Abnormal pseudospin-degenerate states in a graphene quantum dot with double vacancy defects

We study valley-polarized states in an armchair graphene quantum dot with double vacancy defects. Half-filled doubly degenerate states are found in the middle of the gap only when two vacancies occupy certain specific sites in each of the sublattices of the quantum dot. The doubly degenerate states forming around the vacancies are shown to be entirely localized in their respective sublattice, which results in that the two parallel-spin electrons in the degenerate Fermi level carry purely opposite valley pseudospins. Surprisingly, the pseudospin-degenerate states are found to be symmetric even when the reflection symmetry of the structure has been broken by the vacancies. It is further shown that the pseudospin degeneracy, similar to the Kramer’s degeneracy lifted by a magnetic field, can be removed by an applied electric field. Like the Zeeman effect, the split states would retain their original valley pseudospins and exhibit linear splitting energy with respect to the applied field.