4
1 Introduction
transition occurs in ferroelectric materials, which are a type of electric materials.
Thus, the superconducting transition can be regarded as just one of the general phase
transitions, and its one exceptional point is a very low transition temperature. If a
room temperature superconductor is discovered in the future, the idea of peculiarity
will be weakened. Recently, it was discovered that H 3 S became superconducting at
203 K (−70
◦ C) under a very high pressure of 155 million atm. In addition, LaH 10
showed superconductivity at 250–260 K (−23 to − 13
◦ C) under a similar high pressure. These discoveries create the strong impression that the discovery of a room
temperature superconductor is not a pipe dream.
1.2 Zero Electrical Resistance
Here we discuss the zero resistivity, which is the most outstanding property of a
superconductor, from various aspects. Firstly, the zero resistivity is proved theoretically. Then, we try to check if it is possible to prove it experimentally. It is necessary
to measure the voltage drop V across a specimen when a current I is applied to it.
The resistance is obtained as R = V /I . This measurement is applied to a square rod
made of high purity copper with a cross-sectional area of 1 cm
2 and length of 10 cm
that has been cooled down to liquid helium temperature −269 °C. The electrical
resistivity ρ r of pure copper at this temperature is about 1 × 10
−11
m, and the electrical resistance is estimated from Ohm’s law as R = ρ r l/S = 1 × 10
−6 [], where l
and S are the length and cross-sectional area, respectively. Hence, when a current of
1 A is applied, the potential drop is 1 µV
= 1 × 10
−6 V
. Thus, the measurement is
possible. When the electrical resistivity is smaller by two orders in magnitude, the
measurement is difficult due to the noise in the voltmeter. That is, it is difficult to
measure a resistivity smaller than 1 × 10
−13
m by this measurement method. Thus,
it is impossible to prove the zero resistivity in superconductors.
Then, we try to measure the resistivity by another method. We assume a closed
circle 10 cm in diameter (D) made of a round wire 1 mm in diameter (d). The electrical
resistance of this closed circle is R = 4ρ r D/d
2 and the self-inductance
1 is
L ∼ =
μ 0 D
2
log
8D
d
∼ = 4.2 × 10
−7 [H],
(1.1)
where μ 0 = 4π × 10
−7
N/A
2
is the magnetic permeability of vacuum, the unit of
the inductance H is the Henry, and N in the magnetic permeability is the Newton.
When a current is induced in the closed loop by magnetic induction, the current
decays with time t as
1 The magnetic flux that penetrates a closed circuit is denoted by , when current I is applied to the
circuit. The coefficient L = /I is the self-inductance.
1 Introduction
transition occurs in ferroelectric materials, which are a type of electric materials.
Thus, the superconducting transition can be regarded as just one of the general phase
transitions, and its one exceptional point is a very low transition temperature. If a
room temperature superconductor is discovered in the future, the idea of peculiarity
will be weakened. Recently, it was discovered that H 3 S became superconducting at
203 K (−70
◦ C) under a very high pressure of 155 million atm. In addition, LaH 10
showed superconductivity at 250–260 K (−23 to − 13
◦ C) under a similar high pressure. These discoveries create the strong impression that the discovery of a room
temperature superconductor is not a pipe dream.
1.2 Zero Electrical Resistance
Here we discuss the zero resistivity, which is the most outstanding property of a
superconductor, from various aspects. Firstly, the zero resistivity is proved theoretically. Then, we try to check if it is possible to prove it experimentally. It is necessary
to measure the voltage drop V across a specimen when a current I is applied to it.
The resistance is obtained as R = V /I . This measurement is applied to a square rod
made of high purity copper with a cross-sectional area of 1 cm
2 and length of 10 cm
that has been cooled down to liquid helium temperature −269 °C. The electrical
resistivity ρ r of pure copper at this temperature is about 1 × 10
−11
m, and the electrical resistance is estimated from Ohm’s law as R = ρ r l/S = 1 × 10
−6 [], where l
and S are the length and cross-sectional area, respectively. Hence, when a current of
1 A is applied, the potential drop is 1 µV
= 1 × 10
−6 V
. Thus, the measurement is
possible. When the electrical resistivity is smaller by two orders in magnitude, the
measurement is difficult due to the noise in the voltmeter. That is, it is difficult to
measure a resistivity smaller than 1 × 10
−13
m by this measurement method. Thus,
it is impossible to prove the zero resistivity in superconductors.
Then, we try to measure the resistivity by another method. We assume a closed
circle 10 cm in diameter (D) made of a round wire 1 mm in diameter (d). The electrical
resistance of this closed circle is R = 4ρ r D/d
2 and the self-inductance
1 is
L ∼ =
μ 0 D
2
log
8D
d
∼ = 4.2 × 10
−7 [H],
(1.1)
where μ 0 = 4π × 10
−7
N/A
2
is the magnetic permeability of vacuum, the unit of
the inductance H is the Henry, and N in the magnetic permeability is the Newton.
When a current is induced in the closed loop by magnetic induction, the current
decays with time t as
1 The magnetic flux that penetrates a closed circuit is denoted by , when current I is applied to the
circuit. The coefficient L = /I is the self-inductance.