Super conductor
Experiment as part of the F-Praktikum
Winter semester 2023/2024
Leonhard Steiner and Lukas Ritzer
,Inhaltsverzeichnis
1 Introduction 3
2 Theory 4
2.1 Superconductor basics . . . . . . . . . . . . . . . . . . . . . . 4
2.2 BCS Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 Behavior of Electrons in the Lattice . . . . . . . . . . . 6
2.2.2 Virtual Phonons . . . . . . . . . . . . . . . . . . . . . 7
2.2.3 Macroscopic State . . . . . . . . . . . . . . . . . . . . . 9
2.2.4 Energy Gap . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Superconductors in Magnetic Fields . . . . . . . . . . . . . . 10
2.3.1 Decay of the Magnetic Field Inside a Superconductor . 11
2.3.2 Critical Magnetic Field . . . . . . . . . . . . . . . . . . 13
2.3.3 Ginsburg-Landau Theory . . . . . . . . . . . . . . . . . 15
2.3.4 Types of Superconductors . . . . . . . . . . . . . . . . 15
2.4 High-Temperature Superconductivity . . . . . . . . . . . . . . 17
2.5 Hazards in Handling Superconductors . . . . . . . . . . . . . . 18
3 Additional Theory 19
3.1 Four-Point Measurement . . . . . . . . . . . . . . . . . . . . . 19
3.2 Thermocouple . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
, 3.3 Lock-In Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . 22
4 Experimental procedure 23
4.1 Low-Temperature Superconductivity . . . . . . . . . . . . . . 23
4.1.1 Solid Pb Coil Body . . . . . . . . . . . . . . . . . . . . 23
4.2 High-Temperature Superconductivity . . . . . . . . . . . . . . 27
4.2.1 YBCO . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2.2 Levitation . . . . . . . . . . . . . . . . . . . . . . . . . 28
5 Conclusion 30
6 Appendix 31
6.1 Important Data . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.2 Relationship between Thermoelectric Voltage and Temperature 32
6.3 Measurement Series - Measurements on the Solid Coil Body . 33
6.3.1 Temperature is being increased . . . . . . . . . . . . . 33
6.3.2 Temperature is being lowered . . . . . . . . . . . . . . 38
, Page 3 from 40
1 Introduction
At the beginning of the 20th century, superconductivity was discovered for
the first time. In this phenomenon, electricity can be conducted nearly loss-
lessly at temperatures close to 0 Kelvin, contradicting the contemporary
explanation of resistances and their behavior. These low temperatures were
achieved by the coldness of liquid helium.
The initial attempt to explain superconductivity posited that the thermal
vibrations within atomic bonds decrease steadily with decreasing tempera-
tures, resulting in a reduction of resistance. The question then arose whether
the resistance continues to decrease all the way to zero at T = 0K, causing
the atomic bonds to freeze, or if the resistance reaches a minimum at a cer-
tain temperature and then increases again. Half a century after the discovery,
the effect was quantitatively interpreted in the BCS theory.
Dutch physicist Heike Kamerlingh Onnes first observed superconductivity
in mercury, for which he was awarded the Nobel Prize in Physics in 1913.
Just above 4K, the resistance suddenly dropped so significantly that it could
no longer be accurately determined with the instruments of that time. This
temperature was termed the critical temperature. Over the years, more me-
tals exhibiting this behavior were discovered and labeled as superconductors,
categorized by their critical temperatures.
Current research on superconductors focuses primarily on finding materials
with increasingly higher critical temperatures, aiming to harness the advan-
tages of superconductivity while minimizing the need for extensive cooling.
This is referred to as high-temperature superconductivity (HTSL) and is a
component of this experiment. Superconductors enable the realization of ex-
tremely strong magnets (with field strengths of several Tesla), employed, for
instance, in the medical field in magnetic resonance imaging (MRI) using
superconducting coils. Other applications include maglev trains, particle ac-
celerators, generators, or rapid switching devices.
This experiment is divided into three sections. First, low-temperature su-
perconductivity is investigated using niobium film and a coil, followed by the
high-temperature superconductor YBCO, and finally, levitation is examined.
Experiment as part of the F-Praktikum
Winter semester 2023/2024
Leonhard Steiner and Lukas Ritzer
,Inhaltsverzeichnis
1 Introduction 3
2 Theory 4
2.1 Superconductor basics . . . . . . . . . . . . . . . . . . . . . . 4
2.2 BCS Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 Behavior of Electrons in the Lattice . . . . . . . . . . . 6
2.2.2 Virtual Phonons . . . . . . . . . . . . . . . . . . . . . 7
2.2.3 Macroscopic State . . . . . . . . . . . . . . . . . . . . . 9
2.2.4 Energy Gap . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Superconductors in Magnetic Fields . . . . . . . . . . . . . . 10
2.3.1 Decay of the Magnetic Field Inside a Superconductor . 11
2.3.2 Critical Magnetic Field . . . . . . . . . . . . . . . . . . 13
2.3.3 Ginsburg-Landau Theory . . . . . . . . . . . . . . . . . 15
2.3.4 Types of Superconductors . . . . . . . . . . . . . . . . 15
2.4 High-Temperature Superconductivity . . . . . . . . . . . . . . 17
2.5 Hazards in Handling Superconductors . . . . . . . . . . . . . . 18
3 Additional Theory 19
3.1 Four-Point Measurement . . . . . . . . . . . . . . . . . . . . . 19
3.2 Thermocouple . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
, 3.3 Lock-In Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . 22
4 Experimental procedure 23
4.1 Low-Temperature Superconductivity . . . . . . . . . . . . . . 23
4.1.1 Solid Pb Coil Body . . . . . . . . . . . . . . . . . . . . 23
4.2 High-Temperature Superconductivity . . . . . . . . . . . . . . 27
4.2.1 YBCO . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2.2 Levitation . . . . . . . . . . . . . . . . . . . . . . . . . 28
5 Conclusion 30
6 Appendix 31
6.1 Important Data . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.2 Relationship between Thermoelectric Voltage and Temperature 32
6.3 Measurement Series - Measurements on the Solid Coil Body . 33
6.3.1 Temperature is being increased . . . . . . . . . . . . . 33
6.3.2 Temperature is being lowered . . . . . . . . . . . . . . 38
, Page 3 from 40
1 Introduction
At the beginning of the 20th century, superconductivity was discovered for
the first time. In this phenomenon, electricity can be conducted nearly loss-
lessly at temperatures close to 0 Kelvin, contradicting the contemporary
explanation of resistances and their behavior. These low temperatures were
achieved by the coldness of liquid helium.
The initial attempt to explain superconductivity posited that the thermal
vibrations within atomic bonds decrease steadily with decreasing tempera-
tures, resulting in a reduction of resistance. The question then arose whether
the resistance continues to decrease all the way to zero at T = 0K, causing
the atomic bonds to freeze, or if the resistance reaches a minimum at a cer-
tain temperature and then increases again. Half a century after the discovery,
the effect was quantitatively interpreted in the BCS theory.
Dutch physicist Heike Kamerlingh Onnes first observed superconductivity
in mercury, for which he was awarded the Nobel Prize in Physics in 1913.
Just above 4K, the resistance suddenly dropped so significantly that it could
no longer be accurately determined with the instruments of that time. This
temperature was termed the critical temperature. Over the years, more me-
tals exhibiting this behavior were discovered and labeled as superconductors,
categorized by their critical temperatures.
Current research on superconductors focuses primarily on finding materials
with increasingly higher critical temperatures, aiming to harness the advan-
tages of superconductivity while minimizing the need for extensive cooling.
This is referred to as high-temperature superconductivity (HTSL) and is a
component of this experiment. Superconductors enable the realization of ex-
tremely strong magnets (with field strengths of several Tesla), employed, for
instance, in the medical field in magnetic resonance imaging (MRI) using
superconducting coils. Other applications include maglev trains, particle ac-
celerators, generators, or rapid switching devices.
This experiment is divided into three sections. First, low-temperature su-
perconductivity is investigated using niobium film and a coil, followed by the
high-temperature superconductor YBCO, and finally, levitation is examined.
