Chapter 4
Fundamental Electromagnetic Properties
of Superconductors
Abstract In this chapter fundamental properties such as quantization of magnetic
flux, the normal core in the central region in each packet of quantized magnetic flux,
and the induced electric field under the motion of quantized magnetic flux driven
by the Lorentz force are described by using the Ginzburg–Landau theory. These are
important for understanding the electromagnetic characteristics of superconductors
that will be introduced in Chap. 5. Reference [1] covers a wide area of the material
in this chapter.
4.1 Type II Superconductor
Superconductors used as materials for magnets are type II superconductors. Magnetic
properties of type I and type II superconductors are compared in Fig. 4.1. A type
I superconductor shows perfect diamagnetism until the external magnetic field H 0
reaches a certain value, H c , as shown in Fig. 4.1a, and the magnetization (magnetic
moment density) defined by (3.49) is
M = −H 0 .
(4.1)
This state is called the Meissner state. At a higher field the superconductor changes
to the normal state and the magnetization is M = 0. The magnetic field H c at which
the transition takes place is called the critical field. On the other hand, a type II
superconductor shows the Meissner state until the external magnetic field reaches
H c1 and changes to a partially diamagnetic state with penetration of the magnetic flux
above this field. This state is called the mixed state. When the external field exceeds
H c2 , the superconductor goes into the normal state, and M = 0. These characteristic
fields, H c1 and H c2 , are called the lower and upper critical fields, respectively. The
magnetic flux in the superconductor is quantized as shown in Fig. 4.2 in the mixed
state. The quantized packet of magnetic flux is called the magnetic flux line. When
the magnetization is expresses as a property of the equivalent type I superconductor
with the same area, as shown in Fig. 4.1b, H c is called the thermodynamic critical
field. The phase diagrams on the temperature vs magnetic field plane for type I and
type II superconductors are shown in Fig. 4.3a, b, respectively.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
T. Matsushita, Superconductivity and Electromagnetism, Springer Series
in Solid-State Sciences 195, https://doi.org/10.1007/978-3-030-67568-4_4
51
Fundamental Electromagnetic Properties
of Superconductors
Abstract In this chapter fundamental properties such as quantization of magnetic
flux, the normal core in the central region in each packet of quantized magnetic flux,
and the induced electric field under the motion of quantized magnetic flux driven
by the Lorentz force are described by using the Ginzburg–Landau theory. These are
important for understanding the electromagnetic characteristics of superconductors
that will be introduced in Chap. 5. Reference [1] covers a wide area of the material
in this chapter.
4.1 Type II Superconductor
Superconductors used as materials for magnets are type II superconductors. Magnetic
properties of type I and type II superconductors are compared in Fig. 4.1. A type
I superconductor shows perfect diamagnetism until the external magnetic field H 0
reaches a certain value, H c , as shown in Fig. 4.1a, and the magnetization (magnetic
moment density) defined by (3.49) is
M = −H 0 .
(4.1)
This state is called the Meissner state. At a higher field the superconductor changes
to the normal state and the magnetization is M = 0. The magnetic field H c at which
the transition takes place is called the critical field. On the other hand, a type II
superconductor shows the Meissner state until the external magnetic field reaches
H c1 and changes to a partially diamagnetic state with penetration of the magnetic flux
above this field. This state is called the mixed state. When the external field exceeds
H c2 , the superconductor goes into the normal state, and M = 0. These characteristic
fields, H c1 and H c2 , are called the lower and upper critical fields, respectively. The
magnetic flux in the superconductor is quantized as shown in Fig. 4.2 in the mixed
state. The quantized packet of magnetic flux is called the magnetic flux line. When
the magnetization is expresses as a property of the equivalent type I superconductor
with the same area, as shown in Fig. 4.1b, H c is called the thermodynamic critical
field. The phase diagrams on the temperature vs magnetic field plane for type I and
type II superconductors are shown in Fig. 4.3a, b, respectively.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
T. Matsushita, Superconductivity and Electromagnetism, Springer Series
in Solid-State Sciences 195, https://doi.org/10.1007/978-3-030-67568-4_4
51