A non-centrosymmetric material lacks an inversion center, which means that it is not symmetric under the operation of inversion through a point. This absence of inversion symmetry can lead to unique electronic and magnetic properties.

UPt3 was the first discovered non-centrosymmetric superconductor. It is a uranium-platinum compound that exhibits superconductivity below a critical temperature of 0.5 K.

Spin-orbit coupling is the primary mechanism responsible for superconductivity in non-centrosymmetric materials. This interaction between the electron's spin and its momentum can lead to the formation of Cooper pairs and the onset of superconductivity.

Spin-orbit coupling in non-centrosymmetric superconductors can lead to the formation of unconventional superconducting states, such as chiral p-wave or d-wave states. These states exhibit unique properties and behaviors that are not observed in conventional s-wave superconductors.

Sr2RuO4 is an example of a topological superconductor. It is a non-centrosymmetric material that exhibits unconventional superconductivity with a chiral p-wave order parameter. This material has attracted significant attention due to its potential applications in spintronics and quantum computing.

The superconducting energy gap in non-centrosymmetric superconductors plays a crucial role in determining the critical temperature, the density of superconducting electrons, and the coherence length. These parameters are essential for understanding the behavior and properties of superconducting materials.

The absence of inversion symmetry in non-centrosymmetric superconductors leads to the splitting of the electronic bands. This splitting can result in the formation of new electronic states and can significantly influence the electronic properties of the material.

Impurities and defects in non-centrosymmetric superconductors can have a profound impact on the superconducting properties. They can enhance or suppress superconductivity, induce unconventional superconducting states, and affect the critical temperature. Understanding the role of impurities and defects is crucial for optimizing the performance of non-centrosymmetric superconductors.

Scanning tunneling microscopy (STM), angle-resolved photoemission spectroscopy (ARPES), and muon spin rotation (μSR) are experimental techniques commonly used to probe the superconducting properties of non-centrosymmetric materials. These techniques provide valuable insights into the electronic structure, superconducting order parameter, and magnetic properties of these materials.

Non-centrosymmetric superconductors have the potential for various applications, including spintronics devices, quantum computing, energy-efficient electronics, and medical imaging. Their unique properties and unconventional superconducting states make them promising candidates for next-generation technologies.