3.2.4 Energy Shift

As it has been pointed out above in a strained solid the energy of an extremum is expanded into the Taylor series in powers of some small quantity characterizing the strength of the lattice strain. For weak strain it is natural to perform the expansion in powers of the strain tensor components around the unstrained point. The energy shift of the $k$-th non-degenerate band extremum is in general expressed as:

$$\Delta\epsilon^{(k)}=\sum_{ij}\Xi_{ij}^{(k)}\varepsilon_{ij}.$$ (3.28)

The coefficients of this expansion form a second rank tensor called the deformation potential tensor. This tensor is a characteristic of a given non-degenerate band of a solid. Due to the symmetry property of the strain tensor the deformation potential tensor is also symmetric:

$$\Xi_{ij}^{(k)}=\Xi_{ji}^{(k)}.$$ (3.29)

Such tensor has only six independent components. For cubic crystals the number of independent components reduces to three, denoted as $\Xi_{u}$, $\Xi_{d}$ and $\Xi_{p}$.
S. Smirnov: