PHD
  1. Classical mechanics  1.1. Newtonian mechanics  1.1.1. Laws of motion in Newtonian mechanics  1.1.2. Dynamics of particles and systems  1.1.3. Conservation laws  1.1.4. Central force motion  1.2. Lagrangian mechanics  1.2.1. Principle of minimum action  1.2.2. Euler–Lagrange equations  1.2.3. Constraints and normalized coordinates  1.2.4. Noether's theorem  1.3. Hamiltonian mechanics  1.3.1. Hamilton's equations  1.3.2. Canonical conversion  1.3.3. Poisson bracket  1.3.4. Action-angle variable  1.4. Rigid body mobility  1.4.1. Rotation of rigid bodies  1.4.2. Moment of inertia tensor  1.4.3. Euler's equations in rigid body dynamics  1.4.4. Gyroscopic motion  1.5. Chaos and nonlinear dynamics  1.5.1. Stage space and attractive  1.5.2. Bifurcation and chaos theory  1.5.3. Hamiltonian Chaos  1.5.4. Lyapunov exponent
  2. Electrodynamics  2.1. Maxwell's equations  2.1.1. Gauss's law for electricity  2.1.2. Gauss's law for magnetism  2.1.3. Faraday's Law  2.1.4. Ampere's Law  2.1.5. Boundary conditions in Maxwell's equations  2.2. Electromagnetic waves  2.2.1. Wave equation  2.2.2. Polarization  2.2.3. Reflection and Refraction  2.2.4. Waveguides and resonators  2.3. Special relativity  2.3.1. Lorentz transformations  2.3.2. Relativistic energy and momentum  2.3.3. Relativistic electrodynamics  2.3.4. Minkowski spacetime  2.4. Radiation and scattering  2.4.1. Dipole radiation  2.4.2. Multipole expansion  2.4.3. Compton scattering  2.4.4. Thomson and Rayleigh scattering  2.5. Plasma Physics  2.5.1. Debye Screening  2.5.2. Magnetohydrodynamics  2.5.3. Plasma instability  2.5.4. Fusion Plasma
  3. Quantum mechanics  3.1. Foundations of quantum mechanics  3.1.1. Principles of quantum mechanics  3.1.2. Wave function and probability interpretation  3.1.3. Uncertainty principle  3.1.4. Quantum Tunneling  3.2. Schrödinger Equation  3.2.1. Time-dependent Schrödinger equation  3.2.2. Time-independent Schrödinger equation  3.2.3. Eigenvalues and eigenfunctions in the Schrödinger equation  3.2.4. Path integrals in quantum mechanics  3.3. Quantum operators  3.3.1. Commutators and observables  3.3.2. Angular momentum operator  3.3.3. Ladder Operator  3.3.4. Pauli matrices  3.4. Quantum entanglement and measurement  3.4.1. Bell's theorem  3.4.2. Quantum Teleportation  3.4.3. Quantum entanglement and quantum decoherence in measurement  3.4.4. Quantum entanglement and measurement in quantum mechanics  3.5. Relativistic quantum mechanics  3.5.1. Klein–Gordon equation  3.5.2. Dirac equation  3.5.3. Quantum field theory  3.5.4. Feynman path integral
  4. Statistical mechanics and thermodynamics  4.1. Classical thermodynamics  4.1.1. Laws of Thermodynamics  4.1.2. Carnot cycle  4.1.3. Entropy and free energy  4.1.4. Thermodynamic efficiency  4.2. Kinetic theory of gases  4.2.1. Maxwell–Boltzmann distribution  4.2.2. Transport phenomenon  4.2.3. Mean free path  4.2.4. Non-equilibrium systems in the kinetic theory of gases  4.3. Statistical mechanics  4.3.1. Microstates and Macrostates  4.3.2. Partition function  4.3.3. Bose–Einstein and Fermi–Dirac statistics  4.3.4. Fluctuations and correlations  4.4. Phase transition  4.4.1. Important events  4.4.2. Landau theory  4.4.3. Ising model  4.4.4. Renormalization group theory
  5. Quantum field theory  5.1. Second Quantization  5.1.1. Quantum harmonic oscillator in second quantization  5.1.2. Creation and annihilation operators in second quantization  5.1.3. Path Integral in Second Quantization  5.1.4. Fock space  5.2. Quantum Electrodynamics  5.2.1. Feynman diagrams  5.2.2. Renormalization in quantum electrodynamics  5.2.3. Gauge invariance in quantum electrodynamics  5.2.4. Vacuum polarization  5.3. Quantum Chromodynamics  5.3.1. Quarks and gluons  5.3.2. Color range  5.3.3. Lattice QCD  5.3.4. Asymptotic freedom  5.4. Standard model of particle physics  5.4.1. Electroweak theory  5.4.2. Higgs mechanism  5.4.4. Grand Unified Theories
  6. General relativity and gravity  6.1. Einstein's field equations  6.1.1. Ricci tensor and scalar curvature  6.1.2. Schwarzschild solution  6.1.3. Kerr metric  6.1.4. Gravitational waves  6.2. Cosmology  6.2.1. Friedmann equation  6.2.2. Cosmic inflation  6.2.3. Dark matter and dark energy  6.2.4. Large scale structure  6.3. Black holes and wormholes  6.3.1. Event horizon in black holes and wormholes  6.3.2. Hawking radiation  6.3.3. Penrose process  6.3.4. Information paradox in black holes and wormholes
  7. Condensed matter physics  7.1. Crystal structure and lattice  7.1.1. Bravais lattices  7.1.2. Band theory in crystal structure and lattices  7.1.3. Phonons in crystal structure and lattice  7.1.4. Block's theorem  7.2. Superconductivity  7.2.1. BCS principle  7.2.2. Meissner effect  7.2.3. High Temperature Superconductor  7.2.4. Josephson effect

PHD → Condensed matter physics → Superconductivity ↓


High Temperature Superconductor


Superconductivity is a remarkable phenomenon that occurs in certain materials, typically at very low temperatures, where they exhibit zero electrical resistance and expel magnetic fields. This property has profound implications for a variety of applications, from maglev trains to magnetic resonance imaging (MRI). The discovery of superconductors that work at higher temperatures, close to room temperature, is important because it would greatly expand the practicality and cost-effectiveness of superconducting technologies.

Introduction to superconductivity

Superconductivity was first discovered by Heike Kamerlingh Onnes in 1911, when he observed that mercury exhibited zero electrical resistance when cooled below 4.2 K.

Key properties of superconductors

  1. Zero electrical resistance: In the superconducting state, electric current can flow without any energy loss.
  2. Meissner effect: Superconductors expel magnetic fields, resulting in magnetic levitation.

The critical temperature (T c) is the temperature below which a material becomes a superconductor. Conventional superconductors, such as elemental mercury or lead, have low T c values, typically less than 10 K. This necessitates the use of expensive cooling techniques such as liquid helium, making widespread application difficult.

Discovery of high temperature superconductors

In 1986 Georg Bednorz and K. Alex Muller made a major breakthrough, discovering a class of copper-oxide materials, known as cuprates, that are superconducting at temperatures up to 35 Kelvin. For this achievement, they were awarded the Nobel Prize in physics a year later.

This discovery sparked a revolution in condensed matter physics, as researchers worked rapidly toward discovering new materials and understanding the fundamental physics behind high-temperature superconductivity. Within a few years, several materials were discovered that could superconduct at temperatures above 77 Kelvin, the boiling point of liquid nitrogen, making it much more practical and less expensive than liquid helium as a coolant.

Theoretical background

The BCS (Bardeen-Cooper-Schrieffer) theory, developed in 1957, successfully explains superconductivity in conventional superconductors. It describes how electrons pair up into "Cooper pairs" through lattice vibrations or phonons at low temperatures, allowing them to move without any resistance.

However, high temperature superconductivity cannot be fully explained by the BCS theory. A striking feature of these materials is that they are generally insulators in their pure (undoped) form, which become superconductors upon doping. Despite intense research, a complete and unified theory for high temperature superconductivity still remains elusive.

Understanding cuprate superconductors

Cuprates are layered materials with copper-oxygen planes that are important for their superconducting properties. T c of a cuprate superconductor is sensitive to the number of charge carriers introduced through a process called doping. For example, La 2-x Ba x CuO 4 is a family of cuprate superconductors where x denotes the doping level.

Cuprate Structure:
,
,
|copper-oxygen|
| plane |
,
,

The relationship between T c and doping in cuprates is often represented using a "dome" diagram. These diagrams show how T c initially increases with doping, reaches a peak, and then decreases with further doping.

Visual example: superconducting dome

Superconducting dome Doping Levels T C

Applications of high temperature superconductors

The practical applications of high-temperature superconductors arise from their ability to conduct electricity without resistance and to expel magnetic fields, which has led to advances in several areas:

  • Power cables: Superconducting cables can carry more electric current than conventional copper cables, reducing energy losses in the power grid.
  • Magnetic levitation: Superconductors used in maglev trains enable frictionless travel.
  • Medical imaging: MRI machines take advantage of superconducting magnets to create high-resolution images.
  • Scientific instruments: Superconductors are essential for particle accelerators and other scientific instruments.

Challenges and future directions

Despite these promising applications, there are challenges that need to be addressed. The brittleness of ceramic high-temperature superconductors makes them difficult to form into wires and coils. Researchers are exploring new materials and methods to overcome these challenges.

The search for room-temperature superconductors remains a major focus in condensed matter physics. Advances in computational methods and experimental techniques are expected to accelerate this search.

A better understanding of the mechanisms that enable high-temperature superconductivity could pave the way for the design of new materials with optimized properties.

Conclusion

High-temperature superconductors represent a field in physics that combines profound theoretical challenges with broad technological opportunities. Although much progress has been made since their discovery, the quest to understand and harness their properties continues to drive research. Achieving superconductivity at room temperature would be a transformative milestone in technology, impacting energy transmission, transportation, and many other sectors.


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High Temperature Superconductor

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