Theory of the normal resistivity and specific heat of high-temperature superconducting materials

The conduction of free electrons inside a conductor is best described by quantum mechanics. However, a classical model makes predictions close to the results of quantum mechanics. It is called the theory of metallic conduction.
In this theory, Newton's second law of motion is used to determine the acceleration of an electron in the presence of an applied electric field. Then, its velocity is expressed via this acceleration.
An electron moves through the crystal, containing positive ions,...

A substance that reaches superconductivity, a state in which magnetic fields cannot penetrate, and there is no electrical resistance, is referred to as a superconductor. In 1911, Heike Kamerlingh Onnes of Leiden University, a Dutch physicist, observed a relation between the temperature and the resistance of the element mercury. The mercury sample was then cooled in liquid helium to study the linear dependence of resistance on temperature. It was observed that, as the temperature decreased, the...

A superconductor is a substance that offers zero resistance to the electric current when it drops below a critical temperature. Zero resistance is not the only interesting phenomenon as materials reach their transition temperatures. A second effect is the exclusion of magnetic fields. This is known as the Meissner effect. A light, permanent magnet placed over a superconducting sample will levitate in a stable position above the superconductor. High-speed trains that levitate on strong...

When a voltage is applied to a conductor, an electrical field is generated, and charges in the conductor feel the force due to the electrical field. The current density that results depends on the electrical field and the properties of the material. In some materials, including metals at a given temperature, the current density is approximately proportional to the electrical field. In these cases, the current density can be modeled as:

In perfect conductors, the electric field inside is always zero due to the abundance of free electrons, which nullify any field by flowing. As a result, any residual charge resides on the surface.
In a practical conductor, an applied electric field may be sustained, causing a flow of electrons, which produce a current. The differential form of the current, the current density, is related to the electric field.
More generally, it is related to the force per unit charge, which involves the...

The specific heat capacity of a substance refers to the energy required to increase the temperature of one gram of that substance by one degree Celcius. Specific heat capacity is often represented in calories (cal), grams (g), and degrees Celsius (oC), but can also be expressed in joules (J), kilograms (kg), and Kelvin (K), among other units.
For example, increasing the temperature of one gram of water by 1°C requires one calorie of heat energy and can be written as 1 cal/g-°C, or 4186 J/kg/K.