Metallic Properties
Thermodynamic properties
12 / 41

What is a Metal? – Survey of Metallic Properties
Thermodynamic properties
Magnetic properties
12 / 41

What is a Metal? – Survey of Metallic Properties
Thermodynamic properties
Magnetic properties
Transport properties
12 / 41

Metals – Thermodynamic Properties
13 / 41

Metals – Thermodynamic 6.4 Properties The Specific Heat Capacity of Electrons in Me
Fig. 6.8. Plot of c v /T (Ibach againstand T 2 Lüth) for copper. The experimental points (*
from two separate measurements [6.3]
Table 6.2. Comparison of experimentally determined values of the coe cien
nic specific heat with values calculated using the free-electron-gas model. At
13 / 41
3 3

Metals – Thermodynamic 6.4 Properties The Specific Heat Capacity of Electrons in Me
Fig. 6.8. Plot of c v /T (Ibach againstand T 2 Lüth) for copper. The experimental points (*
from two separate measurements [6.3]
Low temperature specific heat goes as
Table 6.2. ComparisonC of V
metal experimentally = βT 3 + γT determined values of the coe cien
nic specific heat with values calculated using the free-electron-gas model. At
13 / 41
3 3

Metals – Magnetic Properties
14 / 41

Metals – Magnetic Properties
Focus on “non-magnetic” metals
14 / 41

Metals – Magnetic Properties
Focus on “non-magnetic” metals
14 / 41

Metals – Magnetic Properties
Focus on “non-magnetic” metals
Magnetic susceptibility is essentially independent of temperature!
14 / 41

tribution R ph (T)!1/r ph to the resistivity of metals:
Metals – DC Electrical H=T …
Transport
x 5 dx
R ph …T† ˆA…T=H† 5
At low temperatures, this varies as T
Electrical resistivity of metals
5 .
0
…e x 1†…1 e x †
…9:62†
260 9 Motion of Electrons and Transport Phenomen
(Ibach and Lüth)
Fig. 9.7. R
of coppersitions.
(A
Fig. 9.6. Electrical resistance of sodium compared to the value at 290 K as a function of
temperature. The data points (*, *, `) were measured for three different samples with
differing defect concentrations. (After [9.3])
According to (9.59) we can write the resistivit
as the sum of a temperature-independent residual
fects) and a part due to phonon scattering R ph (T)
ture at high temperature:
R ˆ R ph …T†‡R def :
This behavior, which was first identified experim
thiesen's Rule. Note that (9.63) is valid only appro
Figure 9.6 shows the experimentally measured 15 / 41

tribution R ph (T)!1/r ph to the resistivity of metals:
Metals – DC Electrical H=T …
Transport
x 5 dx
R ph …T† ˆA…T=H† 5
At low temperatures, this varies as T
Electrical resistivity of metals
5 .
0
…e x 1†…1 e x †
…9:62†
260 9 Motion of Electrons and Transport Phenomen
(Ibach and Lüth)
Fig. 9.7. R
of coppersitions.
(A
Fig. 9.6. Electrical resistance of sodium compared to the value at 290 K as a function of
temperature. The data points (*, *, `) were measured for three different samples with
differing defect concentrations. (After [9.3])
According to (9.59) we can write the resistivit
as the sum of a temperature-independent residual
fects) and a part due to phonon scattering R ph (T)
ture at high temperature:
R ˆ R ph …T†‡R def :
This behavior, which was first identified experim
thiesen's Rule. Note that (9.63) is valid only appro
Figure 9.6 shows the experimentally measured 15 / 41
Resistivity regimes

tribution R ph (T)!1/r ph to the resistivity of metals:
Metals – DC Electrical H=T …
Transport
x 5 dx
R ph …T† ˆA…T=H† 5
At low temperatures, this varies as T
Electrical resistivity of metals
5 .
0
…e x 1†…1 e x †
…9:62†
260 9 Motion of Electrons and Transport Phenomen
(Ibach and Lüth)
Fig. 9.7. R
of coppersitions.
(A
Fig. 9.6. Electrical resistance of sodium compared to the value at 290 K as a function of
temperature. The data points (*, *, `) were measured for three different samples with
differing defect concentrations. (After [9.3])
According to (9.59) we can write the resistivit
as the sum of a temperature-independent residual
ρ = ρ 0 + A 1 T 2 “Low Temperature”
fects) and a part due to phonon scattering R ph (T)
ture at high temperature:
ρ = ρ 0 + A 2 T 5 “Intermediate Temperature”
R ˆ R ph …T†‡R def :
ρ = ρ
This behavior, which was first identified experim
0 + A 3 T “High Temperature”
thiesen's Rule. Note that (9.63) is valid only appro
Figure 9.6 shows the experimentally measured
Resistivity regimes

tribution R ph (T)!1/r ph to the resistivity of metals:
Metals – DC Electrical H=T …
Transport
x 5 dx
R ph …T† ˆA…T=H† 5
At low temperatures, this varies as T
Electrical resistivity of metals
5 .
0
…e x 1†…1 e x †
…9:62†
260 9 Motion of Electrons and Transport Phenomen
(Ibach and Lüth)
Fig. 9.7. R
of coppersitions.
(A
Fig. 9.6. Electrical resistance of sodium compared to the value at 290 K as a function of
temperature. The data points (*, *, `) were measured for three different samples with
differing defect concentrations. (After [9.3])
According to (9.59) we can write the resistivit
as the sum of a temperature-independent residual
ρ = ρ 0 + A 1 T 2 “Low Temperature”
fects) and a part due to phonon scattering R ph (T)
ture at high temperature:
R ˆ R ph …T†‡R def :
ρ = ρ
This behavior, which was first identified experim
0 + A 3 T “High Temperature”
thiesen's Rule. Note that (9.63) is valid only appro
Figure 9.6 shows the experimentally measured
Resistivity regimes

tribution R ph (T)!1/r ph to the resistivity of metals:
Metals – DC Electrical H=T …
Transport
x 5 dx
R ph …T† ˆA…T=H† 5
At low temperatures, this varies as T
Electrical resistivity of metals
5 .
0
…e x 1†…1 e x †
…9:62†
260 9 Motion of Electrons and Transport Phenomen
(Ibach and Lüth)
Fig. 9.7. R
of coppersitions.
(A
Fig. 9.6. Electrical resistance of sodium compared to the value at 290 K as a function of
temperature. The data points (*, *, `) were measured for three different samples with
differing defect concentrations. (After [9.3])
According to (9.59) we can write the resistivit
as the sum of a temperature-independent residual
ρ = ρ 0 + A 1 T 2 “Low Temperature”
fects) and a part due to phonon scattering R ph (T)
ture at high temperature:
ρ = ρ 0 + A 2 T 5 “Intermediate Temperature”
R ˆ R ph …T†‡R def :
ρ = ρ
This behavior, which was first identified experim
0 + A 3 T “High Temperature”
thiesen's Rule. Note that (9.63) is valid only appro
Figure 9.6 shows the experimentally measured 15 / 41
Resistivity regimes

Metals: AC Conductivity
16 / 41

Metals: AC Conductivity
All metals show a “Drude peak” in their AC conductivity
16 / 41

Metals: AC Conductivity
All metals show a “Drude peak” in their AC conductivity
ΣΩ
Σ 0
1.0
0.8
0.6
0.4
0.2
2 4 6 8 10
Τ Ω
(Schematic)
16 / 41

Metals: AC Conductivity
All metals show a “Drude peak” in their AC conductivity
ΣΩ
Σ 0
1.0
0.8
0.6
0.4
0.2
2 4 6 8 10
Τ Ω
(Schematic)
σ 0 is the DC conductivity, τ is “some” time scale
16 / 41

Metals: There’s More!
Widemann-Franz Law
17 / 41

Metals: There’s More!
Widemann-Franz Law – Ratio of thermal conductivity and DC
electrical conductivity is proportional to temperature
9.7 The Wiede
Table 9.1. Experimentally L =
κ derived values of the Lorentz
σ 0 T
number at 0°C, L =k E /rT, deduced from published
L is INDEPENDENT data for electrical of the metal!! and thermal conductivity
Metal L(10 ±8 WX/K 2 )
Na 2.10
Ag 2.31
Au 2.35
Cu 2.23
Pb 2.47
Pt 2.51
(Ibach and Lüth)
17 / 41

Metals: There’s More!
Widemann-Franz Law – Ratio of thermal conductivity and DC
electrical conductivity is proportional to temperature
9.7 The Wiede
Table 9.1. Experimentally L =
κ derived values of the Lorentz
σ 0 T
number at 0°C, L =k E /rT, deduced from published
L is INDEPENDENT data for electrical of the metal!! and thermal conductivity
Metal L(10 ±8 WX/K 2 )
Na 2.10
Ag 2.31
Au 2.35
Cu 2.23
Pb 2.47
Pt 2.51
...getting intriguing!
(Ibach and Lüth)
17 / 41

Metals: There’s EVEN More!
Universal resistivity!
9.6 Thermoelectric Effects
Fig. 9.8. The universal cur
the reduced resistance (R/
a function of reduced te
plotted for a number of di
ture (T/H, where H is the
temperature). Data poin
metals
(Ibach and Lüth)
9.6 Thermoelectric E€ects
18 / 41

Metals: There’s EVEN More!
Universal resistivity!
9.6 Thermoelectric Effects
Why?
(Ibach and Lüth)
9.6 Thermoelectric E€ects
Fig. 9.8. The universal cur
the reduced resistance (R/
a function of reduced te
plotted for a number of di
ture (T/H, where H is the
temperature). Data poin
metals
18 / 41

What is a Metal?
A state of matter with “Universal” properties in
19 / 41

What is a Metal?
A state of matter with “Universal” properties in
Thermodynamics
19 / 41

What is a Metal?
A state of matter with “Universal” properties in
Thermodynamics
Magnetism
19 / 41

What is a Metal?
A state of matter with “Universal” properties in
Thermodynamics
Magnetism
Transport
19 / 41

What is a Metal?
A state of matter with “Universal” properties in
Thermodynamics
Magnetism
Transport
What is the simplest theory that describes this?
19 / 41

Metals
Notes on simple model of metals
20 / 41

Metals
Notes on simple model of metals
Notes on sat-mech of metals
20 / 41

Metals
Notes on simple model of metals
Notes on sat-mech of metals
Magnetism of metals
20 / 41

Metals
Notes on simple model of metals
Notes on sat-mech of metals
Magnetism of metals
...
This gets the T of the specific heat...but it is really T + T 3 !
20 / 41

Metals
Notes on simple model of metals
Notes on sat-mech of metals
Magnetism of metals
...
This gets the T of the specific heat...but it is really T + T 3 !
...
We need to include phonons
20 / 41

Metals
Notes on simple model of metals
Notes on sat-mech of metals
Magnetism of metals
...
This gets the T of the specific heat...but it is really T + T 3 !
...
We need to include phonons
Back to stat-mech notes
20 / 41

Metals
Notes on simple model of metals
Notes on sat-mech of metals
Magnetism of metals
...
This gets the T of the specific heat...but it is really T + T 3 !
...
We need to include phonons
Back to stat-mech notes
Notes of transport of metals
20 / 41

Metals
Notes on simple model of metals
Notes on sat-mech of metals
Magnetism of metals
...
This gets the T of the specific heat...but it is really T + T 3 !
...
We need to include phonons
Back to stat-mech notes
Notes of transport of metals
...
A gas of non interacting electrons and a gas of non interacting
phonons which mutually interact provides the simplest picture of
metals!
20 / 41

Metals
Notes on simple model of metals
Notes on sat-mech of metals
Magnetism of metals
...
This gets the T of the specific heat...but it is really T + T 3 !
...
We need to include phonons
Back to stat-mech notes
Notes of transport of metals
...
A gas of non interacting electrons and a gas of non interacting
phonons which mutually interact provides the simplest picture of
metals!
Question: What about Coulomb interaction?
20 / 41

Metals
Notes on simple model of metals
Notes on sat-mech of metals
Magnetism of metals
...
This gets the T of the specific heat...but it is really T + T 3 !
...
We need to include phonons
Back to stat-mech notes
Notes of transport of metals
...
A gas of non interacting electrons and a gas of non interacting
phonons which mutually interact provides the simplest picture of
metals!
Question: What about Coulomb interaction?
Question: Are there phenomenon that this model cannot explain?
20 / 41

On to Superconductivity
Kamerlingh Onnes @ Leiden was obsessed with low temperatures...he
liquified helium!
21 / 41

On to Superconductivity
Kamerlingh Onnes @ Leiden was obsessed with low temperatures...he
liquified helium!
21 / 41

On to Superconductivity
Kamerlingh Onnes @ Leiden was obsessed with low temperatures...he
liquified helium!
(Wikipedia)
21 / 41

On to Superconductivity
Kamerlingh Onnes @ Leiden was obsessed with low temperatures...he
liquified helium!
(Wikipedia)
Discovered (1911) that the resistance of mercury drops to “zero”
below 4.2K!
21 / 41

On to Superconductivity
Kamerlingh Onnes @ Leiden was obsessed with low temperatures...he
liquified helium!
(Wikipedia)
Discovered (1911) that the resistance of mercury drops to “zero”
below 4.2K!
Aptly called superconductivity
21 / 41

Superconductivity “everywhere”
Most elemental metals yield to the charms of superconductivity...
22 / 41

Superconductivity “everywhere”
Most elemental metals yield to the charms of superconductivity...
(From somewhere on the web!)
22 / 41

Superconductivity “everywhere”
Most elemental metals yield to the charms of superconductivity...
(From somewhere on the web!)
...perhaps under duress!
22 / 41

Superconductivity Period Table
Periodic Table of Superconductivity
Some elements have to be pressurised!
(dedicated to the memory of Bernd Matthias)
30 elements superconduct at ambient pressure, 23 more superconduct at high pressure.
(From somewhere on the web!)
23 / 41

Superconductivity Period Table
Periodic Table of Superconductivity
Some elements have to be pressurised!
(dedicated to the memory of Bernd Matthias)
30 elements superconduct at ambient pressure, 23 more superconduct at high pressure.
(From somewhere on the web!)
23 / 41

Superconductivity in Metals and Alloys
Some of the “best” conventional superconductors are
alloys/intermetallics
24 / 41

Fig. 1.3. Histor
first 70 years f
tivity in 1911.
interest in the
Superconductivity in Metals and Alloys
Some of the “best” conventional superconductors are
alloys/intermetallics
Fig. 1.2
(blue)
superc
tion m
Other
marke
tempe
(Benemmann and Ketterson)
24 / 41

Fig. 1.3. Histor
first 70 years f
tivity in 1911.
interest in the
Superconductivity in Metals and Alloys
Some of the “best” conventional superconductors are
alloys/intermetallics
Fig. 1.2
(blue)
superc
tion m
Other
marke
tempe
(Benemmann and Ketterson)
Key observation: Almost all metallic elements and alloys become
superconducting
24 / 41

Fig. 1.3. Histor
first 70 years f
tivity in 1911.
interest in the
Superconductivity in Metals and Alloys
Some of the “best” conventional superconductors are
alloys/intermetallics
Fig. 1.2
(blue)
superc
tion m
Other
marke
tempe
(Benemmann and Ketterson)
Key observation: Almost all metallic elements and alloys become
superconducting
Strategy: Explore other properties and describe the state using the
24 / 41

Meissner Effect
Superconductor does not like to have an electric field inside it (just
like a normal metal)...
25 / 41

Meissner Effect
Superconductor does not like to have an electric field inside it (just
like a normal metal)...
Meissner-Ochsenfeld found that a superconductor also expels all
magnetic field...
25 / 41

Meissner Effect
Superconductor does not like to have an electric field inside it (just
like a normal metal)...
Meissner-Ochsenfeld found that a superconductor also expels all
magnetic field...superconductors hates electromagnetic fields!!
25 / 41

Meissner Effect
Superconductor does not like to have an electric field inside it (just
like a normal metal)...
Meissner-Ochsenfeld found that a superconductor also expels all
magnetic field...superconductors hates electromagnetic fields!!
The magnetic susceptibility χ = M/H = −1 for a superconductor –
perfect diamagnet
25 / 41

Meissner Effect
Superconductor does not like to have an electric field inside it (just
like a normal metal)...
Meissner-Ochsenfeld found that a superconductor also expels all
magnetic field...superconductors hates electromagnetic fields!!
The magnetic susceptibility χ = M/H = −1 for a superconductor –
perfect diamagnet
...
25 / 41

Meissner Effect
Superconductor does not like to have an electric field inside it (just
like a normal metal)...
Meissner-Ochsenfeld found that a superconductor also expels all
magnetic field...superconductors hates electromagnetic fields!!
The magnetic susceptibility χ = M/H = −1 for a superconductor –
perfect diamagnet
...
This leads to spectacular effects...
25 / 41

Meissner Effect
Superconductor does not like to have an electric field inside it (just
like a normal metal)...
Meissner-Ochsenfeld found that a superconductor also expels all
magnetic field...superconductors hates electromagnetic fields!!
The magnetic susceptibility χ = M/H = −1 for a superconductor –
perfect diamagnet
...
This leads to spectacular effects...and technological applications!
25 / 41

Penetration Depth
The magnetic field can penetrate into the superconductor near the
surfaces...but dies exponentially as we move into the bulk
26 / 41

Penetration Depth
The magnetic field can penetrate into the superconductor near the
surfaces...but dies exponentially as we move into the bulk
There is a length scale associated with this decay...called the
penetration depth
26 / 41

Penetration Depth
The magnetic field can penetrate into the superconductor near the
surfaces...but dies exponentially as we move into the bulk
There is a length scale associated with this decay...called the
penetration depth
Most interestingly, the penetration depth is a function temperature...
26 / 41

Penetration Depth
The magnetic field can penetrate into the superconductor near the
surfaces...but dies exponentially as we move into the bulk
There is a length scale associated with this decay...called the
penetration depth
Most interestingly, the penetration depth is a function temperature...
26 / 41

Penetration Depth
The magnetic field can penetrate into the superconductor near the
surfaces...but dies exponentially as we move into the bulk
There is a length scale associated with this decay...called the
penetration depth
Most interestingly, the penetration depth is a function temperature...
...and diverges at T c !
26 / 41

Type I and Type II superconductors
27 / 41

Type I and Type II superconductors
Superconductors do not remain perfect diamagmet for all magnetic
fields...there are two types of behaviour
27 / 41

Type I and Type II superconductors
Superconductors do not remain perfect diamagmet for all magnetic
fields...there are two types of behaviour
Type I: At a critical magnetic field (H c ) superconductivity is lost and
normal state is restored...typically found in elemental metals
27 / 41

Type I and Type II superconductors
Superconductors do not remain perfect diamagmet for all magnetic
fields...there are two types of behaviour
Type I: At a critical magnetic field (H c ) superconductivity is lost and
normal state is restored...typically found in elemental metals
M
M c
0.2
0.5 1.0 1.5 2.0
H
H c
0.4
0.6
0.8
1.0
Type I
27 / 41

Type I and Type II superconductors
Superconductors do not remain perfect diamagmet for all magnetic
fields...there are two types of behaviour
Type I: At a critical magnetic field (H c ) superconductivity is lost and
normal state is restored...typically found in elemental metals
M
M c
0.2
0.5 1.0 1.5 2.0
H
H c
M
M c
0.2
1 2 3 4 5
H
H c
0.4
0.4
0.6
0.6
0.8
0.8
1.0
Type I
1.0
Type II
27 / 41

Type I and Type II superconductors
Superconductors do not remain perfect diamagmet for all magnetic
fields...there are two types of behaviour
Type I: At a critical magnetic field (H c ) superconductivity is lost and
normal state is restored...typically found in elemental metals
M
M c
0.2
0.5 1.0 1.5 2.0
H
H c
M
M c
0.2
1 2 3 4 5
H
H c
0.4
0.4
0.6
0.6
0.8
0.8
1.0
Type I
Type II
Type II: There are two characteristic magnetic fields (H c1 and
H c2 < H c1 )...at H c1 the magnetic field begins to penetrate the
superconductor (not a perfect diagmagnet) and at H c2 normal state
is restored
H c (Type I) and H c1 ,H c2 are functions of temperature!
1.0
27 / 41

Phase Diagram
28 / 41

Phase Diagram
Type I
28 / 41

Phase Diagram
Type I
(Ramakrishnan and Rao)
28 / 41

Phase Diagram
Type I
Type II
(Ramakrishnan and Rao)
28 / 41

Phase Diagram
Type I
Type II
(Ramakrishnan and Rao)
28 / 41

Thermodynamic Properties
Electronic specific heat goes to zero exponentially
29 / 41

Thermodynamic Properties
Electronic 294 specific 10 Superconductivity heat goes to zero exponentially
part (c ne *T (Ibach forand a normal Lüth) conductor) must be replaced by a component
which, well below the critical temperature, decreases exponentially
c se exp… A= T† : …10:3†
k
Fig. 10.3. Specific heat of normally conducting
(c n ) and superconducting (c s )
aluminium. Below the transition temperature
T c , the normally conducting
phase is created by applying a weak
magnetic field of 300 G. (After [10.3])
Afurther distinctive property of a superconductor is its magnetic behavior.
29 / 41

Thermodynamic Properties
Electronic 294 specific 10 Superconductivity heat goes to zero exponentially
Fig. 10.3. Specific heat of normally conducting
(c n ) and superconducting (c s )
aluminium. Below the transition temperature
T c , the normally conducting
phase is created by applying a weak
magnetic field of 300 G. (After [10.3])
(Ramakrishnan and Rao)
part (c ne *T (Ibach forand a normal Lüth) conductor) must be replaced by a component
which, well below the critical temperature, decreases exponentially
c se exp… A= T† : …10:3†
k
Afurther distinctive property of a superconductor is its magnetic behavior.
29 / 41

Thermodynamic Properties
Electronic 294 specific 10 Superconductivity heat goes to zero exponentially
Fig. 10.3. Specific heat of normally conducting
(c n ) and superconducting (c s )
aluminium. Below the transition temperature
T c , the normally conducting
phase is created by applying a weak
magnetic field of 300 G. (After [10.3])
(Ramakrishnan and Rao)
part (c ne *T (Ibach forand a normal Lüth) conductor) must be replaced by a component
which, well below the critical temperature, decreases exponentially
c se exp… A= T† : …10:3†
Jump in the specific heat at T c – Phase Transition??
k
Afurther distinctive property of a superconductor is its magnetic behavior.
29 / 41

Thermodynamic Properties
Electronic 294 specific 10 Superconductivity heat goes to zero exponentially
Fig. 10.3. Specific heat of normally conducting
(c n ) and superconducting (c s )
aluminium. Below the transition temperature
T c , the normally conducting
phase is created by applying a weak
magnetic field of 300 G. (After [10.3])
(Ramakrishnan and Rao)
part (c ne *T (Ibach forand a normal Lüth) conductor) must be replaced by a component
which, well below the critical temperature, decreases exponentially
c se exp… A= T† : …10:3†
Jump in the specific heat at T c – Phase Transition??
k
Afurther distinctive property of a superconductor is its magnetic behavior.
29 / 41

Thermal Conductivity
30 / 41

Thermal Conductivity
Thermal conductivity also falls with temperature (approximately
exponentially)
30 / 41

Thermal Conductivity
Thermal conductivity also falls with temperature (approximately
exponentially)
else Cs ~~~~~~~~~~~~~~~~~~~~~
? ? ? ? ? >~~~~~~~~~~~~~~~~~~~~~~~~T
X f4iz
C) 0
tC~
0 1 =0C
7t X ,0 arC
g o4o o
o o c o
iw
3
/0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~c
0 Ct V
C)4
,X, o :) eD0
0~~~~~~~~4
546 P. M. Rowell
30 / 41

Thermal Conductivity
Thermal conductivity also falls with temperature (approximately
exponentially)
else Cs ~~~~~~~~~~~~~~~~~~~~~
? ? ? ? ? >~~~~~~~~~~~~~~~~~~~~~~~~T
X f4iz
C) 0
tC~
0 1 =0C
7t X ,0 arC
g o4o o
o o c o
iw
3
Superconductors are poor thermal conductors!!...Widemann-Franz
goes for a six!!
/0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~c
0 Ct V
C)4
,X, o :) eD0
0~~~~~~~~4
546 P. M. Rowell
30 / 41

Optical Properties
31 / 41

Optical Properties
Doesn’t look like a metal...
31 / 41

Optical Properties
Doesn’t look like a metal...
E k ˆ…n 2 k ‡ D2 † 1=2 (10.58) obeys Fermi statistics with the Fermi dis
f (E k ,T) (Sect. 6.3). In the equation determining D (10.61) this fact
into account by including the non-occupation of the correspond
states. In place of (10.61) one thus has
(Ibach and Lüth)
Fig. 10.15. Infrared
of various materia
mined from the inte
multiply reflected
radiation. The inte
and I N refer respecti
superconducting an
states of the mate
curves thus represent
ence between the in
flectivity of the sup
ing and normally c
states. (After [10.11])
31 / 41

Optical Properties
Doesn’t look like a metal...
E k ˆ…n 2 k ‡ D2 † 1=2 (10.58) obeys Fermi statistics with the Fermi dis
f (E k ,T) (Sect. 6.3). In the equation determining D (10.61) this fact
into account by including the non-occupation of the correspond
states. In place of (10.61) one thus has
(Ibach and Lüth)
...looks more like a semiconductor! Has a GAP!!
Fig. 10.15. Infrared
of various materia
mined from the inte
multiply reflected
radiation. The inte
and I N refer respecti
superconducting an
states of the mate
curves thus represent
ence between the in
flectivity of the sup
ing and normally c
states. (After [10.11])
31 / 41

Optical Properties
Doesn’t look like a metal...
E k ˆ…n 2 k ‡ D2 † 1=2 (10.58) obeys Fermi statistics with the Fermi dis
f (E k ,T) (Sect. 6.3). In the equation determining D (10.61) this fact
into account by including the non-occupation of the correspond
states. In place of (10.61) one thus has
(Ibach and Lüth)
...looks more like a semiconductor! Has a GAP!!
Superconductor HAS A GAP!!!!
Fig. 10.15. Infrared
of various materia
mined from the inte
multiply reflected
radiation. The inte
and I N refer respecti
superconducting an
states of the mate
curves thus represent
ence between the in
flectivity of the sup
ing and normally c
states. (After [10.11])
31 / 41

0 F
Temperature Dependence of Gap
Gap is temperature dependent
0
2 T c
Anumerical treatment of the integral (10.78) yields
1 ˆ V 0 Z…E 0 F † ln 1:14hx D
or …10:79 a
T c
kT c ˆ 1:14hx D e 1=V0Z…E0 F † :
k
k
…10:79 b
(Ibach and Lüth)
Fig. 10.16. Temperature dependence of the gap energy D(T) relative to the value D(0)
T=0 for In, Sn and Pb. Values determined from tunnel experiments (Panel IX) are com
pared with those predicted by BCS theory (dashed). (After [10.12])
32 / 41

0 F
Temperature Dependence of Gap
Gap is temperature dependent
0
2 T c
Anumerical treatment of the integral (10.78) yields
1 ˆ V 0 Z…E 0 F † ln 1:14hx D
or …10:79 a
T c
kT c ˆ 1:14hx D e 1=V0Z…E0 F † :
k
k
…10:79 b
(Ibach and Lüth)
Fig. 10.16. Temperature dependence of the gap energy D(T) relative to the value D(0)
T=0 for In, Sn and Pb. Values determined from tunnel experiments (Panel IX) are com
pared with those predicted by BCS theory (dashed). (After [10.12])
Gap vanishes at T c
32 / 41

Critical Current
A superconductor cannot support an arbitrary large current
density...there is a critical current density j c
33 / 41

Critical Current
A superconductor cannot support an arbitrary large current
density...there is a critical current density j c
The critical current is temperature dependent
33 / 41

MAGNETIC
J c T versus T curve (g–h–i–a) drawn for
Critical Current B app = 0, which also appears in Figs. 2.43
in the previous section and 2.47. Figure 2.46 shows three B c T
l magnetic A superconductor field has the cannot
versus T
support
curves projected
an arbitrary
onto
large
the J tr
current
= 0
dence on
density...there
temperature given plane, while Fig. 2.47 presents three J
is a critical current density j c T
c
d this is plotted in Fig. 2.41. versus T curves projected onto the B app = 0
e curve near The Tcritical c is given current by plane. is temperature Finally, Fig. dependent 2.48 gives projections of
ay also Phase be written diagram in H-T -I plane
2B c 0
=− (2.71)
T c
I superconductors this ratio
−15 and −50 mT/K; for
a value of −223mT/K
uperconductor has two criter-critical
field B c1 and an
ld B c2 , where B c1

Flux Quantization
34 / 41

Flux Quantization
The flux through a superconducting ring seems to be quantized
34 / 41

Flux Quantization
The flux through a superconducting ring seems to be quantized
(Daever and Fairbank, 1961)
34 / 41

Flux Quantization
The flux through a superconducting ring seems to be quantized
(Daever and Fairbank, 1961)
Some sort of “macroscopic quantum phenomenon”
34 / 41

Isotope Effect
35 / 41

Isotope Effect
The strangest thing...the T c depends on the isotope!!
35 / 41

Fig. 10.17. Isotope eff
The results of sever
summarized [10.13]:
Lock, Pippard, Shoen
Reynolds and Lohman
Isotope Effect
The strangest thing...the T c depends on the isotope!!
10.7 Supercurrents and Critical Cur
(Ibach and Lüth)
10.7 Supercurrents and Critical Currents
The main goal of a theory of superconductivity is of course to ex
fundamental properties of the superconducting phase: the
35 / 41
disa

Superconductivity – Summary of Observations
36 / 41

Superconductivity – Summary of Observations
Zero resistance
36 / 41

Superconductivity – Summary of Observations
Zero resistance
Meissner effect (Penetration depth)
36 / 41

Superconductivity – Summary of Observations
Zero resistance
Meissner effect (Penetration depth)
Type I and II superconductors
36 / 41

Superconductivity – Summary of Observations
Zero resistance
Meissner effect (Penetration depth)
Type I and II superconductors
Vanishing specific heat
36 / 41

Superconductivity – Summary of Observations
Zero resistance
Meissner effect (Penetration depth)
Type I and II superconductors
Vanishing specific heat
Poor thermal conductivity
36 / 41

Superconductivity – Summary of Observations
Zero resistance
Meissner effect (Penetration depth)
Type I and II superconductors
Vanishing specific heat
Poor thermal conductivity
Gap in excitations
36 / 41

Superconductivity – Summary of Observations
Zero resistance
Meissner effect (Penetration depth)
Type I and II superconductors
Vanishing specific heat
Poor thermal conductivity
Gap in excitations
Critical current
36 / 41

Superconductivity – Summary of Observations
Zero resistance
Meissner effect (Penetration depth)
Type I and II superconductors
Vanishing specific heat
Poor thermal conductivity
Gap in excitations
Critical current
Flux quantization
36 / 41

Superconductivity – Summary of Observations
Zero resistance
Meissner effect (Penetration depth)
Type I and II superconductors
Vanishing specific heat
Poor thermal conductivity
Gap in excitations
Critical current
Flux quantization
Isotope effect
36 / 41

Superconductivity – Summary of Observations
Zero resistance
Meissner effect (Penetration depth)
Type I and II superconductors
Vanishing specific heat
Poor thermal conductivity
Gap in excitations
Critical current
Flux quantization
Isotope effect
...
36 / 41

Superconductivity – Summary of Observations
Zero resistance
Meissner effect (Penetration depth)
Type I and II superconductors
Vanishing specific heat
Poor thermal conductivity
Gap in excitations
Critical current
Flux quantization
Isotope effect
...
This is what we need to explain!
36 / 41

Development of a Theory
37 / 41

Development of a Theory
Phenomenological Approach
37 / 41

Development of a Theory
Phenomenological Approach
Microscopic Approach
37 / 41

Superconductor = Perfect Conductor?
38 / 41

Superconductor = Perfect Conductor?
38 / 41

Superconductor = Perfect Conductor?
Given that the superconducting state has zero resistance, let us
consider a perfect conductor and do the following thought experiment
38 / 41

Superconductor = Perfect Conductor?
Given that the superconducting state has zero resistance, let us
10.1 Some Fundamental Phenomena Associated with Superconductivity 295
consider a perfect conductor and do the following thought experiment
Fig. 10.4. Magnetic behavior of an ideal conductor (A) and a superconductor (B): (A) Inan
ideal conductor, the final (Ibach state (d) and or(g) depends Lüth) on whether the sample is first cooled to
below T c before applying the magnetic field B ext, or alternatively, cooled in the presence of
the field. (a ? b) The sample loses its resistance when cooled in a field-free region. (c) Application
of B ext to sample with zero resistance. (d) MagneticfieldB ext switched off. (e?f )
Sample loses its resistance in the magnetic field. (g) MagneticfieldB ext switched off. (B)
For a superconductor, the final states (d) and(g) are identical, regardless of whether B ext is
switched on before or after cooling the sample: (a?b) sample loses its resistance upon
cooling in the absence of a magnetic field. (c) Application of the field Bext to the supercon-
38 / 41

Superconductor = Perfect Conductor?
Given that the superconducting state has zero resistance, let us
10.1 Some Fundamental Phenomena Associated with Superconductivity 295
consider a perfect conductor and do the following thought experiment
Fig. 10.4. Magnetic behavior of an ideal conductor (A) and a superconductor (B): (A) Inan
ideal conductor, the final (Ibach state (d) and or(g) depends Lüth) on whether the sample is first cooled to
below T c before applying the magnetic field B ext, or alternatively, cooled in the presence of
the field. (a ? b) The sample loses its resistance when cooled in a field-free region. (c) Application
of B ext to sample with zero resistance. (d) MagneticfieldB ext switched off. (e?f )
Sample loses its resistance in the magnetic field. (g) MagneticfieldB ext switched off. (B)
For a superconductor, the final states (d) and(g) are identical, regardless of whether B ext is
switched on before or after cooling the sample: (a?b) sample loses its resistance upon
cooling in the absence of a magnetic field. (c) Application of the field Bext to the supercon-
Superconductor and perfect conductor are very different! “Perfect
conductor” does not lead to a consistent thermodynamic state!
38 / 41

39 / 41

40 / 41

41 / 41