Comparing the specific heat to the cyclotron mass in two dopings of YBCO in the underdoped regime*

Two underdoped High T$_{\mathrm{c}}$ superconductors, YBa$_{2}$Cu$_{3}$O$_{6.51}$ and YBa$_{2}$Cu$_{3}$O$_{6.56}$, show finite electronic specific heat even in vanishing magnetic field and temperature as well as quantum magneto-oscillations at high magnetic~ fields. Previous results show the high-field electronic specific heat up to 45 T to be a sum of contributions from superconducting vortices and quantum magneto-oscillations, the latter a signature of an un-gapped Fermi surface. The vortex contribution appears as a smooth square-root field dependence of the Sommerfeld coefficient that shows no sign of diminished superconductivity up to 45 T. We present new results which allow a comparison between the cyclotron mass from high field experiments to the zero field Sommerfeld coefficient in the same crystal. The discussion will include implications of the new results on the interpretation of the previous data.