Question

(a) What is the superconducting transition temperature, \(T_{c} ?(\mathrm{~b})\) The discovery by Müller and Bednorz of superconductivity in a copper oxide ceramic at \(35 \mathrm{~K}\) set off a frantic scramble among physicists and chemists to find materials that exhibit superconductivity at higher temperatures. What is the significance of achieving \(T_{c}\) values above \(77 \mathrm{~K}\) ?

Short answer

The superconducting transition temperature, \(T_c\), is the temperature below which a material exhibits superconductivity, a state of zero electrical resistance and expulsion of the magnetic field. In this case, the \(T_c\) is 35 K for the copper oxide ceramic. Achieving \(T_c\) values above 77 K is significant as it allows the use of more common and less expensive cooling techniques, like liquid nitrogen, and leads to the development of new technologies and applications in areas such as power transmission, energy storage, electronics, and medical equipment.

Step-by-step solution

Part (a): Define the Superconducting Transition Temperature

The superconducting transition temperature, \(T_c\), is the temperature below which a material exhibits superconductivity, which is a state of zero electrical resistance and the expulsion of the magnetic field (Meissner effect). In other words, \(T_c\) is the threshold temperature for a material to become a superconductor. For the given problem, the superconducting transition temperature, \(T_c\), is 35 K as mentioned in the exercise. This temperature is where the copper oxide ceramic starts to show superconducting properties.

Part (b): Significance of achieving \(T_c\) values above 77 K

The significance of achieving \(T_c\) values above 77 K is that it would allow the use of more common and less expensive cooling techniques for the superconducting materials. Liquid nitrogen, which is a widely available and relatively inexpensive coolant, has a boiling point of 77 K (-196°C). If a material has a \(T_c\) value above 77 K, it can be cooled using liquid nitrogen, making it more feasible for practical applications. Moreover, higher \(T_c\) values would also create opportunities for new technologies and applications that were not possible with previous low-temperature superconductors. Such applications could include more efficient power transmission, better energy storage, faster electronic devices, and improved medical equipment such as MRI machines. In summary, achieving \(T_c\) values above 77 K is essential for the field of superconductivity, as it facilitates the use of more practical cooling methods and opens up opportunities for groundbreaking technologies and applications.

Key concepts

Meissner Effect

Imagine placing a magnet over a material and it floats as if by magic. This phenomenon is part of what we call the Meissner effect, which occurs in superconductors. The essence of the Meissner effect is the complete expulsion of magnetic field lines from the interior of a superconducting material when it is cooled below its superconducting transition temperature, \(T_c\).
This startling effect was first discovered in 1933, and it serves as a key indicator that a material has become superconducting. Contrary to what one might think, this isn't simply the material becoming a perfect diamagnet. Instead, the superconductor actively cancels the internal magnetic field by producing its own magnetic field in opposition. This field is generated by supercurrents, which flow on the surface of the material without any energy loss. These supercurrents are what allow the material to levitate magnets placed near them.

Understanding Superconductivity Through Meissner Effect

To assess whether a material is a true superconductor, observing the Meissner effect is pivotal. Here's another standout point: If you cool the material below \(T_c\) in the presence of a magnetic field, then remove that field, the superconductor will 'remember' and maintain the expelled field state. This provides a striking contrast to merely perfect conductors, whose behavior is quite different when cooled in the presence of a magnetic field.
This effect is a cornerstone in teaching about superconductivity because it is not only captivating but also conceptually vital. It's an exquisite demonstration of the unique quantum mechanical properties that govern superconductors, and it helps us understand the extraordinary characteristics that such materials can exhibit.

High-Temperature Superconductivity

High-temperature superconductivity refers to the phenomenon where certain materials exhibit superconducting properties at temperatures higher than those of traditional superconductors. Traditionally, materials would have to be cooled to near absolute zero to become superconducting, which was not practical for widespread application.
The breakthrough discovery of superconductivity in ceramic copper oxides, like the one mentioned in the exercise, at 35 K (\-238°C) was surprising because these materials had much higher \(T_c\) values than previously known superconductors. This discovery spawned immense research into what is known as 'high-temperature' superconductors, which are materials that superconduct above the boiling point of liquid nitrogen (77 K or \-196°C).

Why Is High-Temperature Superconductivity Significant?

Achieving superconductivity above 77 K is monumental because it means that more accessible and affordable cryogenic technology, like liquid nitrogen, can be used, reducing operational costs and complexity. The quest for room-temperature superconductors—ones that would work at even higher temperatures—remains a holy grail in the field because it would revolutionize many technological fronts, from power grids to transportation. Despite enormous progress, understanding the mechanisms that lead to high-temperature superconductivity is still one of the most challenging and active areas of research in condensed matter physics.

Applications of Superconductivity

Superconductivity isn't just a cool (pun intended) laboratory curiosity—it has real-world applications that affect various industries and could transform future technologies. Some of the headline-grabbing applications of superconductivity include:

• Magnetic resonance imaging (MRI): Superconducting magnets are cornerstone components in MRI machines, providing strong and stable magnetic fields necessary for high-resolution imaging.
• Power transmission: Superconductor-based cables can transmit electricity with minimal energy loss, leading to more efficient power grids and reduced costs.
• Particle accelerators: Superconducting magnets are used to steer and accelerate particles in particle accelerators, crucial for research in physics.
• Maglev trains: The magnetic levitation (maglev) technology relies heavily on superconductors for frictionless, high-speed train travel.

Futuristic and Emerging Applications

Research continually unearths new potential for superconducting materials. As high-temperature superconductivity evolves, so does the scope of its applications. Scientists are exploring superconducting materials for quantum computing, energy storage systems, ultra-sensitive sensor technology, and even for potential use in fusion reactors. The success in these applications hinges on overcoming the hurdles of cooling and material stability. Nonetheless, the potential benefits to energy efficiency, computing, transportation, and medical fields make the pursuit of understanding and utilizing superconductivity a highly valuable endeavor.