The following pictures shows some typical examples of density of states:
and for superconductor:
Here is my interpretation: Energy level zero represents Fermi energy level. Positive energy represents energy levels for holes. Negative energy level represents energy levels for electrons. Density of states (DOS) on positive axis represents probability of electrons/holes to be found if we multiply DOS with Fermi function. For superconductor example, we have two curves separated by gap of aproximately +/- 1meV. It is a superconducting gap. Within that gap we have superconducting state.
My question is for insulator DOS example. Top unshaded peak represents electron bands and and shaded one represents hole bands. What is the physical interpretation if unshaded peak is on negative axis instead positive and shaded peak is still positive? Is there such thing as negative energy levels? (antiparticle?)