Weyl semimetals are characterized by the presence of Weyl nodes, which are points in the Brillouin zone where the conduction and valence bands touch and the energy dispersion is linear. This unique electronic structure gives rise to a number of interesting properties, including the possibility of superconductivity.

Superconductivity in Weyl semimetals can arise from a variety of mechanisms, including electron-phonon coupling, magnetic fluctuations, and spin-orbit coupling. The relative importance of each mechanism depends on the specific material and its properties.

TaAs, NbAs2, and MoTe2 are all Weyl semimetals that have been shown to exhibit superconductivity under certain conditions. These materials have attracted considerable attention due to their potential for hosting unconventional superconducting states.

As of 2023, the highest Tc observed in a Weyl semimetal is 2.0 K, which was achieved in the material TaAs. This is still significantly lower than the Tc of conventional superconductors, but it represents a promising step towards the development of new superconducting materials with higher Tc.

Superconducting Weyl semimetals have the potential to enable a wide range of applications, including energy-efficient electronics, quantum computing, and medical imaging. Their unique electronic properties make them promising candidates for these and other emerging technologies.

There are a number of challenges associated with the practical use of superconducting Weyl semimetals. These include the high cost of materials, the difficulty in fabricating devices, and the sensitivity of these materials to magnetic fields. Overcoming these challenges will be essential for realizing the full potential of these materials.

Research on superconducting Weyl semimetals is a rapidly growing field with many active research groups around the world. There are still many fundamental questions to be answered about these materials, but the potential for technological applications is driving a great deal of interest and investment.

There are many promising directions for future research on superconducting Weyl semimetals. These include exploring new materials with higher Tc, developing new methods for fabricating devices, and investigating the interplay between superconductivity and other physical phenomena, such as magnetism and topological insulators.

The Berry curvature is a topological invariant that characterizes the electronic structure of a material. It is directly related to the presence of Weyl nodes in a Weyl semimetal. Therefore, measuring the Berry curvature is a direct way to distinguish between a Weyl semimetal and a conventional metal.

The chirality of a Weyl node is related to the direction of the Fermi arc by a topological invariant known as the Chern number. The Chern number determines the number of times the Fermi arc wraps around the Brillouin zone. Therefore, the chirality of a Weyl node determines the direction of the Fermi arc.

Spin-orbit coupling is a relativistic effect that arises from the interaction between the spin of an electron and its motion in an electric field. It is essential for the formation of Weyl nodes in most materials. Spin-orbit coupling breaks the time-reversal symmetry of the system, which allows for the formation of Weyl nodes with opposite chiralities.

The properties of Weyl semimetals can be controlled by applying a magnetic field, an electric field, or by doping the material. A magnetic field can induce a chiral anomaly, which can lead to the formation of Weyl nodes with opposite chiralities. An electric field can break the time-reversal symmetry of the system, which can also lead to the formation of Weyl nodes. Doping the material can change the Fermi level, which can affect the position and number of Weyl nodes.

Weyl semimetals have a number of potential applications, including quantum computing, topological insulators, and superconductivity. Their unique electronic structure makes them promising candidates for these and other emerging technologies.

There are a number of challenges associated with the practical use of Weyl semimetals. These include the high cost of materials, the difficulty in fabricating devices, and the sensitivity of these materials to magnetic fields. Overcoming these challenges will be essential for realizing the full potential of these materials.