TFAW K2 survey: an insight into a few hundreds of new Earth-sized planetary candidates

Kepler's extended mission (K2) Earth-sized planetary legacy is a niche that still remains to be fully exploited. We reanalyzed all light curves in K2 C1-C8, C12-C18 campaigns with a wavelet-based detrending method \texttt{TFAW} developed by our team, 
and the period search algorithm \texttt{TLS}. The combination of these two methods allows to detect and characterize planetary transit candidates around fainter targets ($12.5<K_{\mathrm{p}}<18.5$) than any previous study.
We present 220 new planetary candidates as a result of a preliminary survey. All of them have passed a vetting procedure including: candidate periods with SDE${}_{\mathrm{T}\mathrm{L}\mathrm{S}}>$9.0, visual inspection of the candidate light curve, inspection of archival Pan-STARRS1 images and Gaia DR2 to discard close stellar companions and statistical FPP$<$2$\mathrm{\%}$. 
We assigned our candidates sample three levels of priority: six top-priority detected in two or more separate but overlapping K2 campaigns, 110 high-priority meeting the above requirements, and 104 low-priority still meeting the same requirements, but having either FPP close to 2$\mathrm{\%}$ or pending further reanalysis.
The bulk of our \texttt{TFAW} K2 survey are small planet candidates with $R_p<2R_{\oplus }$, most of them orbiting faint low-mass stars. Our survey adds new candidates to different areas of interest in exoplanetary science: several dozens in the small planet radius gap, four in the Hot-Super-Earths desert, and a few in the Ultra-Short-Period planets. We also present six candidates within the Habitable Zones of their host stars.