The split-off band refers to an energy band that is formed when the spin-orbit coupling is strong enough to cause a splitting of the energy levels in an atom or molecule. It is often seen in semiconductor materials and can affect the electronic properties of the material.
The split-off band differs from other energy bands in that it has a different origin. While the valence and conduction bands are formed by the bonding and antibonding combinations of atomic orbitals, the split-off band is formed due to the interaction between the spin and orbital motion of the electrons.
The longitudinal mass is a measure of the effective mass of an electron in a split-off band. It is important because it affects the electron's motion and behavior in the material, such as its mobility and response to external fields.
The transverse mass is a measure of the effective mass of an electron in a different energy band, such as the valence or conduction bands. It differs from the longitudinal mass in that it is affected by different factors, such as the crystal structure and the electron's wave function.
Understanding these concepts can be useful in designing and engineering electronic devices and materials. For example, knowing the effective masses of electrons in different energy bands can help in predicting the behavior of a material under different conditions, and in optimizing its properties for specific applications.