Jia-Su Wang and Su-Yu Wang
1 Fundamentals of superconductivity
1.1 Introduction
The electrical resistance of a metallic conductor decreases gradually as tempera-
ture drops. Even near absolute zero, metallic conductor still has residual resistan-
ce. For a superconductor, the resistance drops abruptly to zero below its critical
temperatureTc.
Conventional superconductors are those that can be explained by the Bardeen-
CooperSchrieffer (BCS) theory or its derivatives. Superconductors that cannot be
explained by the BCS theory are defined as the unconventional superconductors.
Superconductivity was discovered first in mercury by Onnes in 1911, [1] and the
perfect diamagnetic phenomenon was discovered in 1933. Various superconducting
theories appeared in succession. The characteristic parameters of superconductors
can be well described by phenomenological macroscopic theories. These are the well-
known London theory [2] and the Ginsburg-Landau theory. [3] The latter has been
extended by Abrikosov [4] and Gorkov [5] and is therefore often called the GLAG
theory. In 1957, Bardeen et al. [6] proposed the BCS superconducting microscopic
theories. This theory assumed that the charge carriers of the superconducting currents
are the bound electron pairs (Cooper pairs) and that there exists an energy gap
between the normal and superconductive states.
High-Tcsuperconductor (HTSC) is a family of superconducting ceramic materials.
“High” temperature in this context refers to the critical temperature which is higher
than the boiling point of liquid nitrogen (77 K or− 196 °C). The construction and opera-
tional cost of the cryogenic system for holding the liquid nitrogen are much cheaper
than that for liquid helium. The HTSC offers the highest transition temperatures of
all superconductors. Thus, the HTSC is dominant for commercial applications since
liquid nitrogen is much easier to maintain. For these reasons, the HTSC is particularly
attractive for the practical engineering applications.
The London and GLAG theories form a complete set of superconducting macros-
copic theories and are always used to explain the magnetic properties of type II HTSC.
However, these macroscopic theories are approximations of the BCS microscopic
theory. Conventional superconductors can be properly explained by the BCS theory;
however, to date, there is no widely accepted theory to explain the superconductivity
of HTSC materials as well as other unconventional superconductors.
Superconductors can be classified into types I and II superconductors. Type I
superconductors have a single critical fieldHc, above which their superconductivity
disappears. Type II superconductors have two critical fields, lower critical fieldHc1and