Bogoliubov--de Gennes Hamiltonian (BdG Hamiltonian)

A Bogoliubov--de Gennes Hamiltonian acts on a Nambu particle-hole spinor and describes quadratic fermion hopping and pairing.

Particle-hole symmetry relates $H_{\mathrm{BdG}}(k)$ to $-H_{\mathrm{BdG}}^{\ast }(-k)$. Consequently every energy $E$ at momentum $k$ is paired with energy $-E$ at momentum $-k$.