  We demonstrate laser oscillation in a hexagonal-lattice photonic crystal
nanocavity using an InGaAs quantum dot gain material by optical pumping at 5 K.
The cavity comprises a defect created by shifting several air holes in a
two-dimensional photonic crystal slab structure without removing any air holes
to achieve both small mode volume and a high cavity quality factor. The
measured cavity quality factors and estimated mode volume for the nanocavity
are ~33,000 and ~0.004 um^3. The laser threshold is compared between the
zero-cell and L3-type nanocavity lasers, and the zero-cell nanolasers are found
to have small thresholds of about one-third of the L3-type nanolasers. This
result suggests that a higher Purcell factor of the zero-cell nanolaser is
reflected as a smaller laser threshold.
